ALBERT

Description: 〈p〉Publication date: Available online 8 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): K.T. Huynh〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We are interested in the stochastic modeling of a condition-based maintained system subject to continuous deterioration and maintenance actions such as inspection, partial repair and replacement. The partial repair is assumed dependent on the past in the sense that it cannot bring the system back into a deterioration state better than the one reached at the last repair. Such a past-dependency can affect (〈em〉i〈/em〉) the selection of a type of maintenance actions, (〈em〉ii〈/em〉) the maintenance duration, (〈em〉iii〈/em〉) the deterioration level after a maintenance, and (〈em〉iv〈/em〉) the restarting system deterioration behavior. In this paper, all these effects are jointly considered in an unifying condition-based maintenance model on the basis of restarting deterioration states randomly sampled from a probability distribution truncated by the deterioration levels just before a current repair and just after the last repair/replacement. Using results from the semi-regenerative theory, the long-run maintenance cost rate is analytically derived. Numerous sensitivity studies illustrate the impacts of past-dependent partial repairs on the economic performance of the considered condition-based maintained system.〈/p〉〈/div〉

Description: 〈p〉Publication date: December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Mathematics Letters, Volume 98〈/p〉 〈p〉Author(s): Yujuan Chen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, we investigate a cooperative parabolic system 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈msub〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉Δ〈/mi〉〈mi〉u〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mi〉u〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉λ〈/mi〉〈mo〉−〈/mo〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈mi〉b〈/mi〉〈mi〉v〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mrow〉〈msub〉〈mrow〉〈mi〉v〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉Δ〈/mi〉〈mi〉v〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mi〉v〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉μ〈/mi〉〈mo〉−〈/mo〉〈mi〉v〈/mi〉〈mo〉+〈/mo〉〈mi〉c〈/mi〉〈mi〉u〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 with blow-up initial and boundary values over a smooth bounded domain 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si3.svg"〉〈mi〉Ω〈/mi〉〈/math〉 of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si4.svg"〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈/msup〉〈/math〉 with 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈mrow〉〈mi〉N〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≥〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/math〉. We show existence, nonexistence and uniqueness of solutions. We also provide an exact estimate of the behavior of the solutions near the parabolic boundary.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): Shichen Zhang, Jianxiong Zhang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Nowadays, some suppliers are looking for offline expansion in addition to their preexisting online channels relying on e-tailers. This study focuses on the e-tailer’s demand information sharing strategy with the supplier who may build upon brick-and-mortar stores. Both prevailing agreements between the supplier and the e-tailer are investigated: agency selling and reselling. The equilibrium results are quite different under these two agreements. Specifically, when the supplier’s offline entry cost is very small or large, the e-tailer shares information under agency selling while keeps information private under reselling. When the entry cost is intermediate, channel substitution rate is large and information uncertainty is small, the e-tailer withholds the demand information under agency selling while shares information under reselling to deter the supplier from entering an offline channel. Furthermore, two extensions about consumer behavior in multichannel selection are discussed: showrooming and webrooming. With showrooming or webrooming, the e-tailer’s information sharing decisions qualitatively hold, while with showrooming the drive factor behind may change; that is, withholding information under agency selling and sharing information under reselling may also serve as measures to encourage supplier offline entry when the effect of showrooming is strong.〈/p〉〈/div〉

Description: 〈p〉Publication date: September 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Advances in Applied Mathematics, Volume 110〈/p〉 〈p〉Author(s): Atul Dixit, Rajat Gupta〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A Ramanujan-type formula involving the squares of odd zeta values is obtained. The crucial part in obtaining such a result is to conceive the correct analogue of the Eisenstein series involved in Ramanujan's formula for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉ζ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mn〉2〈/mn〉〈mi〉m〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉. The formula for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msup〉〈mrow〉〈mi〉ζ〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mn〉2〈/mn〉〈mi〉m〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is then generalized in two different directions, one, by considering the generalized divisor function 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈msub〉〈mrow〉〈mi〉σ〈/mi〉〈/mrow〉〈mrow〉〈mi〉z〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉n〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, and the other, by studying a more general analogue of the aforementioned Eisenstein series, consisting of one more parameter 〈em〉N〈/em〉. A number of important special cases are derived from the first generalization. For example, we obtain a series representation for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈mi〉ζ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mi〉ω〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mi〉ζ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉ω〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, where 〈em〉ω〈/em〉 is a non-trivial zero of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si130.svg"〉〈mi〉ζ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉z〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉. We also evaluate a series involving the modified Bessel function of the second kind in the form of a rational linear combination of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.svg"〉〈mi〉ζ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mn〉4〈/mn〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg"〉〈mi〉ζ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mn〉4〈/mn〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si132.svg"〉〈mi〉k〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="double-struck"〉N〈/mi〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Multivariate Analysis, Volume 174〈/p〉 〈p〉Author(s): Julyan Arbel, Marta Crispino, Stéphane Girard〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We study a broad class of asymmetric copulas introduced by Liebscher (2008) as a combination of multiple – usually symmetric – copulas. The main thrust of the paper is to provide new theoretical properties including exact tail dependence expressions and stability properties. A subclass of Liebscher copulas obtained by combining comonotonic copulas is studied in more detail.We establish further dependence properties for copulas of this class and show that they are characterized by an arbitrary number of singular components. Furthermore, we introduce a novel iterative representation for general Liebscher copulas which 〈em〉de facto〈/em〉 insures uniform margins, thus relaxing a constraint of Liebscher’s original construction. Besides, we show that this iterative construction proves useful for inference by developing an Approximate Bayesian computation sampling scheme. This inferential procedure is demonstrated on simulated data and is compared to a likelihood-based approach in a setting where the latter is available.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Pedro G. Massey, Noelia B. Rios, Demetrio Stojanoff〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉S〈/mi〉〈mo〉∈〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="script"〉M〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈msup〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="double-struck"〉C〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mrow〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈/mrow〉〈/msup〉〈/math〉 be a positive semidefinite 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi〉d〈/mi〉〈mo〉×〈/mo〉〈mi〉d〈/mi〉〈/math〉 complex matrix and let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mi mathvariant="bold"〉a〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈msub〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mo〉∈〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉I〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈mo〉∈〈/mo〉〈msubsup〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mo linebreak="badbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉0〈/mn〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msubsup〉〈/math〉, indexed by 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉I〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo stretchy="false"〉{〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈mi〉k〈/mi〉〈mo stretchy="false"〉}〈/mo〉〈/math〉, be a 〈em〉k〈/em〉-tuple of positive numbers. Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.svg"〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉T〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="bold"〉a〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 denote the set of families 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.svg"〉〈mi mathvariant="script"〉G〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈msub〉〈mrow〉〈mo stretchy="false"〉{〈/mo〉〈msub〉〈mrow〉〈mi〉g〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉}〈/mo〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mo〉∈〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉I〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉C〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msup〉〈/math〉 such that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg"〉〈msup〉〈mrow〉〈mo stretchy="false"〉‖〈/mo〉〈msub〉〈mrow〉〈mi〉g〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉‖〈/mo〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/math〉, for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si136.svg"〉〈mi〉i〈/mi〉〈mo〉∈〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉I〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈/math〉; thus, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.svg"〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉T〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="bold"〉a〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is the product of spheres in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.svg"〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉C〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msup〉〈/math〉 endowed with the product metric. For a strictly convex unitarily invariant norm 〈em〉N〈/em〉 in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.svg"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉M〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="double-struck"〉C〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, we consider the generalized frame operator distance function 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg"〉〈msub〉〈mrow〉〈mi mathvariant="normal"〉Θ〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉N〈/mi〉〈mspace width="0.2em"〉〈/mspace〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉S〈/mi〉〈mspace width="0.2em"〉〈/mspace〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi mathvariant="bold"〉a〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈/msub〉〈/math〉 defined on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.svg"〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉T〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="bold"〉a〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, given by〈span〉〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si14.svg"〉〈msub〉〈mrow〉〈mi mathvariant="normal"〉Θ〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉N〈/mi〉〈mspace width="0.2em"〉〈/mspace〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉S〈/mi〉〈mspace width="0.2em"〉〈/mspace〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi mathvariant="bold"〉a〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="script"〉G〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo linebreak="badbreak" linebreakstyle="after"〉=〈/mo〉〈mi〉N〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉S〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈msub〉〈mrow〉〈mi〉S〈/mi〉〈/mrow〉〈mrow〉〈mi mathvariant="script"〉G〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mspace width="1em"〉〈/mspace〉〈mtext〉where〈/mtext〉〈mspace width="1em"〉〈/mspace〉〈msub〉〈mrow〉〈mi〉S〈/mi〉〈/mrow〉〈mrow〉〈mi mathvariant="script"〉G〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈munder〉〈mo movablelimits="false"〉∑〈/mo〉〈mrow〉〈mi〉i〈/mi〉〈mo〉∈〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉I〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/munder〉〈msub〉〈mrow〉〈mi〉g〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mspace width="0.2em"〉〈/mspace〉〈msubsup〉〈mrow〉〈mi〉g〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈mrow〉〈mo〉⁎〈/mo〉〈/mrow〉〈/msubsup〉〈mo〉∈〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="script"〉M〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈msup〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="double-struck"〉C〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mrow〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈/mrow〉〈/msup〉〈mspace width="0.2em"〉〈/mspace〉〈mo〉.〈/mo〉〈/math〉〈/span〉 In this paper we determine the geometrical and spectral structure of local minimizers 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉G〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo〉∈〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉T〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="bold"〉a〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg"〉〈msub〉〈mrow〉〈mi mathvariant="normal"〉Θ〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉N〈/mi〉〈mspace width="0.2em"〉〈/mspace〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉S〈/mi〉〈mspace width="0.2em"〉〈/mspace〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi mathvariant="bold"〉a〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈/msub〉〈/math〉. In particular, we show that local minimizers are global minimizers, and that these families do not depend on the particular choice of 〈em〉N〈/em〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Yu-Xiang Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We consider a variable coefficient wave equation with an acoustic undamped condition. This is a coupled system of second and first order in time partial differential equations, with an acoustic boundary condition on the interface. The Riemannian geometry method is applied to deal with the variable coefficients. Under some checkable conditions on the coefficients we obtain the polynomial energy decay.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Barbara Kaltenbacher, Igor Shevchenko〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The focus of this work is on the analysis of the Westervelt equation modeling nonlinear propagation of high intensity ultrasound, in the practically relevant setting of a truncated computational domain with absorbing boundary conditions. We especially consider the zero and first order nonlinear absorbing boundary conditions devised in [38] in one and two space dimensions. As a matter of fact, the energy identities and estimates presented here were crucial for designing these absorbing boundary conditions in such a way that the desired energy dissipation through the boundary is guaranteed. Under the hypothesis of small initial data, we establish local well-posedness and provide higher order energy estimates, that we expect to be of additional use in boundary control and stabilization.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Alireza Ranjbar-Motlagh〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The main purpose of this article is to generalize a characterization of Lipschitz functions in the context of metric-measure spaces. The results are established in the class of metric-measure spaces which satisfy a strong version of the doubling (Bishop-Gromov regularity) condition. Indeed, we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be essentially Lipschitzian.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Rauan Akylzhanov, Michael Ruzhansky, Erlan Nursultanov〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we prove new inequalities describing the relationship between the “size” of a function on a compact homogeneous manifold and the “size” of its Fourier coefficients. These inequalities can be viewed as noncommutative versions of the Hardy-Littlewood inequalities obtained by Hardy and Littlewood [HL27] on the circle. For the example case of the group SU(2) we show that the obtained Hardy-Littlewood inequalities are sharp, yielding a criterion for a function to be in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mrow〉〈mi mathvariant="normal"〉SU〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mn mathvariant="normal"〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 in terms of its Fourier coefficients. We also establish Paley and Hausdorff-Young-Paley inequalities on general compact homogeneous manifolds. The latter is applied to obtain conditions for the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈/math〉-〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/msup〉〈/math〉 boundedness of Fourier multipliers for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si281.svg"〉〈mn〉1〈/mn〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〈〈/mo〉〈mi〉p〈/mi〉〈mo〉≤〈/mo〉〈mn〉2〈/mn〉〈mo〉≤〈/mo〉〈mi〉q〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〈〈/mo〉〈mo〉∞〈/mo〉〈/math〉 on compact homogeneous manifolds as well as the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈/math〉-〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/msup〉〈/math〉 boundedness of general (non-invariant) operators on compact Lie groups. We also record an abstract version of the Marcinkiewicz interpolation theorem on totally ordered discrete sets, to be used in the proofs with different Plancherel measures on the unitary duals.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Alexander Iksanov, Xingang Liang, Quansheng Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We prove necessary and sufficient conditions for the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈/math〉-convergence, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi〉p〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉1〈/mn〉〈/math〉, of the Biggins martingale with complex parameter in the supercritical branching random walk. The results and their proofs are much more involved (especially in the case 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si107.svg"〉〈mi〉p〈/mi〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉) than those for the Biggins martingale with real parameter. Our conditions are ultimate in the case 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si173.svg"〉〈mi〉p〈/mi〉〈mo〉≥〈/mo〉〈mn〉2〈/mn〉〈/math〉 only.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Sandro Zagatti〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present an improved version of a necessary and sufficient condition for strong convergence in the Sobolev space 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉W〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 and provide a nontrivial application to a class of fully nonlinear partial differential equations involving the range of the map 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msup〉〈mrow〉〈mi〉W〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉∋〈/mo〉〈mi〉u〈/mi〉〈mo stretchy="false"〉↦〈/mo〉〈mo stretchy="false"〉|〈/mo〉〈mi mathvariant="normal"〉∇〈/mi〉〈mi〉u〈/mi〉〈msup〉〈mrow〉〈mo stretchy="false"〉|〈/mo〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Differential Equations〈/p〉 〈p〉Author(s): Fabio Punzo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We investigate uniqueness of solutions to the initial value problem for degenerate parabolic equations, posed in bounded domains, where no boundary conditions are prescribed. In order to obtain uniqueness, we need that the solutions satisfy certain integral growth conditions, which are crucially related to the degeneracy of the operator near the boundary. In particular, such solutions can be unbounded near the boundary. Our hypothesis on the behavior of the operator at the boundary is optimal; in fact, we show that if it fails, then nonuniqueness of solutions prevails.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Combinatorial Theory, Series A, Volume 168〈/p〉 〈p〉Author(s): Baptiste Louf〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present bijections for the planar cases of two counting formulas on maps that arise from the KP hierarchy (Goulden-Jackson and Carrell-Chapuy formulas), relying on a “cut-and-slide” operation. This is the first time a bijective proof is given for quadratic map-counting formulas derived from the KP hierarchy. Up to now, only the linear one-faced case was known (Harer-Zagier recurrence and Chapuy-Féray-Fusy bijection). As far as we know, this bijection is new and not equivalent to any of the well-known bijections between planar maps and tree-like objects.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Algebra, Volume 535〈/p〉 〈p〉Author(s): Jesua Epequin Chavez〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We study the Howe correspondence for unipotent representations of irreducible dual pairs 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉,〈/mo〉〈msup〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mo〉′〈/mo〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉U〈/mi〉〈/mrow〉〈mrow〉〈mi〉m〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉F〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉U〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉F〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉,〈/mo〉〈msup〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mo〉′〈/mo〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉Sp〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈mi〉m〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉F〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈msubsup〉〈mrow〉〈mi〉O〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈mi〉n〈/mi〉〈/mrow〉〈mrow〉〈mi〉ϵ〈/mi〉〈/mrow〉〈/msubsup〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉F〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉F〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/msub〉〈/math〉 denotes the finite field with 〈em〉q〈/em〉 elements (〈em〉q〈/em〉 odd) and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈mi〉ϵ〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo〉±〈/mo〉〈mn〉1〈/mn〉〈/math〉. We show how to extract extremal (i.e. minimal and maximal) irreducible subrepresentations from the image 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"〉〈mi mathvariant="normal"〉Θ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mi〉π〈/mi〉〈/mrow〉〈mrow〉〈mo〉′〈/mo〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 of a unipotent representation 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.svg"〉〈msup〉〈mrow〉〈mi〉π〈/mi〉〈/mrow〉〈mrow〉〈mo〉′〈/mo〉〈/mrow〉〈/msup〉〈/math〉 of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg"〉〈msup〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mo〉′〈/mo〉〈/mrow〉〈/msup〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Algebra, Volume 535〈/p〉 〈p〉Author(s): Mikhail V. Bondarko, Vladimir A. Sosnilo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper is dedicated to new methods of constructing weight structures and weight-exact localizations; our arguments generalize their bounded versions considered in previous papers of the authors. We start from a class of objects 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi mathvariant="script"〉P〈/mi〉〈/math〉 of a triangulated category 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈munder〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mo〉_〈/mo〉〈/munder〉〈/math〉 that satisfies a certain 〈em〉(countable) negativity〈/em〉 condition (there are no 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈munder〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mo〉_〈/mo〉〈/munder〉〈/math〉-extensions of positive degrees between elements of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi mathvariant="script"〉P〈/mi〉〈/math〉; we actually need a somewhat stronger condition of this sort) to obtain a weight structure both “halves” of which are closed either with respect to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈munder〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mo〉_〈/mo〉〈/munder〉〈/math〉-coproducts of less than 〈em〉α〈/em〉 objects (where 〈em〉α〈/em〉 is a fixed regular cardinal) or with respect to all coproducts (provided that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈munder〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mo〉_〈/mo〉〈/munder〉〈/math〉 is closed with respect to coproducts of this sort). This construction gives all “reasonable” weight structures satisfying the latter conditions. In particular, one can obtain certain weight structures on spectra (in SH) consisting of less than 〈em〉α〈/em〉 cells, and on certain localizations of SH; these results are new.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Hyeonbae Kang, KiHyun Yun〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper studies in a quantitatively precise manner the field enhancement due to presence of an emitter of the dipole type near the bow-tie structure of perfectly conducting inclusions in the two-dimensional space. We put special emphasis on field enhancement near vertices of the bow-tie structure, and derive upper and lower bounds of the gradient blow-up there. All three different kinds of symmetries are considered by varying locations and directions of the emitter, and a different estimate is derived for each case.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Antoine Dailly, Florent Foucaud, Adriana Hansberg〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A graph is 〈em〉diameter-2-critical〈/em〉 if its diameter is 2 but the removal of any edge increases the diameter. A well-studied conjecture, known as the Murty–Simon conjecture, states that any diameter-2-critical graph of order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉n〈/mi〉〈/math〉 has at most 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mrow〉〈mo〉⌊〈/mo〉〈msup〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo〉∕〈/mo〉〈mn〉4〈/mn〉〈mo〉⌋〈/mo〉〈/mrow〉〈/math〉 edges, with equality if and only if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1002.svg"〉〈mi〉G〈/mi〉〈/math〉 is a balanced complete bipartite graph. Many partial results about this conjecture have been obtained, in particular it is known to hold for all sufficiently large graphs, for all triangle-free graphs, and for all graphs with a dominating edge. In this paper, we discuss ways in which this conjecture can be strengthened. Extending previous conjectures in this direction, we conjecture that, when we exclude the class of complete bipartite graphs and one particular graph, the maximum number of edges of a diameter-2-critical graph is at most 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si80.svg"〉〈mrow〉〈mrow〉〈mo〉⌊〈/mo〉〈msup〉〈mrow〉〈mrow〉〈mo〉(〈/mo〉〈mi〉n〈/mi〉〈mo〉−〈/mo〉〈mn〉1〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo〉∕〈/mo〉〈mn〉4〈/mn〉〈mo〉⌋〈/mo〉〈/mrow〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/math〉. The family of extremal examples is conjectured to consist of certain twin-expansions of the 5-cycle (with the exception of a set of thirteen special small graphs). Our main result is a step towards our conjecture: we show that the Murty–Simon bound is not tight for non-bipartite diameter-2-critical graphs that have a dominating edge, as they have at most 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈mrow〉〈mrow〉〈mo〉⌊〈/mo〉〈msup〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo〉∕〈/mo〉〈mn〉4〈/mn〉〈mo〉⌋〈/mo〉〈/mrow〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/math〉 edges. Along the way, we give a shorter proof of the Murty–Simon conjecture for this class of graphs, and stronger bounds for more specific cases. We also characterize diameter-2-critical graphs of order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉n〈/mi〉〈/math〉 with maximum degree 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si7.svg"〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/math〉: they form an interesting family of graphs with a dominating edge and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mrow〉〈mn〉2〈/mn〉〈mi〉n〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉4〈/mn〉〈/mrow〉〈/math〉 edges.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Numerical Mathematics〈/p〉 〈p〉Author(s): B. Pedretscher, B. Kaltenbacher, O. Pfeiler〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a computational framework, which enables efficient and robust parameter identification, as well as uncertainty quantification in state space models based on Itô stochastic processes, is presented. For optimization, a Maximum Likelihood approach based on the system's corresponding Fokker-Planck equation is followed. Gradient information is included by means of an adjoint approach, which is based on the Lagrangian of the optimization problem. To quantify the uncertainty of the Maximum-A-Posteriori estimates of the model parameters, a Bayesian inference approach based on Markov Chain Monte Carlo simulations, as well as profile likelihoods are implemented and compared in terms of runtime and accuracy. The framework is applied to experimental electron backscatter diffraction data of a fatigued metal film, where the aim is to develop a model, which consistently and physically meaningfully captures the metal's microstructural changes that are caused by external loading.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 10 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Yaonan Shan, Kun She, Shouming Zhong, Jun Cheng, Wenyong Wang, Can Zhao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper investigates the passivity of Markovian jump discrete-time systems (MJDTSs) with channel fading via event-triggered state feedback control. First, the concerned MJDTSs contain infinitely distributed delays and switching rules with partially known transition probability (TP) information. Next, the fading channel, as an unreliable channel, is introduced into MJDTSs to better reflect the engineering practice in networked environment. Due to the present of channel fading, a series of random variables satisfying some certain probability density functions (PDFs) will be obstacles in the process of proof. Then, an event-triggered controller is designed for MJDTSs with channel fading and incomplete transition probability (ITP) for the first time. Thanks to this event-triggered mechanism, the state feedback control could greatly reduce energy consumption during transmission. Subsequently, under the above controller, we obtain some novel sufficient criteria in the form of linear matrix inequalities (LMIs) to ensure the passivity of closed-loop system. Finally, some simulation results are provided to demonstrate the feasibility and effectiveness of the proposed theoretical method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Linear Algebra and its Applications, Volume 581〈/p〉 〈p〉Author(s): Natália Bebiano, Susana Furtado〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we consider sparse symmetrically banded matrices in which the nonzero off-diagonals are positioned a multiple of 〈em〉k〈/em〉 steps from the main diagonal. We show that such a matrix 〈em〉T〈/em〉 is permutationally similar to direct sum of banded matrices. In particular, when 〈em〉T〈/em〉 has exactly one nonzero off-diagonal above and below the main diagonal, the direct summands are tridiagonal. If 〈em〉T〈/em〉 has a 〈em〉w〈/em〉-Toeplitz structure, the blocks are 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉w〈/mi〉〈/mrow〉〈mrow〉〈mo〉′〈/mo〉〈/mrow〉〈/msup〉〈/math〉-Toeplitz, with 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msup〉〈mrow〉〈mi〉w〈/mi〉〈/mrow〉〈mrow〉〈mo〉′〈/mo〉〈/mrow〉〈/msup〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mi mathvariant="normal"〉lcm〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉w〈/mi〉〈mo〉,〈/mo〉〈mi〉k〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉/〈/mo〉〈mi〉k〈/mi〉〈/math〉. This reduction allows the study of spectral properties of 〈em〉T〈/em〉 from those of the direct summands. Finally, we give a reduction of sparse symmetrically banded matrices relatively to the main antidiagonal.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Differential Equations〈/p〉 〈p〉Author(s): Yuhui Chen, Wei Luo, Zheng-an Yao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we mainly investigate the Cauchy problem for the periodic Phan-Thein-Tanner (PTT) model. This model is derived from network theory for the polymeric fluid. We prove that the strong solutions of PTT model will blow up in finite time if the trace of initial stress tensor 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mrow〉〈mi mathvariant="normal"〉tr〈/mi〉〈/mrow〉〈mspace width="0.2em"〉〈/mspace〉〈msub〉〈mrow〉〈mi〉τ〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is negative. It is thus very different from the other viscoelastic model. On the other hand, we obtain the global existence result with small initial data when 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si108.svg"〉〈mrow〉〈mi mathvariant="normal"〉tr〈/mi〉〈/mrow〉〈mspace width="0.2em"〉〈/mspace〉〈msub〉〈mrow〉〈mi〉τ〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉≥〈/mo〉〈msub〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉0〈/mn〉〈/math〉 for some 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈msub〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉. Moreover, we study about the large time behavior.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Combinatorial Theory, Series B〈/p〉 〈p〉Author(s): H.A. Kierstead, Landon Rabern〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We prove that every 〈em〉k〈/em〉-list-critical graph (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉k〈/mi〉〈mo〉≥〈/mo〉〈mn〉7〈/mn〉〈/math〉) on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi〉n〈/mi〉〈mo〉≥〈/mo〉〈mi〉k〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉2〈/mn〉〈/math〉 vertices has at least 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/mfrac〉〈mrow〉〈mo stretchy="true"〉(〈/mo〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mfrac〉〈mrow〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉3〈/mn〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉c〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉3〈/mn〉〈/mrow〉〈/mfrac〉〈mo stretchy="true"〉)〈/mo〉〈/mrow〉〈mi〉n〈/mi〉〈/math〉 edges where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈mi〉c〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉3〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈mrow〉〈mo stretchy="true"〉(〈/mo〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/mfrac〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈/mfrac〉〈mo stretchy="true"〉)〈/mo〉〈/mrow〉〈/math〉. This improves the bound established by Kostochka and Stiebitz [11]. The same bound holds for online 〈em〉k〈/em〉-list-critical graphs, improving the bound established by Riasat and Schauz [16]. Both bounds follow from a more general result stating that either a graph has many edges or it has an Alon-Tarsi orientable induced subgraph satisfying a certain degree condition.〈/p〉〈/div〉

Description: 〈p〉Publication date: September 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Finite Fields and Their Applications, Volume 59〈/p〉 〈p〉Author(s): Luis H. Gallardo, Olivier Rahavandrainy〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We work over the field with two elements. We establish a new correspondence between Mersenne polynomials and trinomials so that corresponding polynomials have the same number of irreducible factors. This allows us to get a partial but nontrivial result about the factorization of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msup〉〈mrow〉〈mi〉M〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈mi〉h〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈/math〉, for a Mersenne prime 〈em〉M〈/em〉 and for a positive integer 〈em〉h〈/em〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Combinatorics, Volume 81〈/p〉 〈p〉Author(s): Brice Huang, Mustazee Rahman〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈/mrow〉〈/math〉 is a sequence of finite and connected graphs that share a common universal cover 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mi〉T〈/mi〉〈/math〉 and such that the proportion of eigenvalues of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si3.svg"〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉 that lie within the support of the spectrum of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mi〉T〈/mi〉〈/math〉 tends to 1 in the large 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈mi〉n〈/mi〉〈/math〉 limit. This is a weak notion of being Ramanujan. We prove such a sequence of graphs is asymptotically locally tree-like. This is deduced by way of an analogous theorem proved for certain infinite sofic graphs and unimodular networks, which extends results for regular graphs and certain infinite Cayley graphs.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): François Dross, Pascal Ochem〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A graph is 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mo〉(〈/mo〉〈msub〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉-colorable if it admits a vertex partition into a graph with maximum degree at most 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈msub〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈/math〉 and a graph with maximum degree at most 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si3.svg"〉〈msub〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈/math〉. We show that every 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mrow〉〈mo〉(〈/mo〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉6〈/mn〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉-free planar graph is 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈mrow〉〈mo〉(〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉6〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉-colorable. We also show that deciding whether a 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mrow〉〈mo〉(〈/mo〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉6〈/mn〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉-free planar graph is 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1083.svg"〉〈mrow〉〈mo〉(〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉3〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉-colorable is NP-complete.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Numerical Mathematics〈/p〉 〈p〉Author(s): Jiao Wen, Chengming Huang, Min Li〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper is concerned with the stability properties of Runge-Kutta methods for Volterra integro-differential equations. Both the basic test equation and a convolution test equation are considered. Some fixed order recurrence relations and the corresponding stability conditions are derived for general methods. The concept of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi〉V〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉-stability is introduced for the convolution test equation and some 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi〉V〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉-stable one-stage methods are found. The 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msub〉〈mrow〉〈mi〉A〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉-stability and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi〉V〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉-stability of the fully implicit discretized collocation methods with one or two stages are investigated in details. Finally, some numerical experiments are given to illustrate the obtained theoretical results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 10 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Ahmed Bendib, Aissa Chouder, Kamel Kara, Abdelhammid Kherbachi, Said Barkat, Walid Issa〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In a microgrid (MG) topology, the secondary control is introduced to compensate for the voltage amplitude and frequency deviations, mainly caused by the inherent characteristics of the droop control strategy. This paper proposes an accurate approach to derive small signal models of the frequency and amplitude voltage at the point of common coupling (PCC) of a single-phase MG by analyzing the dynamics of the second-order generalized integrator-based frequency-locked loop (SOGI-FLL). The frequency estimate model is then introduced in the frequency restoration control loop, while the derived model of the amplitude estimate is introduced for the voltage restoration loop. Based on the obtained models, the MG stability analysis and proposed controllers’ parameters tuning are carried out. Also, this study includes the modeling and design of the synchronization control loop that enables a seamless transition from island mode to grid-connected mode operation. Simulation and practical experiments of a hierarchical control scheme, including traditional droop control and the proposed secondary control for two single-phase parallel inverters, are implemented to confirm the effectiveness and the robustness of the proposal under different operating conditions. The obtained results validate the proposed modeling approach to provide the expected transient response and disturbance rejection in the MG.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Differential Equations〈/p〉 〈p〉Author(s): Hui Li, Wei Wang, Zhifei Zhang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition, which ensures that the evolution equation describing the free boundary is strictly hyperbolic. Our result gives a rigorous confirmation that the elasticity has a stabilizing effect on the Rayleigh-Taylor instability.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Numerical Mathematics〈/p〉 〈p〉Author(s): Rasool Hosseini, Mehdi Tatari〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, a new splitting technique is implemented for solving hyperbolic PDEs. As the main result, the new methods preserve the maximum principle unconditionally or with a mild condition on discretization parameters in comparison with well known methods. Damping of numerical solution in time evolution is investigated. For numerical solution of the Burgers' equation, as a nonlinear problem, an iterative method based on the new splitting technique is presented. Efficiency of the new methods is examined via numerical examples.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 2 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Mehdi Rajabi Asadabadi, Elizabeth Chang, Ofer Zwikael, Morteza Saberi, Keiran Sharpe〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The requirement specification process is an important part of a project and has the potential to prevent problems that may last for years after a project is delivered. Previous studies on the requirement specification process have focused on clarifying stated fuzzy terms in software requirement engineering. However, in many projects there is information that is not stated, but it is implied and can be inferred. This hidden information is usually ignored due to the assumption that ‘the provider understands what they mean/need’. This assumption is not always true. Such information, if extracted, may include fuzzy terms, namely hidden fuzzy terms (HFTs), which need specification. Therefore, these fuzzy terms have to be identified and then specified to avoid potential future consequences. This study proposes an algorithm to extract the hidden fuzzy terms, utilises a fuzzy inference system (FIS) to specify them, and applies the best worst multi-criteria decision making method (BWM) to evaluate the delivered product and measure the performance of the provider. The model is then used to examine a case from Defence Housing Australia. Such evaluation and measurement enable the project owner/manager to have a transparent basis to support decisions later in different phases of the project, and to ultimately reduce the likelihood of conflict and the receipt of an unsatisfactory product.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 4 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Xi Wang, Shukai Li, Tao Tang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉With the objective to promote the efficiency of heavy haul transportation, this paper investigates the efficiently intermittent cruise control problem for heavy haul trains. Based on the concept of periodically intermittent control, the closed-loop form of the error dynamic state-space model for heavy haul trains is given considering uncertain parameters, which is different from existing heavy haul train control methods in that the control forces are only provided in part of the running period. To facilitate the controller design, a set of linear matrix inequalities (LMIs) are presented as the sufficient conditions for the existence of the periodically intermittent controller, which guarantees both the speed tracking error and the relative coupler displacements are exponentially stable at the equilibrium state. Simulation results indicate that the proposed control scheme can significantly improve the control efficiency without sacrificing too much on speed tracking performance.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 4 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Xin Hu, Chi Huang, Jianquan Lu, Jinde Cao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper studies the stabilization problem of Boolean control networks with stochastic impulses, where stochastic impulses model is described as a series of possible regulatory models with corresponding probabilities. The stochastic impulses model makes the research more realistic. The global stabilization problem is trying to drive all states to reach the predefined target with probability 1. A necessary and sufficient condition is presented to judge whether a given system is globally stabilizable. Meanwhile, an algorithm is proposed to stabilize the given system by designing a state feedback controller and different impulses strategies. As an extension, these results are applied to analyze the global stabilization to a fixed state of probability Boolean control networks with stochastic impulses. Finally, two examples are given to demonstrate the effectiveness of the obtained results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 3 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Chengfu Qin, Weihua He, Kiyoshi Ando〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉An edge of a 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉k〈/mi〉〈/math〉-connected graph is said to be 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉k〈/mi〉〈/math〉-contractible if its contraction results in a 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉k〈/mi〉〈/math〉-connected graph. A 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉k〈/mi〉〈/math〉-connected graph without 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉k〈/mi〉〈/math〉-contractible edge is said to be contraction critically 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉k〈/mi〉〈/math〉-connected. Y. Egawa and W. Mader, independently, showed that the minimum degree of a contraction critical 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉k〈/mi〉〈/math〉-connected graph is at most 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mrow〉〈mfrac〉〈mrow〉〈mn〉5〈/mn〉〈mi〉k〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈/mrow〉〈/mfrac〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/math〉. Hence, the minimum degree of a contraction critical 8-connected graph is either 8 or 9. This paper shows that a graph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si9.svg"〉〈mi〉G〈/mi〉〈/math〉 is a contraction critical 8-connected graph with minimum degree 9 if and only if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si9.svg"〉〈mi〉G〈/mi〉〈/math〉 is the strong product of a contraction critical 4-connected graph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si11.svg"〉〈mi〉H〈/mi〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si12.svg"〉〈msub〉〈mrow〉〈mi〉K〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 3 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Joshua D. Laison, Erin M. McNicholas, Nicole S. Seaders〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The determining number or fixing number of a graph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉Γ〈/mi〉〈/math〉 is the smallest size of a subset of vertices 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mi〉S〈/mi〉〈/math〉 of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉Γ〈/mi〉〈/math〉 such that any automorphism of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉Γ〈/mi〉〈/math〉 that stabilizes 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mi〉S〈/mi〉〈/math〉 stabilizes all of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉Γ〈/mi〉〈/math〉. The determining set 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si7.svg"〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 of a finite group 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mi〉G〈/mi〉〈/math〉 is the set of all determining numbers of all finite graphs for which 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mi〉G〈/mi〉〈/math〉 is the automorphism group.〈/p〉 〈p〉Similarly, the base size of a permutation representation 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si10.svg"〉〈mrow〉〈mi〉ρ〈/mi〉〈mo〉:〈/mo〉〈mi〉G〈/mi〉〈mo〉→〈/mo〉〈mo〉Sym〈/mo〉〈mrow〉〈mo〉(〈/mo〉〈mi〉S〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 of a group 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mi〉G〈/mi〉〈/math〉 is the smallest size of a subset 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si12.svg"〉〈mi〉B〈/mi〉〈/math〉 of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mi〉S〈/mi〉〈/math〉 such that its pointwise stabilizer in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mi〉G〈/mi〉〈/math〉 is trivial. The base size set 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si15.svg"〉〈mrow〉〈mi mathvariant="script"〉B〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 of a finite group 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mi〉G〈/mi〉〈/math〉 is the set of all base sizes of all faithful representations of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mi〉G〈/mi〉〈/math〉 on finite sets.〈/p〉 〈p〉In this paper we compare the sets 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si7.svg"〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si15.svg"〉〈mrow〉〈mi mathvariant="script"〉B〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉. We show that for finite abelian groups, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si20.svg"〉〈mrow〉〈mi mathvariant="script"〉B〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mi mathvariant="script"〉D〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mrow〉〈mo〉{〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈mi〉k〈/mi〉〈mo〉}〈/mo〉〈/mrow〉〈/mrow〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si21.svg"〉〈mi〉k〈/mi〉〈/math〉 is the number of elementary divisors of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mi〉G〈/mi〉〈/math〉. We characterize 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si15.svg"〉〈mrow〉〈mi mathvariant="script"〉B〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si7.svg"〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 for dihedral groups of the form 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si25.svg"〉〈msub〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈mrow〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msup〉〈/mrow〉〈/msub〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si26.svg"〉〈msub〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msup〉〈/mrow〉〈/msub〉〈/math〉 for an odd prime 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si27.svg"〉〈mi〉p〈/mi〉〈/math〉 and prove 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si28.svg"〉〈mrow〉〈mi mathvariant="script"〉B〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≠〈/mo〉〈mi mathvariant="script"〉D〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉G〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 for dihedral groups of the form 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si29.svg"〉〈msub〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈mi〉q〈/mi〉〈/mrow〉〈/msub〉〈/math〉 where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si27.svg"〉〈mi〉p〈/mi〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si31.svg"〉〈mi〉q〈/mi〉〈/math〉 are distinct odd primes.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 3 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Taras Banakh, Dominic van der Zypen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For a hypergraph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mi〉H〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mrow〉〈mo〉(〈/mo〉〈mi〉V〈/mi〉〈mo〉,〈/mo〉〈mi mathvariant="script"〉E〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉, a subfamily 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mrow〉〈mi mathvariant="script"〉C〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉⊆〈/mo〉〈mi mathvariant="script"〉E〈/mi〉〈/mrow〉〈/math〉 is called a cover of the hypergraph if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si3.svg"〉〈mrow〉〈mo〉⋃〈/mo〉〈mi mathvariant="script"〉C〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉⋃〈/mo〉〈mi mathvariant="script"〉E〈/mi〉〈/mrow〉〈/math〉. A cover 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si4.svg"〉〈mi mathvariant="script"〉C〈/mi〉〈/math〉 is called minimal if each cover 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉⊆〈/mo〉〈mi mathvariant="script"〉C〈/mi〉〈/mrow〉〈/math〉 of the hypergraph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mi〉H〈/mi〉〈/math〉 coincides with 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si4.svg"〉〈mi mathvariant="script"〉C〈/mi〉〈/math〉. We prove that for a hypergraph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mi〉H〈/mi〉〈/math〉 the following conditions are equivalent: (i) each countable subhypergraph of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mi〉H〈/mi〉〈/math〉 has a minimal cover; (ii) each non-empty subhypergraph of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mi〉H〈/mi〉〈/math〉 has a maximal edge; (iii) 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mi〉H〈/mi〉〈/math〉 contains no isomorphic copy of the hypergraph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si12.svg"〉〈mrow〉〈mo〉(〈/mo〉〈mi〉ω〈/mi〉〈mo〉,〈/mo〉〈mi〉ω〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉. This characterization implies that a countable hypergraph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si13.svg"〉〈mrow〉〈mo〉(〈/mo〉〈mi〉V〈/mi〉〈mo〉,〈/mo〉〈mi mathvariant="script"〉E〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 has a minimal cover if every infinite set 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si14.svg"〉〈mrow〉〈mi〉I〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉⊆〈/mo〉〈mi〉V〈/mi〉〈/mrow〉〈/math〉 contains a finite subset 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si15.svg"〉〈mrow〉〈mi〉F〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉⊆〈/mo〉〈mi〉I〈/mi〉〈/mrow〉〈/math〉 such that the family of edges 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si16.svg"〉〈mrow〉〈msub〉〈mrow〉〈mi mathvariant="script"〉E〈/mi〉〈/mrow〉〈mrow〉〈mi〉F〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≔〈/mo〉〈mrow〉〈mo〉{〈/mo〉〈mi〉E〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="script"〉E〈/mi〉〈mo〉:〈/mo〉〈mi〉F〈/mi〉〈mo〉⊆〈/mo〉〈mi〉E〈/mi〉〈mo〉}〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 is finite. Also we prove that a hypergraph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si13.svg"〉〈mrow〉〈mo〉(〈/mo〉〈mi〉V〈/mi〉〈mo〉,〈/mo〉〈mi mathvariant="script"〉E〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 has a minimal cover if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si18.svg"〉〈mrow〉〈mo〉sup〈/mo〉〈mrow〉〈mo〉{〈/mo〉〈mrow〉〈mo〉|〈/mo〉〈mi〉E〈/mi〉〈mo〉|〈/mo〉〈/mrow〉〈mo〉:〈/mo〉〈mi〉E〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="script"〉E〈/mi〉〈mo〉}〈/mo〉〈/mrow〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〈〈/mo〉〈mi〉ω〈/mi〉〈/mrow〉〈/math〉 or for every 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si19.svg"〉〈mrow〉〈mi〉v〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉∈〈/mo〉〈mi〉V〈/mi〉〈/mrow〉〈/math〉 the family 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si20.svg"〉〈mrow〉〈msub〉〈mrow〉〈mi mathvariant="script"〉E〈/mi〉〈/mrow〉〈mrow〉〈mi〉v〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≔〈/mo〉〈mrow〉〈mo〉{〈/mo〉〈mi〉E〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="script"〉E〈/mi〉〈mo〉:〈/mo〉〈mi〉v〈/mi〉〈mo〉∈〈/mo〉〈mi〉E〈/mi〉〈mo〉}〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 is finite.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 3 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Shengxiang Lv, Yichao Chen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We introduce a handle-inserting operation in order to construct a minimum genus embedding of the tripartite graph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈msub〉〈mrow〉〈mi〉K〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈mo〉,〈/mo〉〈mi〉n〈/mi〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈/math〉 for odd 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si7.svg"〉〈mi〉n〈/mi〉〈/math〉. The construction is used to solve the conjecture of Kurauskas that for odd  〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si7.svg"〉〈mi〉n〈/mi〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si4.svg"〉〈msub〉〈mrow〉〈mi〉K〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈mo〉,〈/mo〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉 has an embedding of genus 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈mrow〉〈mo〉⌈〈/mo〉〈mrow〉〈mo〉(〈/mo〉〈mi〉n〈/mi〉〈mo〉−〈/mo〉〈mn〉1〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈mrow〉〈mo〉(〈/mo〉〈mi〉n〈/mi〉〈mo〉−〈/mo〉〈mn〉2〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈mo〉∕〈/mo〉〈mn〉4〈/mn〉〈mo〉⌉〈/mo〉〈/mrow〉〈/math〉, such that one face is bounded by a Hamilton cycle. Such embeddings have an application to modeling road junctions with minimal number of bridges.〈/p〉〈/div〉

Description: 〈p〉Publication date: December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Mathematics Letters, Volume 98〈/p〉 〈p〉Author(s): Yang Cao, Zhiyong Wang, Jingxue Yin〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We consider the Cauchy problem for the semilinear pseudo-parabolic equation with initial data with compact support. We find the life span of the solution, when the power exponent 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉p〈/mi〉〈/math〉 is smaller than the Fujita exponent.〈/p〉〈/div〉

Description: 〈p〉Publication date: December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Mathematics Letters, Volume 98〈/p〉 〈p〉Author(s): Hongbo Guan, Yong Wang, Huiqing Zhu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, two meshless schemes are proposed for solving Dirichlet boundary optimal control problems governed by elliptic equations. The first scheme uses radial basis function collocation method (RBF-CM) for both state equation and adjoint state equation, while the second scheme employs the method of fundamental solution (MFS) for the state equation when it has a zero source term, and RBF-CM for the adjoint state equation. Numerical examples are provided to validate the efficiency of the proposed schemes.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 3 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Annals of Pure and Applied Logic〈/p〉 〈p〉Author(s): Erik Palmgren〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type theories. Categories with families (cwfs) is an established semantical structure for dependent type theories, such as Martin-Löf type theory. We introduce in this article a notion of 〈em〉hyperdoctrine over a cwf〈/em〉, and show how FOLDS and DFOL fit in this semantical framework. A soundness and completeness theorem is proved for DFOL. The semantics is functorial in the sense of Lawvere, and uses a dependent version of the Lindenbaum-Tarski algebra for a DFOL theory. Agreement with standard first-order semantics is established. Applications of DFOL to constructive mathematics and categorical foundations are given. A key feature is a 〈em〉local propositions-as-types principle.〈/em〉〈/p〉〈/div〉

Description: 〈p〉Publication date: December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Mathematics Letters, Volume 98〈/p〉 〈p〉Author(s): Christos Sourdis〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We establish the energy minimality property of a solution to the generalized Painlevé-II equation 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mi〉Δ〈/mi〉〈mi〉y〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mi〉y〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈msup〉〈mrow〉〈mi〉y〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msup〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mn〉0〈/mn〉〈/mrow〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mrow〉〈mrow〉〈mo〉(〈/mo〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈mo linebreak="goodbreak" linebreakstyle="after"〉∈〈/mo〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/mrow〉〈/math〉, which is increasing in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si3.svg"〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈/math〉 and converges to the positive and negative Hastings–McLeod solutions as 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si4.svg"〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈mo〉→〈/mo〉〈mo〉±〈/mo〉〈mi〉∞〈/mi〉〈/mrow〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 2 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): Kieran Conboy, Patrick Mikalef, Denis Dennehy, John Krogstie〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉While the topic of analytics is rapidly growing in popularity across various domains, there is still a relatively low amount of empirical work in the field of operations research (OR). While studies of various technical and business aspects of analytics are emerging in OR, little has been done to address how the OR community can leverage business analytics in dynamic and uncertain environments – the very place where OR is supposed to play a key role. To address this gap, this study draws on the dynamic capabilities view of the firm and builds on eight selected case studies of operations research activity in large organisations, each of which have invested significantly in analytics technology and implementation. The study identifies fourteen analytics-enabled micro-foundations of dynamic capabilities, essentially highlighting how organisations can use analytics to manage and enhance their OR activities in dynamic and uncertain environments. This study also identifies six key cross-cutting propositions emerging from the data and develops a roadmap for future OR researchers to address these issues and improve the use and value of analytics as enablers of organisational dynamic capabilities.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research, Volume 279, Issue 2〈/p〉 〈p〉Author(s): 〈/p〉

Description: 〈p〉Publication date: Available online 3 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Khodakhast Bibak, Bruce M. Kapron, Venkatesh Srinivasan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Recently, Grynkiewicz et al. (2013), using tools from additive combinatorics and group theory, proved necessary and sufficient conditions under which the linear congruence 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉⋯〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≡〈/mo〉〈mi〉b〈/mi〉〈mspace width="0.334em"〉〈/mspace〉〈mrow〉〈mo〉(〈/mo〉〈mo〉mod〈/mo〉〈mspace width="0.334em"〉〈/mspace〉〈mi〉n〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mrow〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈mo〉,〈/mo〉〈mi〉n〈/mi〉〈/mrow〉〈/math〉 (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si3.svg"〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≥〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/math〉) are arbitrary integers, has a solution 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si4.svg"〉〈mrow〉〈mrow〉〈mo〉〈〈/mo〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈mo〉〉〈/mo〉〈/mrow〉〈mo linebreak="goodbreak" linebreakstyle="after"〉∈〈/mo〉〈msubsup〉〈mrow〉〈mi mathvariant="double-struck"〉Z〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msubsup〉〈/mrow〉〈/math〉 with all 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/math〉 distinct. So, it would be an interesting problem to give an explicit formula for the number of such solutions. Quite surprisingly, this problem was first considered, in a special case, by Schönemann almost two centuries ago(!) but his result seems to have been forgotten. Schönemann (1839), proved an explicit formula for the number of such solutions when 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mrow〉〈mi〉b〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mn〉0〈/mn〉〈/mrow〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si7.svg"〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mi〉p〈/mi〉〈/mrow〉〈/math〉 a prime, and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mrow〉〈msubsup〉〈mrow〉〈mo〉∑〈/mo〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msubsup〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≡〈/mo〉〈mn〉0〈/mn〉〈mspace width="0.334em"〉〈/mspace〉〈mrow〉〈mo〉(〈/mo〉〈mo〉mod〈/mo〉〈mspace width="0.334em"〉〈/mspace〉〈mi〉p〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 but 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si9.svg"〉〈mrow〉〈msub〉〈mrow〉〈mo〉∑〈/mo〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mo〉∈〈/mo〉〈mi〉I〈/mi〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo〉⁄〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≡〈/mo〉〈mn〉0〈/mn〉〈mspace width="0.334em"〉〈/mspace〉〈mrow〉〈mo〉(〈/mo〉〈mo〉mod〈/mo〉〈mspace width="0.334em"〉〈/mspace〉〈mi〉p〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 for all 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si10.svg"〉〈mrow〉〈mo〉0̸〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉≠〈/mo〉〈mi〉I〈/mi〉〈mo〉⊊︀〈/mo〉〈mrow〉〈mo〉{〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈mi〉k〈/mi〉〈mo〉}〈/mo〉〈/mrow〉〈/mrow〉〈/math〉. In this paper, we generalize Schönemann’s theorem using a result on the number of solutions of linear congruences due to D. N. Lehmer and also a result on graph enumeration. This seems to be a rather uncommon method in the area; besides, our proof technique or its modifications may be useful for dealing with other cases of this problem (or even the general case) or other relevant problems.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Operations Research, Volume 111〈/p〉 〈p〉Author(s): Omar Foutlane, Issmail El Hallaoui, Pierre Hansen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The integral simplex using decomposition (ISUD) is a primal algorithm dedicated to solve set partitioning problems (SPP). Given an integer solution, the integral simplex using decomposition (ISUD) seeks a descent direction that leads to an improved adjacent integer solution. It uses a horizontal decomposition (of a linear transformation of the constraint matrix). We propose the integral simplex using double decomposition (ISU2D) which is a parallel version of ISUD. It uses an innovative disjoint vertical decomposition to find in parallel orthogonal descent directions leading to an integer solution with a larger improvement. Each descent direction identifies a set of variables that will leave the current solution and a set of entering variables with better costs. To find these directions, we develop a dynamic decomposition approach that splits the original problem into subproblems that are then solved in parallel by ISUD. Our main innovation is the use of the current solution as a foundation for the construction of the set of subproblems; the set changes during the optimization process as the current solution changes. In addition, we use bounding and pricing strategies and implement parallel processing techniques. We show that ISU2D is 3 to 4 times faster than ISUD on large instances.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Combinatorics, Volume 81〈/p〉 〈p〉Author(s): Bhaswar B. Bhattacharya, Sumit Mukherjee〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mi〉T〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉H〈/mi〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 be the number of monochromatic copies of a fixed connected graph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mi〉H〈/mi〉〈/math〉 in a uniformly random coloring of the vertices of the graph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si3.svg"〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉. In this paper we give a complete characterization of the limiting distribution of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mi〉T〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉H〈/mi〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉, when 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈msub〉〈mrow〉〈mrow〉〈mo〉{〈/mo〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mo〉}〈/mo〉〈/mrow〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈mo〉≥〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈/math〉 is a converging sequence of dense graphs. When the number of colors grows to infinity, depending on whether the expected value remains bounded, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mi〉T〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉H〈/mi〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 either converges to a finite linear combination of independent Poisson variables or a normal distribution. On the other hand, when the number of colors is fixed, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mi〉T〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉H〈/mi〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 converges to a (possibly infinite) linear combination of independent centered chi-squared random variables. This generalizes the classical birthday problem, which involves understanding the asymptotics of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si8.svg"〉〈mrow〉〈mi〉T〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈msub〉〈mrow〉〈mi〉K〈/mi〉〈/mrow〉〈mrow〉〈mi〉s〈/mi〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉K〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉, the number of monochromatic 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si9.svg"〉〈mi〉s〈/mi〉〈/math〉-cliques in a complete graph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si10.svg"〉〈msub〉〈mrow〉〈mi〉K〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉 (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si9.svg"〉〈mi〉s〈/mi〉〈/math〉-matching birthdays among a group of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si12.svg"〉〈mi〉n〈/mi〉〈/math〉 friends), to general monochromatic subgraphs in a network.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 30 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Operations Research〈/p〉 〈p〉Author(s): Lucas Kletzander, Nysret Musliu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉In many professions the demand for work requires employees to work in different shifts to cover varying requirements including areas like health care, protection services, transportation, manufacturing or call centers. However, there are many constraints that need to be satisfied in order to create feasible schedules. The demands can be specified in various ways, different legal requirements need to be respected and employee satisfaction has to be taken into account. Therefore, automated solutions are mandatory to stay competitive. However, even then it is often hard to provide good solutions in reasonable time as many of the problems are NP-hard.〈/p〉 〈p〉While not each problem will require the whole set of available restrictions, it is cumbersome to develop a new specification format and corresponding solver for each problem. Often these can not be well applied to similar problems differing in some requirements. On the other hand it is a challenging task to provide a general formulation and solution methods that can solve large integrated problems, as even several sub-problems on their own are known to be NP-hard.〈/p〉 〈p〉Therefore a new framework is proposed for the general employee scheduling problem that allows the implementation of various heuristic algorithms and their application to a wide range of problems. This is realized by proposing a unified handling of constraints and the possibility to implement various moves that can be reused across different algorithms. Further, a new search method is developed and implemented in the framework.〈/p〉 〈p〉In order to show the applicability to a wide range of problems, we take different problems from literature that cover different types of demand and constraints, translate their instances to our formulation and apply our solver to those instances as well as our own instances with good results. For one problem class our framework could obtain better solutions for several benchmark instances.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 29 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): Claudio Arbib, Mustafa Ç. Pınar, Matteo Tonelli〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉Consider a three-level non-capacitated location/pricing problem: a firm first decides which facilities to open, out of a finite set of candidate sites, and sets service prices with the aim of revenue maximization; then a second firm makes the same decisions after checking competing offers; finally, customers make individual decisions trying to minimize costs that include both purchase and transportation. A restricted two-level problem can be defined to model an optimal reaction of the second firm to known decision of the first.〈/p〉 〈p〉For non-metric costs, the two-level problem corresponds to 〈span〉Envy-free Pricing〈/span〉 or to a special 〈span〉Network Pricing〈/span〉 problem, and is 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si65.svg"〉〈mi mathvariant="bold-script"〉APX〈/mi〉〈/math〉-complete even if facilities can be opened at no fixed cost. Our focus is on the metric 1-dimensional case, a model where customers are distributed on a main communication road and transportation cost is proportional to distance. We describe polynomial-time algorithms that solve two- and three-level problems with opening costs and single 1〈sup〉〈em〉st〈/em〉〈/sup〉 level facility. Quite surprisingly, however, even the two-level problem with no opening costs becomes 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si66.svg"〉〈mi mathvariant="bold-script"〉NP〈/mi〉〈/math〉-hard when two 1〈sup〉〈em〉st〈/em〉〈/sup〉 level facilities are considered.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 29 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): Zachary Feinstein〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We construct a continuous time model for price-mediated contagion precipitated by a common exogenous stress to the banking book of all firms in the financial system. In this setting, firms are constrained so as to satisfy a risk-weight based capital ratio requirement. We use this model to find analytical bounds on the risk-weights for assets as a function of the market liquidity. Under these appropriate risk-weights, we find existence and uniqueness for the joint system of firm behavior and the asset prices. We further consider an analytical bound on the firm liquidations, which allows us to construct exact formulas for stress testing the financial system with deterministic or random stresses. Numerical case studies are provided to demonstrate various implications of this model and analytical bounds.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 29 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): Bo Jin〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In a recent paper, Galle, Barnhart, and Jaillet [Galle, V., Barnhart, C., & Jaillet, P. (2018). A new binary formulation of the restricted container relocation problem based on a binary encoding of configurations. 〈em〉European Journal of Operational Research, 267〈/em〉(2), 467–477] introduced a new variant of the container relocation problem (CRP), named the relaxed restricted CRP, where every container can be relocated at most once for retrieving each target container. The authors also proposed a binary integer programming model for formulating the relaxed restricted CRP. In this paper, it is first shown that the proposed model contains two deficiencies in formulating the “last in, first out” (LIFO) policy. These deficiencies will cause the solutions obtained by the model to correspond to infeasible configurations or infeasible relocation sequences. Then, the LIFO policy is analyzed in detail and reformulated as linear constraints correctly. Lastly, the corrected integer programming formulation is presented. Computational experiments show that the corrected model dramatically reduces complexity and improves performance.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 29 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Operations Research〈/p〉 〈p〉Author(s): Cheng-Hung Wu, Yi-Chun Yao, Stéphane Dauzère-Pérès, Cheng-Juei Yu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A dynamic decision model that coordinates dispatching and preventive maintenance decisions for failure-prone parallel machines in make-to-order (MTO) production environments is developed in this research. The primary objective is to minimize the weighted long-run average waiting costs of MTO systems. Two common but seldom studied stochastic factors, namely, the dispatching-dependent deterioration of machines and machine-health-dependent production rates, are explicitly modeled in the proposed dynamic dispatching and preventive maintenance (DDPM) model. Although the DDPM model is developed using Markov decision processes, it is equally effective in non-Markovian production environments. The performance of the DDPM model is validated in Markovian and non-Markovian production environments. Compared with several methods from the literature, simulation results show an improvement of at least 45.2% in average job waiting times and a minimum reduction of 48.9% in average machine downtimes. The comparison results between the optimal dynamic dispatching policies with and without coordinated preventive maintenance show that performance improvement can be mostly attributed to the coordination between preventive maintenance and dispatching decisions.〈/p〉〈/div〉

Description: 〈p〉Publication date: 7 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Advances in Mathematics, Volume 356〈/p〉 〈p〉Author(s): Florentin Münch, Radosław K. Wojciechowski〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Discrete time random walks on a finite set naturally translate via a one-to-one correspondence to discrete Laplace operators. Typically, Ollivier curvature has been investigated via random walks. We first extend the definition of Ollivier curvature to general weighted graphs and then give a strikingly simple representation of Ollivier curvature using the graph Laplacian. Using the Laplacian as a generator of a continuous time Markov chain, we connect Ollivier curvature with the heat equation which is strongly related to continuous time random walks. In particular, we prove that a lower bound on the Ollivier curvature is equivalent to a certain Lipschitz decay of solutions to the heat equation. This is a discrete analogue to a celebrated Ricci curvature lower bound characterization by Renesse and Sturm. Our representation of Ollivier curvature via the Laplacian allows us to deduce a Laplacian comparison principle by which we prove non-explosion and improved diameter bounds.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Advances in Mathematics, Volume 355〈/p〉 〈p〉Author(s): Brian C. Hall, Todd Kemp〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The free multiplicative Brownian motion 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈/math〉 is the large-〈em〉N〈/em〉 limit of Brownian motion 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msubsup〉〈mrow〉〈mi〉B〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈/msubsup〉〈/math〉 on the general linear group 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mrow〉〈mi mathvariant="normal"〉GL〈/mi〉〈/mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉N〈/mi〉〈mo〉;〈/mo〉〈mi mathvariant="double-struck"〉C〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉. We prove that the Brown measure for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈/math〉—which is an analog of the empirical eigenvalue distribution for matrices—is supported on the closure of a certain domain 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si130.svg"〉〈msub〉〈mrow〉〈mi mathvariant="normal"〉Σ〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈/math〉 in the plane. The domain 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si130.svg"〉〈msub〉〈mrow〉〈mi mathvariant="normal"〉Σ〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈/math〉 was introduced by Biane in the context of the large-〈em〉N〈/em〉 limit of the Segal–Bargmann transform associated to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mrow〉〈mi mathvariant="normal"〉GL〈/mi〉〈/mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉N〈/mi〉〈mo〉;〈/mo〉〈mi mathvariant="double-struck"〉C〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉.〈/p〉 〈p〉We also consider a two-parameter version, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si364.svg"〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉s〈/mi〉〈mo〉,〈/mo〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈/math〉: the large-〈em〉N〈/em〉 limit of a related family of diffusion processes on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mrow〉〈mi mathvariant="normal"〉GL〈/mi〉〈/mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉N〈/mi〉〈mo〉;〈/mo〉〈mi mathvariant="double-struck"〉C〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 introduced by the second author. We show that the Brown measure of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si364.svg"〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉s〈/mi〉〈mo〉,〈/mo〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈/math〉 is supported on the closure of a certain planar domain 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si357.svg"〉〈msub〉〈mrow〉〈mi mathvariant="normal"〉Σ〈/mi〉〈/mrow〉〈mrow〉〈mi〉s〈/mi〉〈mo〉,〈/mo〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈/math〉, generalizing 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si130.svg"〉〈msub〉〈mrow〉〈mi mathvariant="normal"〉Σ〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈/math〉, introduced by Ho.〈/p〉 〈p〉In the process, we introduce a new family of spectral domains related to any operator in a tracial von Neumann algebra: the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si398.svg"〉〈msub〉〈mrow〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉〈em〉-spectrum〈/em〉 for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.svg"〉〈mi〉n〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="double-struck"〉N〈/mi〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.svg"〉〈mi〉p〈/mi〉〈mo〉≥〈/mo〉〈mn〉1〈/mn〉〈/math〉, a subset of the ordinary spectrum defined relative to potentially-unbounded inverses. We show that, in general, the support of the Brown measure of an operator is contained in its 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg"〉〈msubsup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msubsup〉〈/math〉-spectrum.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 29 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Rui Pedro Carpentier, Roger Picken〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Bowlin and Brin defined the class of color graphs, whose vertices are triangulated polygons compatible with a fixed four-coloring of the polygon vertices. In this article it is proven that each color graph has a vertex-induced embedding in a hypercube, and an upper bound is given for the hypercube dimension. The color graphs for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mi〉n〈/mi〉〈/math〉-gons up to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mn〉8〈/mn〉〈/mrow〉〈/math〉 are listed and studied, in particular enabling a question by Bowlin and Brin concerning the diameter of color graphs to be answered. Finally it is shown that color graphs with a certain type of subgraph cannot be isometrically embedded in a hypercube of any dimension.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 29 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Quanxin Zhu, S. Vimal Kumar, R. Raja, Fathalla Rihan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper addresses the issue of reliable feedback control of an uncertain aircraft flight control systems with disturbances via non-fragile sampled-data control approach. In particular, the parameter uncertainties are assumed to be randomly occurring which is described by the Bernoulli distributed sequences. By constructing a suitable Lyapunov-Krasovskii functional together with Wirtinger-based inequality, a new set of sufficient conditions in terms of linear matrix inequalities is obtained to ensure the asymptotic stability and extended dissipativity of the aircraft flight control systems not only when all actuators are operational, but also in case of some actuator failures. Finally, simulation results are conducted to validate the effectiveness of the proposed control design technique.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 2 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Numerical Mathematics〈/p〉 〈p〉Author(s): Jun Zhang, Xiaofeng Yang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we consider time marching numerical schemes to solve a two-mode phase field crystal model with face-centered-cubic ordering. We propose two type, linear, and unconditionally energy stable schemes by combining the recently developed IEQ and SAV approaches with the stabilization technique, where several extra stabilizing terms are added to enhance the stability and keep the required accuracy while using large time steps. We further prove the unconditional energy stabilities of the developed schemes rigorously. Through the comparisons with some other prevalent schemes like the fully-implicit, semi-implicit, and convex-splitting schemes for some benchmark numerical examples in 2D and 3D, we demonstrate the stability and the accuracy of the schemes numerically.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 29 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Operations Research〈/p〉 〈p〉Author(s): Janniele A.S. Araujo, Haroldo G. Santos, Bernard Gendron, Sanjay Dominik Jena, Samuel S. Brito, Danilo S. Souza〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Resource Constrained Project Scheduling Problems (RCPSPs) without preemption are well-known 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mrow〉〈mi mathvariant="bold-script"〉N〈/mi〉〈mi mathvariant="bold-script"〉P〈/mi〉〈/mrow〉〈/math〉-hard combinatorial optimization problems. A feasible RCPSP solution consists of a time-ordered schedule of jobs with corresponding execution modes, respecting precedence and resources constraints. In this paper, we propose a cutting plane algorithm to separate five different cut families, as well as a new preprocessing routine to strengthen resource-related constraints. New lifted versions of the well-known precedence and cover inequalities are employed. At each iteration, a dense conflict graph is built considering feasibility and optimality conditions to separate cliques, odd-holes and strengthened Chvátal-Gomory cuts. The proposed strategies considerably improve the linear relaxation bounds, allowing a state-of-the-art mixed-integer linear programming solver to find provably optimal solutions for 754 previously open instances of different variants of the RCPSPs, which was not possible using the original linear programming formulations.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 28 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): Mike G. Tsionas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Mitropoulos et al. (Mitropoulos P., M. A. Talias, and I. Mitropoulos, 2015, Combining stochastic DEA with Bayesian analysis to obtain statistical properties of the efficiency scores: An application to Greek public hospitals. European Journal of Operational Research 243, 302-311) suggested the use of a Bayesian approach in Data Envelopment Analysis (DEA) which can be used to obtain posterior distributions of efficiency scores. In this paper, we avoid their assumption that alternative data sets are simulated from the predictive distribution obtained from their simple data generating process of a normal distribution for the data. The new approach has two significant advantages. First, the posterior proposed in this paper is coherent or principled in the sense that it is consistent with the DEA formulation. Second, and perhaps surprisingly, it is not necessary to solve linear programming problems for each observation in the sample. Bayesian inference is organized around Markov Chain Monte Carlo techniques that can be implemented quite easily. We conduct extensive Monte Carlo experiments to investigate the finite-sample properties of the new approach. We also provide an application to a large U.S banking data set. The sample is an unbalanced panel of US banks with 2,397 bank–year observations for 285 banks. The main purpose of the analysis is to compare distributions of efficiency scores. Relative to DEA, Bayes DEA provides different efficiency scores and their sample distribution has significantly less probability concentration around unity. The comparison with bootstrap-DEA shows that results from Bayes DEA are in broad agreement.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Annals of Pure and Applied Logic〈/p〉 〈p〉Author(s): Marcos Mazari-Armida〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉We study limit models in the class of abelian groups with the subgroup relation and in the class of torsion-free abelian groups with the pure subgroup relation. We show: 〈span〉〈span〉Theorem 0.1.〈/span〉〈p〉〈/p〉 〈dl〉 〈dt〉(1)〈/dt〉 〈dd〉〈p〉〈em〉If G is a limit model of cardinality λ in the class of abelian groups with the subgroup relation, then〈/em〉 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉G〈/mi〉〈mo〉≅〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mo〉⊕〈/mo〉〈/mrow〉〈mrow〉〈mi〉λ〈/mi〉〈/mrow〉〈/msub〉〈mi mathvariant="double-struck"〉Q〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉⊕〈/mo〉〈msub〉〈mrow〉〈mo〉⊕〈/mo〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈mspace width="0.25em"〉〈/mspace〉〈mtext mathvariant="italic"〉prime〈/mtext〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mo〉⊕〈/mo〉〈/mrow〉〈mrow〉〈mi〉λ〈/mi〉〈/mrow〉〈/msub〉〈mi mathvariant="double-struck"〉Z〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉)〈/mo〉〈/math〉〈em〉.〈/em〉〈/p〉〈/dd〉 〈dt〉(2)〈/dt〉 〈dd〉 〈p〉〈em〉If G is a limit model of cardinality λ in the class of torsion-free abelian groups with the pure subgroup relation, then:〈/em〉〈/p〉 〈dl〉 〈dt〉•〈/dt〉 〈dd〉〈p〉〈em〉If the length of the chain has uncountable cofinality, then〈/em〉〈span〉〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi〉G〈/mi〉〈mo〉≅〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mo〉⊕〈/mo〉〈/mrow〉〈mrow〉〈mi〉λ〈/mi〉〈/mrow〉〈/msub〉〈mi mathvariant="double-struck"〉Q〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉⊕〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="italic"〉Π〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈mspace width="0.25em"〉〈/mspace〉〈mtext mathvariant="italic"〉prime〈/mtext〉〈/mrow〉〈/msub〉〈mover accent="true"〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mo〉⊕〈/mo〉〈/mrow〉〈mrow〉〈mi〉λ〈/mi〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉Z〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉p〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mo〉‾〈/mo〉〈/mover〉〈mo〉.〈/mo〉〈/math〉〈/span〉〈/p〉〈/dd〉 〈dt〉•〈/dt〉 〈dd〉〈p〉〈em〉If the length of the chain has countable cofinality, then G is not algebraically compact.〈/em〉〈/p〉〈/dd〉 〈/dl〉 〈/dd〉 〈/dl〉〈/span〉〈/p〉 We also study the class of finitely Butler groups with the pure subgroup relation, we show that it is an AEC, Galois-stable and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si178.svg"〉〈mo stretchy="false"〉(〈/mo〉〈mo linebreak="badbreak" linebreakstyle="after"〉〈〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="normal"〉ℵ〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈/math〉-tame and short.〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Markus Holzleitner〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schrödinger operators. It provides more details and suitable extensions to already existing results, that are needed in other recent contributions dealing with these kinds of operators.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Koichi Komada〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We study the large time asymptotics of the solutions to nonlinear dispersive equations of the form〈span〉〈span〉(0.1)〈/span〉〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mo〉∂〈/mo〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈mi〉u〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉P〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉i〈/mi〉〈msub〉〈mrow〉〈mo〉∂〈/mo〉〈/mrow〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈msub〉〈mrow〉〈mo〉∂〈/mo〉〈/mrow〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈/msub〉〈mi〉u〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈msub〉〈mrow〉〈mo〉∂〈/mo〉〈/mrow〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈mspace width="2em"〉〈/mspace〉〈mi〉t〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mspace width="0.25em"〉〈/mspace〉〈mi〉x〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="double-struck"〉R〈/mi〉〈mo〉,〈/mo〉〈/math〉〈/span〉 where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi〉P〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉i〈/mi〉〈msub〉〈mrow〉〈mo〉∂〈/mo〉〈/mrow〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is a pseudo-differential operator defined by the symbol 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mi〉P〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉ξ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉. In this paper, we consider the case that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mi〉P〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉ξ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is nonlocal and nonhomogeneous and show the existence of the solution to (0.1) around a given modified free solution.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Thu Hien Nguyen, Anna Vishnyakova〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For an entire function 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉z〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈msubsup〉〈mrow〉〈mo〉∑〈/mo〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉=〈/mo〉〈mn〉0〈/mn〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msubsup〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈msup〉〈mrow〉〈mi〉z〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msup〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈/math〉 we show that 〈em〉f〈/em〉 does not belong to the Laguerre-Pólya class if the quotients 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mfrac〉〈mrow〉〈msubsup〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msubsup〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/mfrac〉〈/math〉 are increasing in 〈em〉n〈/em〉, and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mi〉c〈/mi〉〈mo〉:〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈munder〉〈mi mathvariant="normal"〉lim〈/mi〉〈mrow〉〈mi〉n〈/mi〉〈mo stretchy="false"〉→〈/mo〉〈mo〉∞〈/mo〉〈/mrow〉〈/munder〉〈mo〉⁡〈/mo〉〈mfrac〉〈mrow〉〈msubsup〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msubsup〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/mfrac〉〈/math〉 is smaller than an absolute constant 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈msub〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msub〉〈/math〉 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msub〉〈mo〉≈〈/mo〉〈mn〉3〈/mn〉〈mo〉.〈/mo〉〈mn〉2336〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics, Volume 342, Issue 12〈/p〉 〈p〉Author(s): Lon Mitchell〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉An 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si219.svg"〉〈mi〉n〈/mi〉〈/math〉-satisfactory coloring of the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si219.svg"〉〈mi〉n〈/mi〉〈/math〉-smooth integers is an assignment of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si219.svg"〉〈mi〉n〈/mi〉〈/math〉 colors to the positive integers whose prime factors are at most 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si219.svg"〉〈mi〉n〈/mi〉〈/math〉 so that for each such 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si5.svg"〉〈mi〉m〈/mi〉〈/math〉, the integers 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mrow〉〈mi〉m〈/mi〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mi〉m〈/mi〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈mi〉n〈/mi〉〈mi〉m〈/mi〉〈/mrow〉〈/math〉 receive different colors. In this note, we give a short proof that infinitely many 6-satisfactory colorings of the 6-smooth integers exist and show how the technique of the proof can be applied more generally, including for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si7.svg"〉〈mrow〉〈mi〉n〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉∈〈/mo〉〈mrow〉〈mo〉{〈/mo〉〈mn〉8〈/mn〉〈mo〉,〈/mo〉〈mn〉10〈/mn〉〈mo〉,〈/mo〉〈mn〉12〈/mn〉〈mo〉}〈/mo〉〈/mrow〉〈/mrow〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Angela Aguglia, Francesco Pavese〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We provide a characterization of the non-singular Hermitian variety of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mrow〉〈mi mathvariant="normal"〉PG〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mn〉4〈/mn〉〈mo〉,〈/mo〉〈msup〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 as a hypersurface of degree 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mrow〉〈mi〉q〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/math〉 over 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si3.svg"〉〈mrow〉〈mi mathvariant="normal"〉GF〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈msup〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉 with 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si4.svg"〉〈mrow〉〈msup〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mn〉7〈/mn〉〈/mrow〉〈/msup〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈msup〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mn〉5〈/mn〉〈/mrow〉〈/msup〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈msup〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/math〉 rational points, which does not contain linear subspaces of dimension greater than 1 and having exactly one line in common with at least a plane of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si6.svg"〉〈mrow〉〈mi mathvariant="normal"〉PG〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mn〉4〈/mn〉〈mo〉,〈/mo〉〈msup〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Differential Geometry and its Applications, Volume 67〈/p〉 〈p〉Author(s): A.M. Grundland, J. de Lucas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods for obtaining Lie algebras of conditional symmetries from known conditional symmetries, and unnecessary previous assumptions of the theory are removed. As a consequence, new insights into other types of conditional symmetries arise. We then apply the so-called PDE Lie systems to the derivation and analysis of Lie algebras of conditional symmetries. In particular, we develop a method for obtaining solutions of a higher-order system of PDEs via the solutions and geometric properties of a PDE Lie system, whose form gives a Lie algebra of conditional symmetries of the Clairin type. Our methods are illustrated with physically relevant examples such as nonlinear wave equations, the Gauss–Codazzi equations for minimal soliton surfaces, and generalised Liouville equations.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Numerical Mathematics〈/p〉 〈p〉Author(s): Vincenzo Citro, Raffaele D'Ambrosio〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We analyze long-term properties of stochastic 〈em〉θ〈/em〉-methods for damped linear stochastic oscillators. The presented a-priori analysis of the error in the correlation matrix allows to infer the long-time behaviour of stochastic 〈em〉θ〈/em〉-methods and their capability to reproduce the same long-term features of the continuous dynamics. The theoretical analysis is also supported by a selection of numerical experiments.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Numerical Mathematics〈/p〉 〈p〉Author(s): Jiansong Zhang, Xiaomang Shen, Hui Guo, Hongfei Fu, Huiran Han〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A combined method is provided for simulating the compressible wormhole propagation, in which, the splitting mixed finite element (SMFE) method is applied for the parabolic-type pressure equation, the modified mass-conservative characteristic (MCC) method is presented for the convection-diffusion type solute transport equation, and the traditional finite element method is applied for the porosity equation. The application of the splitting mixed element method results in a symmetric positive definite coefficient matrix of the separated mixed element system and the mass-conservative characteristic finite element method not only does well in handling convection-dominant diffusion problem but also keeps mass balance globally. The convergence of this method is considered and the optimal 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/math〉-norm error estimate is also derived. Finally, some numerical examples are provided to confirm theoretical analysis and effectiveness of the proposed method.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Operations Research〈/p〉 〈p〉Author(s): Carl Axel Folkestad, Nora Hansen, Kjetil Fagerholt, Henrik Andersson, Giovanni Pantuso〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Carsharing has received increased attention from the Operations Research community in recent years. Currently, many systems are adopting electric vehicles that require charging when battery levels fall below a given level. To do this, staff is often used to move cars to charging stations. Repositioning cars, rather than simply moving them to the closest charging station, might provide a better distribution of cars and in turn generate increased revenue and customer service while only marginally increase the operational costs. We present a mathematical model for the problem of charging and repositioning a fleet of shared electric cars. The model considers the assignment of cars to charging stations and the routing of staff and service vehicles. The complexity of the resulting mixed integer program makes it impossible to solve real world instances using a commercial solver. Therefore, we propose a new Hybrid Genetic Search with Adaptive Diversity Control algorithm. Tests based on data from a real life carsharing organization demonstrate that the proposed method can handle real size instances and that combining repositioning and charging operations can give significant benefits.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): Zelin Zhang, Minghui Ma, Peter T.L. Popkowski Leszczyc, Hejun Zhuang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉This research proposes an analytical model of the joint optimization of coupon face value and duration together with the product price, and determines the impact of coupon design on consumers’ redemption behavior. A model of rational forward-looking consumers’ redemption behavior is derived that incorporates forgetting (to redeem) and stochastic redemption costs.〈/p〉 〈p〉Results show that when product price is exogenous, long-duration coupons may result in increased seller profits and always increase consumer surplus. Moreover, a one-period coupon is never optimal when (1) the difference in valuations for high-value (loyal) and low-value (non-loyal) consumers or (2) the coupon face value is larger than the redemption costs of high-value consumers. Long-duration coupons tend to be optimal when the level of recall of high-value consumers is sufficiently low, which reduces redemption by high-value consumers.〈/p〉 〈p〉Coupon duration together with face value plays an important role in coupons’ ability to price discriminate between different consumer segments and to avoid head-on competition with other sellers. Results can replicate empirically observed redemptions patterns, which has important implications for the strategic targeting of coupons to different consumer segments.〈/p〉 〈p〉A coupon may result in an increase or decrease in price. When the difference in valuation between high-value and low-value consumers is high (relative to the redemption costs), a seller can either reduce price and lower face value or increase coupon duration for the purpose of avoiding redemption by high-value consumers.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 22 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Operations Research〈/p〉 〈p〉Author(s): Eduardo A.J. Anacleto, Cláudio N. Meneses, Santiago V. Ravelo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The Unconstrained Binary Quadratic Programming problem (〈code〉UBQP〈/code〉) belongs to the NP-hard class and has become a framework for modeling a variety of combinatorial optimization problems. The methods most commonly used to solve instances of the 〈code〉UBQP〈/code〉 explore the concept of neighborhood of a solution. Given a binary vector 〈em〉x〈/em〉 ∈ {0, 1}〈sup〉〈em〉n〈/em〉〈/sup〉, solution to a 〈code〉UBQP〈/code〉 instance, a neighborhood of 〈em〉x〈/em〉 can be defined by flip moves. 〈em〉Flip moves〈/em〉 consist on selecting one or more elements (positions) of 〈em〉x〈/em〉 and “flip” their values to their complementary values (i.e., from 1 to 0 or from 0 to 1). Normally, those methods compute a large number of flip moves, and so the whole process to solve an instance can be quite time consuming. In order to reduce this time, some works have proposed ways to efficiently evaluate one or two flip moves, and also extensions to higher order moves. In this paper we propose two closed-form formulas for evaluating quickly any order of flip moves. To test our theoretical findings, we executed an extensive set of computational experiments over well-known instances for the problem. Against common belief, our results show that it is possible to compute high order flip moves very fast.〈/p〉〈/div〉

Description: 〈p〉Publication date: December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Operations Research, Volume 112〈/p〉 〈p〉Author(s): Alexandre Salles da Cunha, Abilio Lucena〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Assume one is given an angle 〈em〉α〈/em〉 ∈ (0, 2〈em〉π〈/em〉] and a complete undirected graph 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si38.svg"〉〈mrow〉〈mi〉G〈/mi〉〈mo linebreak="goodbreak"〉=〈/mo〉〈mo〉(〈/mo〉〈mi〉V〈/mi〉〈mo〉,〈/mo〉〈mi〉E〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉. The vertices in 〈em〉V〈/em〉 represent points in the Euclidean plane. The edges in 〈em〉E〈/em〉 represent the line segments between these points, with edge weights equal to segment lengths. Spanning trees of 〈em〉G〈/em〉 are called 〈em〉α〈/em〉-spanning trees (〈em〉α〈/em〉-STs) if, for any 〈em〉i〈/em〉 ∈ 〈em〉V〈/em〉, the smallest angle that encloses all line segments corresponding to its 〈em〉i〈/em〉-incident edges does not exceed 〈em〉α〈/em〉. The Angular Constrained Minimum Spanning Tree Problem (〈em〉α〈/em〉-MSTP) seeks an 〈em〉α〈/em〉-ST with the least weight. The problem arises in the design of wireless communication networks operating under directional antennas. We propose two 〈em〉α〈/em〉-MSTP formulations. One, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si39.svg"〉〈msub〉〈mi mathvariant="bold-script"〉F〈/mi〉〈mi〉x〈/mi〉〈/msub〉〈/math〉 requiring, in principle, 〈em〉O〈/em〉(2〈sup〉|〈em〉V〈/em〉|〈/sup〉) inequalities to model the angular constraints (〈em〉α〈/em〉-AC). For 〈em〉α〈/em〉 ∈ (0, 〈em〉π〈/em〉), however, we show that just 〈em〉O〈/em〉(|〈em〉V〈/em〉|〈sup〉3〈/sup〉) of them suffice to attain not only a formulation but also the same Linear Programming relaxation (LPR) bound as the full blown model. The other formulation, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si40.svg"〉〈mrow〉〈msub〉〈mi mathvariant="bold-script"〉F〈/mi〉〈mrow〉〈mi〉x〈/mi〉〈mi〉y〈/mi〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈/mrow〉〈/math〉 enlarges the set of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si39.svg"〉〈msub〉〈mi mathvariant="bold-script"〉F〈/mi〉〈mi〉x〈/mi〉〈/msub〉〈/math〉 variables but manages to model 〈em〉α〈/em〉-AC, compactly. Furthermore, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si41.svg"〉〈msub〉〈mi mathvariant="bold-script"〉F〈/mi〉〈mrow〉〈mi〉x〈/mi〉〈mi〉y〈/mi〉〈/mrow〉〈/msub〉〈/math〉 LPR bounds are proven to dominate their 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si39.svg"〉〈msub〉〈mi mathvariant="bold-script"〉F〈/mi〉〈mi〉x〈/mi〉〈/msub〉〈/math〉 counterparts. That dominance, however, is empirically shown to reduce as 〈em〉α〈/em〉 increases. Finally, exact Branch-and-Cut algorithms implemented for the two formulations are shown, empirically, to exchange roles as top performer, throughout the [0, 2〈em〉π〈/em〉) range of 〈em〉α〈/em〉 values.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 European Journal of Operational Research〈/p〉 〈p〉Author(s): Sturla F. Kvamsdal, José M. Maroto, Manuel Morán, Leif K. Sandal〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Seasonality or periodicity–biological, environmental, or economic–are fundamental properties of most marine fisheries. We propose a generic infinite horizon discrete time fisheries management model by modifying existing models and frameworks of analysis to reflect seasonal variation or more general multiperiodicity in parameters, variables, or functional forms. Our model captures such variations via repeated cycles of multiple intervals with differing characteristics. The framework offers a simple and intuitive set up of arbitrary periodicity and seasonality in any feature, which significantly increases model realism. Further, it distances itself from continuous time modeling approaches where uniqueness and solvability of periodic models generally are difficult to assert. In our setting, the governing equations for the time-dependent value function of the management optimization problem are shown to be equivalent to a high-dimensional contraction and hence ensure uniqueness and a feasible solution algorithm. We illustrate our approach using a simple example to demonstrate that accounting for seasonality in fisheries management can improve outcomes considerably. Our framework also provides for analysis of seasonal regulatory measures. Ultimately, our approach applies to renewable resource management more generally and to many infinite-horizon, discrete time optimization problems with periodic features.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Simone Munao〈/p〉

Description: 〈p〉Publication date: Available online 13 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Guoxing Ji〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi mathvariant="fraktur"〉A〈/mi〉〈/math〉 be a maximal subdiagonal algebra in a 〈em〉σ〈/em〉-finite von Neumann algebra 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi mathvariant="script"〉M〈/mi〉〈/math〉. If every right invariant subspace of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi mathvariant="fraktur"〉A〈/mi〉〈/math〉 in the noncommutative Hardy space 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈msup〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/math〉 is of Beurling type, then we say 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi mathvariant="fraktur"〉A〈/mi〉〈/math〉 is of type 1. We determine generators of these algebras and consider a Riesz type factorization theorem for the noncommutative 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈msup〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈/math〉 space. We show that the right analytic Toeplitz algebra on the noncommutative Hardy space 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"〉〈msup〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈/math〉 associated with a type 1 subdiagonal algebra with multiplicity 1 is hereditary reflexive.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Dawei Lu, Huiyuan Xu, Yi Niu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we establish some lower and upper bounds with explicit expressions for the Mills' ratio of the skew-generalized normal distribution. And for demonstrating the efficiency of our estimates, some numerical computations are provided.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 12 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Le Li, Wenke Wang, Lihong Huang, J. Wu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we introduce a new concept named the weak flocking behavior. That is, if the complex system has the weak flocking property, the agents do not need have the same velocities to keep together when 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉t〈/mi〉〈mo stretchy="false"〉→〈/mo〉〈mo〉∞〈/mo〉〈/math〉. This shows the biggest difference between weak flocking behavior and the flocking behavior. The advantage of this concept is that its practical significance—the agents don't need always keep in step in lots of the complex systems but they still keep together. Then, we propose a weak flocking model with two agents and study two different mechanisms for this model. Moreover, we also consider a system with N agents. Under the weak link mechanism, the system with N agents can keep weak flocking.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 19 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Armando Castro, Fagner B. Rodrigues, Paulo Varandas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we obtain an almost sure invariance principle for convergent sequences of either Anosov diffeomorphisms or expanding maps on compact Riemannian manifolds and prove an ergodic stability result for such sequences. The sequences of maps need not correspond to typical points of a random dynamical system. The methods in the proof rely on the stability of compositions of hyperbolic dynamical systems and shadowing for sequences of maps. We introduce the notion of sequential conjugacies and prove that these vary in a Lipschitz way with respect to the generating sequences of dynamical systems. As a consequence, we prove stability results for both time-dependent expanding maps and time-depending Anosov diffeomorphisms that complement results in [15].〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Yan Li〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉In this paper, a quasilinear chemotaxis system of parabolic-elliptic type〈span〉〈span〉(0.1)〈/span〉〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mrow〉〈mrow〉〈mo stretchy="true"〉{〈/mo〉〈mtable columnspacing="0em"〉〈mtr〉〈mtd columnalign="left"〉〈msub〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈/msub〉〈mo〉=〈/mo〉〈mi mathvariant="normal"〉∇〈/mi〉〈mo〉⋅〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mi〉φ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mi mathvariant="normal"〉∇〈/mi〉〈mi〉u〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉−〈/mo〉〈mi mathvariant="normal"〉∇〈/mi〉〈mo〉⋅〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mi mathvariant="normal"〉∇〈/mi〉〈mi〉v〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mspace width="0.25em"〉〈/mspace〉〈mspace width="0.25em"〉〈/mspace〉〈mspace width="0.25em"〉〈/mspace〉〈mspace width="1em"〉〈/mspace〉〈/mtd〉〈mtd columnalign="left"〉〈mi〉x〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.25em"〉〈/mspace〉〈mi〉t〈/mi〉〈mo〉〉〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈/mtd〉〈/mtr〉〈mtr〉〈mtd columnalign="left"〉〈mn〉0〈/mn〉〈mo〉=〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈mi〉v〈/mi〉〈mo〉−〈/mo〉〈mi〉μ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉+〈/mo〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈mspace width="0.25em"〉〈/mspace〉〈mspace width="0.25em"〉〈/mspace〉〈mi〉μ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉:〈/mo〉〈mo〉=〈/mo〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉|〈/mo〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mo stretchy="false"〉|〈/mo〉〈/mrow〉〈/mfrac〉〈msub〉〈mrow〉〈mo〉∫〈/mo〉〈/mrow〉〈mrow〉〈mi mathvariant="normal"〉Ω〈/mi〉〈/mrow〉〈/msub〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mo〉⋅〈/mo〉〈mo〉,〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈mspace width="0.25em"〉〈/mspace〉〈mspace width="0.25em"〉〈/mspace〉〈mspace width="1em"〉〈/mspace〉〈/mtd〉〈mtd columnalign="left"〉〈mi〉x〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.25em"〉〈/mspace〉〈mi〉t〈/mi〉〈mo〉〉〈/mo〉〈mn〉0〈/mn〉〈/mtd〉〈/mtr〉〈/mtable〉〈/mrow〉〈/mrow〉〈/math〉〈/span〉 is considered associated with homogeneous Neumann boundary conditions in a smooth bounded domain 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mo〉⊂〈/mo〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msup〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mi〉n〈/mi〉〈mo〉≥〈/mo〉〈mn〉1〈/mn〉〈/math〉. The diffusivity 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈mi〉φ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉ξ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mo stretchy="false"〉[〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mo〉∞〈/mo〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is a positive function and we particularly suppose that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"〉〈mi〉φ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉ξ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈msup〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mi〉ξ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mrow〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉m〈/mi〉〈/mrow〉〈/msup〉〈/math〉 for all 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.svg"〉〈mi〉ξ〈/mi〉〈mo〉≥〈/mo〉〈mn〉0〈/mn〉〈/math〉 with 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si54.svg"〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉0〈/mn〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si50.svg"〉〈mi〉m〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/math〉. 〈em〉f〈/em〉 is a suitably regular positive function given by 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.svg"〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉ξ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mi〉K〈/mi〉〈msup〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mi〉ξ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mrow〉〈mi〉κ〈/mi〉〈/mrow〉〈/msup〉〈/math〉 for all 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.svg"〉〈mi〉ξ〈/mi〉〈mo〉≥〈/mo〉〈mn〉0〈/mn〉〈/math〉 with parameters 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.svg"〉〈mi〉K〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉0〈/mn〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.svg"〉〈mi〉κ〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉0〈/mn〉〈/math〉. It is shown that there exist regular initial data 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg"〉〈msub〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉 such that〈/p〉 〈dl〉 〈dt〉•〈/dt〉 〈dd〉〈p〉if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.svg"〉〈mi〉κ〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mi〉m〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〈〈/mo〉〈mfrac〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/mfrac〉〈/math〉, then all solutions of (0.1) are global and bounded;〈/p〉〈/dd〉 〈dt〉•〈/dt〉 〈dd〉〈p〉if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si14.svg"〉〈mi〉κ〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mi〉m〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mfrac〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/mfrac〉〈/math〉, however, there exists nonnegative radially symmetric initial data 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg"〉〈msub〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉 such that the corresponding solution of (0.1) blows up in finite time.〈/p〉〈/dd〉 〈/dl〉 The critical exponent 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg"〉〈mfrac〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/mfrac〉〈/math〉 seems to be essentially optimal which was given by [30].〈/div〉

Description: 〈p〉Publication date: November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Finite Fields and Their Applications, Volume 60〈/p〉 〈p〉Author(s): Gurmeet K. Bakshi, Gurleen Kaur〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The complete algebraic structure of semisimple finite group algebra of a generalized strongly monomial group is provided. This work extends the work of Broche and del Río on strongly monomial groups. The theory is complimented by an algorithm and is illustrated with an example.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 20 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Numerical Mathematics〈/p〉 〈p〉Author(s): Sayer O. Alharbi, Saleh M. Alzahrani〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The present paper proposes an efficient computational method for solving the time-harmonic multiple scattering problem by many small dielectric circular cylinders. The strategy proposed is based on a reduced integral equation formulation associated to diagonalization properties of the integral operators for the interior problem. In addition, we use an asymptotic approximation of the separation matrices to simplify the formulation. Using a GMRES Krylov iterative solver, accelerated by a preconditioner, we solve in a robust and efficient way the generated linear system. Numerical results support the efficiency and accuracy of the new strategy.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Adrien Clarenne〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we consider a cluster model of weighted Euclidean random balls generated by a shot-noise Cox process. It is an example of cluster point process. We perform a scaling on the model by shrinking the radii of the balls and compensate this effect by increasing the (mean) number of balls in each cluster, or/and increasing the (mean) number of clusters. We consider two different scenarios, say a local and a global scenario. Heuristically, in the first scenario, we focus on the mean number of large balls in a cluster while in the second one, we focus on the global mean number of large balls in the model. According to the different scenarios, the cluster structure can persist at the limit or disappear.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Multivariate Analysis, Volume 174〈/p〉 〈p〉Author(s): Michael Falk, Simone A. Padoan, Florian Wisheckel〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉This paper reviews generalized Pareto copulas (GPC), which are a key to multivariate extreme value theory. Any generalized Pareto copula can be represented in an easy analytical way using a particular type of norm on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msup〉〈/math〉, called 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si2.svg"〉〈mi〉D〈/mi〉〈/math〉-norm. The characteristic property of a generalized Pareto copula is its exceedance stability.〈/p〉 〈p〉They might help to end the following debate: What is a multivariate generalized Pareto distribution? We present an easy way to simulate data from an arbitrary generalized Pareto copula and, thus, form an arbitrary generalized Pareto distribution.〈/p〉 〈p〉As an application we derive nonparametric estimates of the probability that a random vector, which follows a generalized Pareto copula, exceeds a high threshold, together with confidence intervals. A case study on joint exceedance probabilities for air pollutants completes the paper.〈/p〉 〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Rodrigo Bañuelos, Daesung Kim〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Using Itô's formula for processes with jumps, we extend the Hardy–Stein identity proved in [7] to non-symmetric pure jump Lévy processes and derive its martingale version. By a symmetrization argument for Littlewood–Paley functions, the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈/msup〉〈/math〉 boundedness of Fourier multipliers arising from non-symmetric pure jump Lévy processes is proved.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Kathrin Bringmann, Jonas Kaszian, Antun Milas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We introduce vector-valued higher depth quantum modular forms and investigate examples coming from characters of representations of vertex algebras. These are expressed as rank two false theta series, generalizing unary false theta series studied from several standpoints. We also discuss certain double integrals, which may be viewed as the obstruction to modularity of the depth two quantum modular forms. We then find explicit formulas for the double error integrals in the form reminiscent of the classical Mordell integral.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 12 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): L.E. Rossovskii, A.A. Tovsultanov〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We study the Dirichlet problem for a functional differential equation containing shifted and contracted argument under the Laplacian sign. We establish conditions for the unique solvability and demonstrate also that the problem may have an infinite dimensional solution manifold.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 20 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Discrete Mathematics〈/p〉 〈p〉Author(s): Suhyung An, JiYoon Jung, Sangwook Kim〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A lattice path matroid is a transversal matroid corresponding to a pair of lattice paths on the plane. A matroid base polytope is the polytope whose vertices are the incidence vectors of the bases of the given matroid. In this paper, we study the facial structures of matroid base polytopes corresponding to lattice path matroids. In the case of a border strip, we show that all faces of a lattice path matroid polytope can be described by certain subsets of deletions, contractions, and direct sums. In particular, we express them in terms of the lattice path obtained from the border strip. Subsequently, the facial structures of a lattice path matroid polytope for a general case are explained in terms of certain tilings of skew shapes inside the given region.〈/p〉〈/div〉

Description: 〈p〉Publication date: February 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied Mathematics Letters, Volume 100〈/p〉 〈p〉Author(s): Lili Li, Dongfang Li〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we investigate the exact and numerical solutions of the time fractional Burgers’ equation. By using Cole–Hopf transformation and the method of variables separation, the exact solution is presented in terms of the Mittag-Leffler functions. Moreover, by using the L1-scheme on graded meshes and the Legendre–Galerkin spectral method, the numerical approximation is obtained. A numerical example is presented to confirm all the results.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Applied and Computational Harmonic Analysis, Volume 47, Issue 3〈/p〉 〈p〉Author(s): 〈/p〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Luis Carretero, José Valero〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set of periodic solutions is bounded.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 16 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Fátima Drubi, Santiago Ibáñez, David Rivela〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper is concerned with Hopf-Bogdanov-Takens singularities, that is, singularities of 4-dimensional vector fields whose 1-jet is linearly conjugate to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉y〈/mi〉〈mfrac〉〈mrow〉〈mo〉∂〈/mo〉〈/mrow〉〈mrow〉〈mo〉∂〈/mo〉〈mi〉x〈/mi〉〈/mrow〉〈/mfrac〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mi〉v〈/mi〉〈mfrac〉〈mrow〉〈mo〉∂〈/mo〉〈/mrow〉〈mrow〉〈mo〉∂〈/mo〉〈mi〉u〈/mi〉〈/mrow〉〈/mfrac〉〈mo linebreak="goodbreak" linebreakstyle="after"〉+〈/mo〉〈mi〉u〈/mi〉〈mfrac〉〈mrow〉〈mo〉∂〈/mo〉〈/mrow〉〈mrow〉〈mo〉∂〈/mo〉〈mi〉v〈/mi〉〈/mrow〉〈/mfrac〉〈/math〉. They first occur in generic 3-parameter families. A normal form for these singularities and their unfoldings is given up to an arbitrary order. Working with a second order truncation of the normal form for the singularity, we provide a formal classification at the level of codimension three. The proof relies on blowing-up techniques and estimation of Abelian integrals. Previous results in the literature about the classification of 3-dimensional nilpotent singularities of codimension four are essential for our purposes.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 14 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Eric Numfor〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A multi-strain within-host model of HIV with age structure, which explicitly incorporates the loss of free viral particles due to absorption into target cells upon infection, and shedding into the environment is formulated and analyzed. In our model, a time delay between viral entry into a target cell and viral replication is incorporated, and multiple virus strains compete for a population of target cells. Control is incorporated into the model via strain-specific reverse transcriptase and protease inhibitors. An optimal control problem subject to multiple drug treatments is formulated and analyzed. Existence, characterization and uniqueness of optimal control is established. Using the forward-backward sweep numerical method, numerical simulations are presented. Simulations suggest that a combination of reverse transcriptase and protease inhibitors for each strain of the infected cells and free viruses results in a delay in initial peak in the populations of infected cells and free viruses, the absence of relapse phase within the entire time horizon of control, and a decrease in the number of infected cells and free viruses.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Dmitry I. Sinelshchikov, Ilia Yu. Gaiur, Nikolay A. Kudryashov〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We consider a family of non-autonomous second-order differential equations, which generalizes the Liénard equation. We explicitly find the necessary and sufficient conditions for members of this family of equations to admit quadratic, with the respect to the first derivative, first integrals. We show that these conditions are equivalent to the conditions for equations in the family under consideration to possess Lax representations. This provides a connection between the existence of a quadratic first integral and a Lax representation for the studied dissipative differential equations, which may be considered as an analogue to the theorem that connects Lax integrability and Arnold–Liouville integrability of Hamiltonian systems. We illustrate our results by several examples of dissipative equations, including generalizations of the Van der Pol and Duffing equations, each of which have both a quadratic first integral and a Lax representation.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 20 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Functional Analysis〈/p〉 〈p〉Author(s): Salvador Pérez-Esteva, Alejandro Uribe〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We consider Berezin-Toeplitz operators whose multipliers are compactly supported densities carried by a submanifold 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi mathvariant="normal"〉Γ〈/mi〉〈mo〉⊂〈/mo〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉C〈/mi〉〈/mrow〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈/msup〉〈/math〉. We compute asymptotically the moments of their spectral measures, and we prove Szegő limit theorems in cases when Γ is isotropic or co-isotropic, from which Weyl estimates follow. We also obtain asymptotics of the Schatten norms of such operators. Rescaled versions of these operators can be thought of as quantum mechanical mixed states, and our results give the semi-classical limit of their entropy.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Topology and its Applications, Volume 266〈/p〉 〈p〉Author(s): Richard J. Smith〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In recent decades, topology has come to play an increasing role in some geometric aspects of Banach space theory. The class of so-called 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉w〈/mi〉〈/mrow〉〈mrow〉〈mo〉⁎〈/mo〉〈/mrow〉〈/msup〉〈/math〉〈em〉-locally relatively compact〈/em〉 sets was introduced recently by Fonf, Pallares, Troyanski and the author, and were found to be a useful topological tool in the theory of isomorphic smoothness and polyhedrality in Banach spaces. We develop the topological theory of these sets and present some Banach space applications.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Advances in Mathematics, Volume 355〈/p〉 〈p〉Author(s): François Greer〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The Gromov-Witten theory of threefolds admitting a smooth K3 fibration can be solved in terms of the Noether-Lefschetz intersection numbers of the fibration and the reduced invariants of a K3 surface. Toward a generalization of this result to families with singular fibers, we introduce completed Noether-Lefschetz numbers using toroidal compactifications of the period space of elliptic K3 surfaces. As an application, we prove quasi-modularity for some genus 0 partition functions of Weierstrass fibrations over ruled surfaces, and show that they satisfy a holomorphic anomaly equation.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 20 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): José Luis Castiglioni, Sergio A. Celani, Hernán J. San Martín〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we give an explicit description of the left adjoint of the forgetful functor from the algebraic category of Gödel algebras (i.e., prelinear Heyting algebras) to the algebraic category of bounded prelinear Hilbert algebras. We apply this result in order to study possible descriptions of the coproduct of two finite algebras in the algebraic category of prelinear Hilbert algebras.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Carolina Grejo, Pablo M. Rodriguez〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work we propose a new extension for the Maki-Thompson rumor model which incorporates inter-group directed contacts. The model is defined on an homogeneously mixing population where the existence of two differentiated groups of individuals is assumed. While individuals of one group have an active role in the spreading process, individuals of the other group only contribute in stifling the rumor provided that they are contacted. For this model we measure the impact of dissemination by studying the remaining proportion of ignorants of both groups at the end of the process. In addition we discuss some examples and possible applications.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Eduard Marušić-Paloka〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We derive the effective models for describing the behavior of the fluid in 1D-1D junctions (pipes) and 2D-2D junctions. Starting from the Navier-Stokes system in thin domain and using the two-scale convergence, we justify the two-scale model describing the flow through a junction. Finally, separating the variables in the two-scale model, we obtain the effective junction condition.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Erel Segal-Halevi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A cake has to be divided fairly among 〈em〉n〈/em〉 agents. When all agents have equal entitlements, it is known that such a division can be implemented with 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉n〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉1〈/mn〉〈/math〉 cuts. When agents may have different entitlements, the paper shows that at least 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mn〉2〈/mn〉〈mi〉n〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈/math〉 cuts may be necessary, and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mi〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉n〈/mi〉〈mi mathvariant="normal"〉log〈/mi〉〈mo〉⁡〈/mo〉〈mi〉n〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 cuts are always sufficient.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications, Volume 480, Issue 1〈/p〉 〈p〉Author(s): Huiling Wu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We are concerned with the linearly coupled elliptic system with critical exponents〈span〉〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mrow〉〈mo stretchy="true"〉{〈/mo〉〈mtable〉〈mtr〉〈mtd columnalign="left"〉〈mo〉−〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈mi〉a〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mi〉u〈/mi〉〈mo〉=〈/mo〉〈mo stretchy="false"〉|〈/mo〉〈mi〉u〈/mi〉〈msup〉〈mrow〉〈mo stretchy="false"〉|〈/mo〉〈/mrow〉〈mrow〉〈msup〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈mrow〉〈mo〉⁎〈/mo〉〈/mrow〉〈/msup〉〈mo〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈mi〉μ〈/mi〉〈mo stretchy="false"〉|〈/mo〉〈mi〉u〈/mi〉〈msup〉〈mrow〉〈mo stretchy="false"〉|〈/mo〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈mo〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈mi〉λ〈/mi〉〈mi〉v〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉x〈/mi〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈/msup〉〈mo〉,〈/mo〉〈/mtd〉〈/mtr〉〈mtr〉〈mtd columnalign="left"〉〈mo〉−〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈mi〉v〈/mi〉〈mo〉+〈/mo〉〈mi〉b〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mi〉v〈/mi〉〈mo〉=〈/mo〉〈mo stretchy="false"〉|〈/mo〉〈mi〉v〈/mi〉〈msup〉〈mrow〉〈mo stretchy="false"〉|〈/mo〉〈/mrow〉〈mrow〉〈msup〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈mrow〉〈mo〉⁎〈/mo〉〈/mrow〉〈/msup〉〈mo〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mi〉v〈/mi〉〈mo〉+〈/mo〉〈mi〉ν〈/mi〉〈mo stretchy="false"〉|〈/mo〉〈mi〉v〈/mi〉〈msup〉〈mrow〉〈mo stretchy="false"〉|〈/mo〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈mo〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mi〉v〈/mi〉〈mo〉+〈/mo〉〈mi〉λ〈/mi〉〈mi〉u〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉x〈/mi〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈/msup〉〈mo〉,〈/mo〉〈/mtd〉〈/mtr〉〈mtr〉〈mtd columnalign="left"〉〈mi〉u〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉v〈/mi〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈/mtd〉〈/mtr〉〈/mtable〉〈/mrow〉〈/math〉〈/span〉 where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi〉N〈/mi〉〈mo〉≥〈/mo〉〈mn〉3〈/mn〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mn〉2〈/mn〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〈〈/mo〉〈mi〉p〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉q〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〈〈/mo〉〈msup〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈mrow〉〈mo〉⁎〈/mo〉〈/mrow〉〈/msup〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mfrac〉〈mrow〉〈mn〉2〈/mn〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉N〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/mfrac〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈mi〉μ〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉ν〈/mi〉〈/math〉 and 〈em〉λ〈/em〉 are nonnegative constants, and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"〉〈mi〉a〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.svg"〉〈mi〉b〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 are positive periodic functions. The existence of a positive ground state and a higher energy solution of this system is proved using variational methods. Additionally, the asymptotic behavior of these solutions as 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg"〉〈mi〉λ〈/mi〉〈mo stretchy="false"〉→〈/mo〉〈msup〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈mrow〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈/mrow〉〈/msup〉〈/math〉 is obtained.〈/p〉〈/div〉