ALBERT

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: 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 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 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 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: 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: 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: 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: 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: 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〉

Description: 〈p〉Publication date: Available online 12 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Gelson dos Santos, Giovany M. Figueiredo, Uberlandio B. Severo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we use sub-supersolution and minimax methods to show the existence and multiplicity of solutions for the following class of singular quasilinear problems:〈span〉〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mrow〉〈mo〉{〈/mo〉〈mtable〉〈mtr〉〈mtd columnalign="left"〉〈mo〉−〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈mi〉u〈/mi〉〈mo〉−〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈mi〉u〈/mi〉〈mo〉=〈/mo〉〈mi〉a〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈msup〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mo〉−〈/mo〉〈mi〉β〈/mi〉〈/mrow〉〈/msup〉〈mo〉+〈/mo〉〈mi〉h〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo〉,〈/mo〉〈mi〉u〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mspace width="1em"〉〈/mspace〉〈mtext〉in〈/mtext〉〈mspace width="1em"〉〈/mspace〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mtext〉,〈/mtext〉〈/mtd〉〈/mtr〉〈mtr〉〈mtd columnalign="left"〉〈mi〉u〈/mi〉〈mo〉〉〈/mo〉〈mn〉0〈/mn〉〈mspace width="1em"〉〈/mspace〉〈mtext〉in〈/mtext〉〈mspace width="1em"〉〈/mspace〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mtext〉,〈/mtext〉〈/mtd〉〈/mtr〉〈mtr〉〈mtd columnalign="left"〉〈mi〉u〈/mi〉〈mo〉=〈/mo〉〈mn〉0〈/mn〉〈mspace width="1em"〉〈/mspace〉〈mtext〉on〈/mtext〉〈mspace width="1em"〉〈/mspace〉〈mo〉∂〈/mo〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mtext〉,〈/mtext〉〈/mtd〉〈/mtr〉〈/mtable〉〈/mrow〉〈/math〉〈/span〉 where Ω is a bounded smooth domain of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈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"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉N〈/mi〉〈mo〉≥〈/mo〉〈mn〉3〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, the function 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈mi〉a〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is nonnegative, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"〉〈mi〉β〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〉〈/mo〉〈mn〉0〈/mn〉〈/math〉 is a constant and the nonlinearity 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.svg"〉〈mi〉h〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo〉,〈/mo〉〈mi〉u〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is continuous. In our first result, the nonlinearity 〈em〉h〈/em〉 has an arbitrary polynomial growth and we obtain the existence of a solution for the problem via sub-supersolution method. For the second result, 〈em〉h〈/em〉 has subcritical growth and we show the existence of a second solution by applying the Mountain Pass Theorem.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 20 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Meihua Dong, Keonhee Lee, Carlos Morales〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We prove that if a homeomorphism of a compact metric space is equicontinuous and pointwise topologically stable, then it is persistent (in the sense of Lewowicz [12]). The proof relies on the notion of 〈em〉persistent measure〈/em〉 which has its own interest. We compute the Borel hierarchy of these measures and prove that they are not necessarily topologically stable (in the sense of [9]).〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 13 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Mathematical Analysis and Applications〈/p〉 〈p〉Author(s): Xueying Wang, Feng-Bin Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, we develop a new modeling framework to study the impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment. Our model is built on a reaction-advection-diffusion system to represent spatiotemporal dynamics of cholera transmission, and incorporates bacterial hyperinfectivity and spatial heterogeneity. Firstly, we define the basic reproduction number 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉R〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉 and establish the global threshold dynamics based on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉R〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉. Secondly, the global attractivity of the unique endemics equilibrium is discussed when the spatial environment is homogeneous and waning cholera immunity, advection and intrinsic growth of bacteria are ignored. Thirdly, the dependence of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉R〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉 on model parameters are numerically investigated. The theoretical results are obtained for some specific cases. Our result highlights the importance of hyperinfectivity and its interplay with spatial heterogeneity. Particularly, our findings indicate ignoring hyperinfectivity may underestimate the risk of infection.〈/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): 〈/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): Ryo Nishimura〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we study monotonicity properties of asymptotic relations for the generalized hypergeometric function 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mmultiscripts〉〈mrow〉〈mi〉F〈/mi〉〈/mrow〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈none〉〈/none〉〈mprescripts〉〈/mprescripts〉〈mrow〉〈mi〉p〈/mi〉〈mo linebreak="badbreak" linebreakstyle="after"〉+〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈none〉〈/none〉〈/mmultiscripts〉〈/math〉 and the Lauricella hypergeometric function 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msubsup〉〈mrow〉〈mi〉F〈/mi〉〈/mrow〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉N〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈/msubsup〉〈/math〉. The results extend known monotonicity properties of the zero-balanced Gaussian hypergeometric function 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mmultiscripts〉〈mrow〉〈mi〉F〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈none〉〈/none〉〈mprescripts〉〈/mprescripts〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈none〉〈/none〉〈/mmultiscripts〉〈/math〉.〈/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): Naoki Tanaka〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper discusses approximation of semigroups of locally Lipschitz operators by discrete semigroups of local quasi-contractions with respect to metric-like functionals. The main approximation result not only extends a product formula for contractive semigroups generated by maximal dissipative operators in real Hilbert spaces but also gives an algorithm for solving a mixed problem for the Kirchhoff equation to which the contractive semigroup theory or Kato's quasilinear theory cannot directly apply.〈/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): Sun Kwang Kim, Han Ju Lee〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A Urysohn-type theorem is introduced for a subalgebra of the algebra 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msub〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Ω〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 of all bounded complex-valued continuous functions on a Hausdorff topological space Ω. With use of this theorem, it is shown that a type of the Bishop-Phelps-Bollobás theorem holds for certain classes of holomorphic functions on the unit ball of a complex Banach space 〈em〉X〈/em〉 if 〈em〉X〈/em〉 is either a locally uniformly convex space or a locally 〈em〉c〈/em〉-uniformly convex, order-continuous sequence space.〈/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): Lanying Hu, Yong Ren, Qian He〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, we discuss a kind of pantograph stochastic functional differential equations driven by 〈em〉G〈/em〉-Brownian motion (〈em〉G〈/em〉-PSDEs, in short). When the coefficients satisfy local Lipschitz and generalized Lyapunov conditions, we establish existence, uniqueness, asymptotic boundedness and exponential stability of the solution for 〈em〉G〈/em〉-PSDEs.〈/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): 〈/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): Zhi-Yi Wu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉q〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mn〉4〈/mn〉〈mi〉r〈/mi〉〈/math〉 with integer 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈mi〉r〈/mi〉〈mo〉≥〈/mo〉〈mn〉1〈/mn〉〈/math〉. Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"〉〈mi〉a〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈mo〉⋯〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"〉〈mi〉b〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈mo〉⋯〈/mo〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mo stretchy="false"〉{〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mn〉3〈/mn〉〈mo stretchy="false"〉}〈/mo〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msup〉〈/math〉 with 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"〉〈mi〉a〈/mi〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〈〈/mo〉〈mi〉b〈/mi〉〈/math〉, i.e., 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.svg"〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉〈〈/mo〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉 for all 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg"〉〈mi〉n〈/mi〉〈mo〉≥〈/mo〉〈mn〉1〈/mn〉〈/math〉. We consider the following generalized Cantor measure〈span〉〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.svg"〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈mo〉,〈/mo〉〈mi〉a〈/mi〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="badbreak" linebreakstyle="after"〉=〈/mo〉〈msub〉〈mrow〉〈mi〉δ〈/mi〉〈/mrow〉〈mrow〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/mfrac〉〈mo stretchy="false"〉{〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉}〈/mo〉〈/mrow〉〈/msub〉〈mo〉⁎〈/mo〉〈msub〉〈mrow〉〈mi〉δ〈/mi〉〈/mrow〉〈mrow〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈msup〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/mrow〉〈/mfrac〉〈mo stretchy="false"〉{〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉}〈/mo〉〈/mrow〉〈/msub〉〈mo〉⁎〈/mo〉〈mo〉⋯〈/mo〉〈mo〉,〈/mo〉〈/math〉〈/span〉 where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.svg"〉〈msub〉〈mrow〉〈mi〉δ〈/mi〉〈/mrow〉〈mrow〉〈mi〉E〈/mi〉〈/mrow〉〈/msub〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mi mathvariant="normal"〉#〈/mi〉〈mi〉E〈/mi〉〈/mrow〉〈/mfrac〉〈msub〉〈mrow〉〈mo〉∑〈/mo〉〈/mrow〉〈mrow〉〈mi〉a〈/mi〉〈mo〉∈〈/mo〉〈mi〉E〈/mi〉〈/mrow〉〈/msub〉〈msub〉〈mrow〉〈mi〉δ〈/mi〉〈/mrow〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈/msub〉〈/math〉 denotes the uniformly discrete probability on 〈em〉E〈/em〉. In this paper we investigate the spectral eigenvalues (of the second type) of the measure 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.svg"〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈mo〉,〈/mo〉〈mi〉a〈/mi〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈/mrow〉〈/msub〉〈/math〉 (the spectrality of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.svg"〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈mo〉,〈/mo〉〈mi〉a〈/mi〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈/mrow〉〈/msub〉〈/math〉 is settled by He et al. (2017) [17]). More precisely, we characterize the possible real numbers 〈em〉t〈/em〉 satisfying that there exists a countable set 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.svg"〉〈mi mathvariant="normal"〉Λ〈/mi〉〈mo〉⊆〈/mo〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/math〉 such that Λ and 〈em〉t〈/em〉Λ are spectra of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.svg"〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈mo〉,〈/mo〉〈mi〉a〈/mi〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈/mrow〉〈/msub〉〈/math〉 simultaneously, i.e., the sets 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg"〉〈mi〉E〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Λ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉:〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo stretchy="false"〉{〈/mo〉〈msup〉〈mrow〉〈mi〉e〈/mi〉〈/mrow〉〈mrow〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈mi〉π〈/mi〉〈mi〉i〈/mi〉〈mi〉λ〈/mi〉〈mi〉x〈/mi〉〈/mrow〉〈/msup〉〈mo〉:〈/mo〉〈mi〉λ〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="normal"〉Λ〈/mi〉〈mo stretchy="false"〉}〈/mo〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.svg"〉〈mi〉E〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉t〈/mi〉〈mi mathvariant="normal"〉Λ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉:〈/mo〉〈mo linebreak="goodbreak" linebreakstyle="after"〉=〈/mo〉〈mo stretchy="false"〉{〈/mo〉〈msup〉〈mrow〉〈mi〉e〈/mi〉〈/mrow〉〈mrow〉〈mo linebreak="badbreak" linebreakstyle="after"〉−〈/mo〉〈mn〉2〈/mn〉〈mi〉π〈/mi〉〈mi〉i〈/mi〉〈mi〉t〈/mi〉〈mi〉λ〈/mi〉〈mi〉x〈/mi〉〈/mrow〉〈/msup〉〈mo〉:〈/mo〉〈mi〉λ〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="normal"〉Λ〈/mi〉〈mo stretchy="false"〉}〈/mo〉〈/math〉 are both orthonormal basis for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si14.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈mo〉,〈/mo〉〈mi〉a〈/mi〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈/math〉.〈/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): Junxian Li, Alexandru Zaharescu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈em〉L〈/em〉 be an automorphic 〈em〉L〈/em〉-function. Assuming the Riemann Hypothesis for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉L〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 and the Selberg normality conjecture, we obtain a lower bound for the second negative moment and extreme small values of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mo〉′〈/mo〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mi〉ρ〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, where 〈em〉ρ〈/em〉 is a zero of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈mi〉L〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉.〈/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): Huynh Minh Hien〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We study expansive properties for the geodesic and horocycle flows on compact Riemann surfaces of constant negative curvature. It is well-known that the geodesic flow is expansive in the sense of Bowen-Walters and the horocycle flow is positive and negative separating in the sense of Gura. In this paper, we give a new proof of the expansiveness in the sense of Bowen-Walters for the geodesic flow and show that the horocycle flow is positive and negative kinematic expensive in the sense of Artigue as well as expansive in the sense of Katok-Hasselblatt but not expensive in the sense of Bowen-Walters. We also point out that the geodesic flow is neither positive nor negative separating.〈/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): Yong-Guo Shi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The Feigenbaum equation describes universal features of period-doubling in interval maps. Based on the known result on existence of continuous solutions, efforts have been made to find specific classes of continuous solutions, which exhibit structure of various continuous solutions. In addition to solutions of simpler structure such as bijective solutions, some non-monotonic solutions such as unimodal solutions and unimodal-extended solutions were obtained. In this paper we find a new and more complicated class of solutions, called multi-modal-extended solutions, and illustrate their structure with 2-modal-extended solutions. Furthermore, we give conditions to guarantee smoothness of those solutions.〈/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): Nathakhun Wiroonsri〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We use Stein's method to provide non asymptotic 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈/math〉 bounds (also known as Wasserstein bounds) to the normal for functionals of associated point processes. As for supporting tools, we use the connection between association and 〈em〉α〈/em〉-mixing properties that was recently uncovered by [29]. We apply our main results to determinantal point processes which are known to be negatively associated. A potential application to determinantal point processes in the Laguerre-Gaussian family is also presented.〈/p〉〈/div〉