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: Telescoping path optimization (TPO) of single-cylinder pin-type multisection boom (SPMB) is a practical engineering problem that is valuable to investigate. This article studies the TPO problem and finds the key of TPO is to obtain the maximum retraction backmost combination. A mathematic model on the basis of the quadratic penalty function of a Hopfield neural network (HNN) is constructed. Two strategies are presented to improve the performance of TPO model: one is proportional integral derivative (PID) strategy that adaptively adjusts the parameter λ of the constrained term and the parameter of the optimization objective term by controlling the value of constraint violation and the other is efficiency factor strategy that an efficiency factor is introduced in model for prioritizing the constrained term over the objective term. Data test shows that compared with the path of boom length changing before optimization, both the number of sections that need to be moved and the total travels of cylinder can be reduced by 10%-30% after optimization. Both the PID strategy and the efficiency factor strategy achieve good optimization effects. The efficiency factor strategy is excellent at moderating the conflicts between the constrained term and the objective term; thus the generations of the valid and the optimal solutions get well improved.

Description: A belt drive and a chain drive are the main types of flexible power transmission. In the traditional belt and chain drive design process, engineers need to do a lot of rework to get a design. To solve this problem, taking the Shell Eco-Marathon vehicle as an example, the traditional design and optimization design of the transmission system are carried out. In the optimization design, component optimization and overall optimization design model of the belt and chain drive are first established. Second, the charts in the design manual are converted into formulas by using MATLAB. Finally, an optimization design model is established in Microsoft Excel, and the Excel Solver tool is used to find the optimal design result. The design method proposed in this paper can effectively determine the optimal design of transmission system and provides a new method for the processing of such problems.

Description: This paper proposes a superresolution two-dimensional (2D) direction of arrival (DOA) estimation algorithm for a rectangular array based on the optimization of the atomic norm and a series of relaxation formulations. The atomic norm of the array response describes the minimum number of sources, which is derived from the atomic norm minimization (ANM) problem. However, the resolution is restricted and high computational complexity is incurred by using ANM for 2D angle estimation. Although an improved algorithm named decoupled atomic norm minimization (DAM) has a reduced computational burden, the resolution is still relatively low in terms of angle estimation. To overcome these limitations, we propose the direct minimization of the atomic norm, which is demonstrated to be equivalent to a decoupled rank optimization problem in the positive semidefinite (PSD) form. Our goal is to solve this rank minimization problem and recover two decoupled Toeplitz matrices in which the azimuth-elevation angles of interest are encoded. Since rank minimization is an NP-hard problem, a novel sparse surrogate function is further proposed to effectively approximate the two decoupled rank functions. Then, the new optimization problem obtained through the above relaxation can be implemented via the majorization-minimization (MM) method. The proposed algorithm offers greatly improved resolution while maintaining the same computational complexity as the DAM algorithm. Moreover, it is possible to use a single snapshot for angle estimation without prior information on the number of sources, and the algorithm is robust to noise due to its iterative nature. In addition, the proposed surrogate function can achieve local convergence faster than existing functions.

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: In this paper, we enrich and develop power-type Aczél-Vasić-Pečarić’s inequalities. First of all, we give some new versions of theorems and corollaries about Aczél-Vasić-Pečarić’s inequalities by quoting some lemmas. Moreover, in combination with Hölder’s inequality, we give some applications of the new version of Aczél-Vasić-Pečarić’s inequality and give its proof process.

Description: We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification of Chebyshev’s method. Computational efficiency is examined and comparison between the efficiencies of presented technique with existing techniques is performed. It is proved that, in general, the new method is more efficient. Numerical problems, including those resulting from practical problems viz. integral equations and boundary value problems, are considered to compare the performance of the proposed method with existing methods. Calculation of computational order of convergence shows that the order of convergence of the new method is preserved in all the numerical examples, which is not so in the case of some of the existing higher order methods. Moreover, the numerical results, including the CPU-time consumed in the execution of program, confirm the accurate and efficient behavior of the new technique.

Description: The elementary symmetric functions play a crucial role in the study of zeros of non-zero polynomials in C [ x ] , and the problem of finding zeros in Q [ x ] leads to the definition of algebraic and transcendental numbers. Recently, Marques studied the set of algebraic numbers in the form P ( T ) Q ( T ) . In this paper, we generalize this result by showing the existence of algebraic numbers which can be written in the form P 1 ( T ) Q 1 ( T ) ⋯ P n ( T ) Q n ( T ) for some transcendental number T, where P 1 , … , P n , Q 1 , … , Q n are prescribed, non-constant polynomials in Q [ x ] (under weak conditions). More generally, our result generalizes results on the arithmetic nature of z w when z and w are transcendental.

Description: Machine learning algorithms have been widely used in the field of client credit assessment. However, few of the algorithms have focused on and solved the problems of concept drift and class imbalance. Due to changes in the macroeconomic environment and markets, the relationship between client characteristics and credit assessment results may change over time, causing concept drift in client credit assessments. Moreover, client credit assessment data are naturally asymmetric and class imbalanced because of the screening of clients. Aiming at solving the joint research issue of concept drift and class imbalance in client credit assessments, in this paper, a novel sample-based online learning ensemble (SOLE) for client credit assessment is proposed. A novel multiple time scale ensemble classifier and a novel sample-based online class imbalance learning procedure are proposed to handle the potential concept drift and class imbalance in the client credit assessment data streams. The experiments are carried out on two real-world client credit assessment cases, which present a comprehensive comparison between the proposed SOLE and other state-of-the-art online learning algorithms. In addition, the base classifier preference and the computing resource consumption of all the comparative algorithms are tested. In general, SOLE achieves a better performance than other methods using fewer computing resources. In addition, the results of the credit scoring model and the Kolmogorov–Smirnov (KS) test also prove that SOLE has good practicality in actual client credit assessment applications.

Description: This paper adapts the multivariate optimal control theory to a Riemannian setting. In this sense, a coherent correspondence between the key elements of a standard optimal control problem and several basic geometric ingredients is created, with the purpose of generating a geometric version of Pontryagin’s maximum principle. More precisely, the local coordinates on a Riemannian manifold play the role of evolution variables (“multitime”), the Riemannian structure, and the corresponding Levi–Civita linear connection become state variables, while the control variables are represented by some objects with the properties of the Riemann curvature tensor field. Moreover, the constraints are provided by the second order partial differential equations describing the dynamics of the Riemannian structure. The shift from formal analysis to optimal Riemannian control takes deeply into account the symmetries (or anti-symmetries) these geometric elements or equations rely on. In addition, various submanifold integral cost functionals are considered as controlled payoffs.

Description: Positioning devices allow users’ movement to be recorded. The GPS (Global Positioning System) trajectory data typically consists of spatiotemporal points, which make up the major part of the big data concerning urban life. Existing knowledge extraction methods about the trajectory share a general limitation—they only investigate data from a spatiotemporal aspect, but fail to take the semantic information of trajectories into consideration. Therefore, extracting the semantic information of trajectories with the context of big data is challenging pattern recognition task that has practical application prospects. In this paper, a system is proposed to extract the semantic trajectory patterns of positioning device users. Firstly, a spatiotemporal threshold and clustering based pre-processing model is proposed to process the raw data. Then, we design a probabilistic generative model to annotate the semantic information of each trajectory after the pre-processing procedure. Finally, we apply the PrefixSpan algorithm to mine the semantic trajectory patterns. We verify our system on a large dataset of users’ real trajectories over a period of 5 years in Beijing, China. The results of the experiment indicate that our system produces meaningful patterns.

Description: Three-way decisions, as a decision-making mode which is consistent with human cognition, have been widely used in various fields. In this paper, we fuse the theory of reliability into the three-way decisions method, replace the conditional probability in the three-way decisions method with reliability, and then propose a novel three-way decisions method. We also describe the loss functions with single-valued triangular neutrosophic numbers (SVTNNs) and propose an operator to calculate the score function of triangular neutrosophic numbers. Then, the result of decision is attained according to the principle of minimizing loss. Finally, we apply this method to the overhaul of machines in a factory, which proves the practicability and effectiveness of the proposed methods.

Description: The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.

Description: Studies related to pattern recognition and visualization using computer technology have been introduced. In particular, deep neural networks (DNNs) provide good performance for image, speech, and pattern recognition. However, a poisoning attack is a serious threat to a DNN’s security. A poisoning attack reduces the accuracy of a DNN by adding malicious training data during the training process. In some situations, it may be necessary to drop a specifically chosen class of accuracy from the model. For example, if an attacker specifically disallows nuclear facilities to be selectively recognized, it may be necessary to intentionally prevent unmanned aerial vehicles from correctly recognizing nuclear-related facilities. In this paper, we propose a selective poisoning attack that reduces the accuracy of only the chosen class in the model. The proposed method achieves this by training malicious data corresponding to only the chosen class while maintaining the accuracy of the remaining classes. For the experiment, we used tensorflow as the machine-learning library as well as MNIST, Fashion-MNIST, and CIFAR10 as the datasets. Experimental results show that the proposed method can reduce the accuracy of the chosen class by 43.2%, 41.7%, and 55.3% in MNIST, Fashion-MNIST, and CIFAR10, respectively, while maintaining the accuracy of the remaining classes.

Description: In this paper, we firstly discuss the existence of the least energy sign-changing solutions for a class of p-Kirchhoff-type problems with a -linear growth nonlinearity. The quantitative deformation lemma and Non-Nehari manifold method are used in the paper to prove the main results. Remarkably, we use a new method to verify that . The main results of our paper are the existence of the least energy sign-changing solution and its corresponding energy doubling property. Moreover, we also give the convergence property of the least energy sign-changing solution as the parameter .

Description: In this manuscript, we define generalized Kincses-Totik type contractions within the context of metric space and consider the existence of a fixed point for such operators. Kincses-Totik type contractions extends the renowned Banach contraction mapping principle in different aspects. First, the continuity condition for the considered mapping is not required. Second, the contraction inequality contains all possible geometrical distances. Third, the contraction inequality is formulated for some iteration of the considered operator, instead of the dealing with the given operator. Fourth and last, the iteration number may vary for each point in the domain of the operator for which we look for a fixed point. Consequently, the proved results generalize the acknowledged results in the field, including the well-known theorems of Seghal, Kincses-Totik, and Banach-Caccioppoli. We present two illustrative examples to support our results. As an application, we consider an Ulam-stability of one of our results.

Description: We propose a derivative free one-point method with memory of order 1.84 for solving nonlinear equations. The formula requires only one function evaluation and, therefore, the efficiency index is also 1.84. The methodology is carried out by approximating the derivative in Newton’s iteration using a rational linear function. Unlike the existing methods of a similar nature, the scheme of the new method is easy to remember and can also be implemented for systems of nonlinear equations. The applicability of the method is demonstrated on some practical as well as academic problems of a scalar and multi-dimensional nature. In addition, to check the efficacy of the new technique, a comparison of its performance with the existing techniques of the same order is also provided.

Description: In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex Δ . Indeed, the differentials in the linear part are simply a compilation of restriction maps in the simplicial cohomology of induced subcomplexes of Δ . Along the way, we also show that if a monomial ideal has at least one generator of degree 2, then the linear strand of its minimal free resolution can be written using only ± 1 coefficients.

Description: In this paper, we propose a branch-and-bound algorithm to solve exactly the minimum vertex cover (MVC) problem. Since a tight lower bound for MVC has a significant influence on the efficiency of a branch-and-bound algorithm, we define two novel lower bounds to help prune the search space. One is based on the degree of vertices, and the other is based on MaxSAT reasoning. The experiment confirms that our algorithm is faster than previous exact algorithms and can find better results than heuristic algorithms.

Description: We present fixed points results of multivalued Prešić type k-step iterative mappings satisfying generalized weakly contraction conditions in metric spaces. An example is presented to support the main result proved herein. The stability of fixed point sets of multivalued Prešić type weakly contractive mappings are also established. Global attractivity result for the class of matrix difference equations is derived as application of the result presented herein. These results generalize and extend various comparable results in the existing literature.

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〉