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Abstract: Abstract Let I be a matroidal ideal of degree d of a polynomial ring \(R=K[x_1,\ldots ,x_n]\) , where K is a field. Let \({\text {astab}}(I)\) and \({\text {dstab}}(I)\) be the smallest integers m and n, for which \({\text {Ass}}(I^m)\) and \({\text {depth}}(I^n)\) stabilize, respectively. In this paper, we show that \({\text {astab}}(I)=1\) if and only if \({\text {dstab}}(I)=1\) . Moreover, we prove that if \(d=3\) , then \({\text {astab}}(I)={\text {dstab}}(I)\) . Furthermore, we show that if I is an almost square-free Veronese type ideal of degree d, then \({\text {astab}}(I)={\text {dstab}}(I)=\lceil \frac{n-1}{n-d}\rceil \) . PubDate: 2022-11-22

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Abstract: Abstract In this paper, we present some lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and inverse M-matrix, by virtue of some eigenvalue inclusion sets with parameter \(\alpha \) and inequality scaling techniques. And we analyze relationships between the sizes of the obtained lower bounds. A series of numerical examples are given to demonstrate that our results can be more accurate than the existing results by selecting an appropriate parameter \(\alpha \) . PubDate: 2022-11-05

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Abstract: Abstract In this note on the foundations of complex analysis, we present for Wirtinger derivatives a short proof of the analogue of the Clairaut–Schwarz theorem. It turns out that, via Fubini’s theorem for disks, it is a consequence of the complex version of the Gauss–Green formula relating planar integrals on disks to line integrals on the boundary circle. At the same time, we obtain a version of Pompeiu’s formula for partial aerolar derivatives (equivalent to Wirtinger derivatives) in several complex variables. PubDate: 2022-10-01

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Abstract: Abstract Let R be a two-torsion free prime ring. In this article, we study the commutativity of the ring with the generalized semi-derivation F that satisfies certain conditions in prime rings and apply our results to \((\sigma ,\tau )\) -Jordan ideals. PubDate: 2022-10-01

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Abstract: Abstract In this paper, we state some characterizations of h-convex function defined on a convex set in a linear space. By doing so, we extend the Jensen–Mercer inequality for h-convex function. We present the concept of operator h-convex functions and give some operator versions of Jensen and Jensen–Mercer type inequalities for some classes of operator h-convex functions and unital positive linear maps. Finally, we introduce the complementary inequality of Jensen’s inequality for h-convex functions. PubDate: 2022-10-01

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Abstract: Abstract In this paper, we study a new class of Sobolev type \((\omega ,{\mathbb {T}})\) -periodic linear and semilinear impulsive evolution equations, where \({\mathbb {T}}\) denotes a linear isomorphism from Banach space X to itself. We give a sufficient and necessary condition depending on the initial value, periodic boundary value and linear isomorphism to guarantee that the homogeneous linear impulsive problem has a \((\omega , {\mathbb {T}})\) -periodic solution. Next, we give the explicit expression of \((\omega ,{\mathbb {T}})\) -periodic solutions for nonhomogeneous linear impulsive problem and derive two important estimations for the certain sum and integration including the Green function. Further, we show the existence and uniqueness of solutions to semilinear impulsive problem, where we remove the compactness of \(AB^{-1}\) and use the compactness of a mapping depending on the nonlinear term. Finally, examples are provided to illustrate the theoretical results. PubDate: 2022-10-01

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Abstract: Abstract Let A be a tame Hecke algebra of type \(\mathbf {A}\) . We construct two comparison maps between the minimal projective bimodule resolution and the reduced bar resolution of A by the contracting homotopy, and then we determine the Gerstenhaber algebraic structure and Batalin–Vilkovisky algebraic structure on Hochschild cohomology of A. PubDate: 2022-10-01

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Abstract: Abstract Analogous to the definition of self-conjugate n-color partitions, we introduce here self-conjugate split n-color partitions. The self-conjugate split n-color partitions arise as a modification of another, existing class of partitions. In addition to the generating function and recurrence relation of self-conjugate split n-color partitions, we find several combinatorial identities which associate these partitions with other combinatorial structures. We give a bijection from the set of split n-color partitions of a positive integer \(\nu \) onto that of partitions of \(\nu \) with \(``{{n+1}\atopwithdelims (){2}}\) copies of n”. Moreover, an explicit bijection between the set of restricted self-conjugate split n-color partitions of \(\nu \) and the set of restricted n-color partitions of \(\nu \) has been constructed. Some results involving new restricted split n-color partition functions are also obtained. PubDate: 2022-10-01

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Abstract: Abstract In this paper, \(N_{\psi }\) -type quotient modules \(H^{2}({\mathbb {T}}^{n})/{\mathcal {K}}\) of the Hardy module on polydisc are defined, where \({\mathcal {K}}\) is the submodule generated by \(\{z_{1}-\psi (z_{k}),2\le k\le n\}\) for a finite Blaschke product. Alternative characterizations are given and an orthonormal basis is constructed. Then we show that the self-commutators and cross-commutators are in trace class, self-commutators are Hilbert–Schmidt. Moreover, the traces and the Hilbert–Schmidt norms are given, respectively. PubDate: 2022-10-01

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Abstract: Abstract This paper concerns a nonlinear inverse stochastic parabolic partial differential equation. The source term of this problem consists branches of science and engineering, of known multiplicative noise. We study the existence of the quasi solution for this problem. Our suggested method to this approach is the minimization method based on the stochastic variational formulation. Moreover, we prove a stability estimation and continuity of minimization functional. In the proof procedure, we show that there is a compact subset of the admissible functions set. These results prove the existence of a quasi solution for the proposed problem. PubDate: 2022-10-01

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Abstract: Abstract We prove a rigidity result for homogeneous generalized Douglas–Weyl metrics of Landsberg-type. We show that such metrics have constant \(\mathbf{H}\) -curvature along geodesics. Then, we prove that every homogeneous D-recurrent Finsler metric is a Douglas metric. It turns out that a homogeneous D-recurrent \((\alpha , \beta )\) -metric is a Randers metric or Berwaldian metric, generalizing the result known only in the case of Douglas metrics. Finally, we show that homogeneous generalized isotropic L-reducible metrics are Randers metrics or L-reducible metrics. PubDate: 2022-10-01

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Abstract: Abstract A new subclass of P-matrices called Ostrowski–Brauer Sparse-B (OBS-B) matrices is introduced, as a generalization of the class of doubly B-matrices. Some characterizations and properties of OBS-B matrices are presented, and for Ostrowski–Brauer Sparse (OBS) matrices some sufficient conditions ensuring that the subdirect sum of OBS matrices lies in the same class are given. Meanwhile, the corresponding questions for the Hadamard product and the Kronecker product and sum of two OBS matrices are also considered. PubDate: 2022-10-01

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Abstract: Abstract In this paper, we study the nonlinear Choquard equation $$\begin{aligned} -\Delta {u}+u=\left( x-y ^{-\mu }*G(u)\right) g(u),\quad \text {in}\ {\mathbb {R}}^N, \end{aligned}$$ where \(0<\mu <\min \{N,4\},\ N\ge 3\) , \(g(u)\in {C({\mathbb {R}},{\mathbb {R}})}\) satisfies very general critical growth conditions in the sense of the Hardy–Littlewood–Sobolev inequality and \(G(u)=\int _{0}^{u}g(s){\mathrm{d}}s\) . Using the Pohozaev constraint, we find that the above problem admits a ground state solution of Pohozaev type. PubDate: 2022-10-01

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Abstract: Abstract For a second countable locally compact abelian group G, we study a system of translates generated by \(f \in L^2 (G)\) . We find some equivalent conditions of this family to have some fundamental frame properties. More precisely, let \(\Gamma \) be a uniform lattice in G (a closed subgroup which is cocompact and discrete) and \(\Gamma ^*\) be the annihilator of \(\Gamma \) in \({\widehat{G}}\) . For \(f \in L^2(G)\) , the \(\Gamma ^*\) -periodic function \(\Phi _f\) is defined as \(\Phi _f (\xi ) = \sum _{\gamma \in {\Gamma } ^*} {\widehat{f}} (\xi + \gamma ) ^2\) on \({\widehat{\Gamma }}\) (the dual group of \(\Gamma \) ) and some of its properties are investigated. In particular, it is shown that if \(\Phi _f\) is continuous, then the family \(\lbrace f(.+ \gamma ) \rbrace _{\gamma \in \Gamma }\) cannot be a redundant frame. Among other things, it is shown that there is an isometry from \(L^2(G)\) into \(L^2({\widehat{\Gamma }})\) in such a way that the system of translates in \(L^2({\widehat{\Gamma }})\) is transferred to a nice Fourier-like system in \(L^2({\widehat{\Gamma }})\) . Also, the canonical and oblique duals of the frames of translates are investigated. PubDate: 2022-10-01

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Abstract: Abstract In this paper, we investigate a class of critical p(x)-Kirchhoff problems with a singular term. A nontrivial positive solution is obtained by combining variational methods with an appropriate truncation argument. PubDate: 2022-10-01

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Abstract: Abstract Infectious diseases are transmitted from one person to another and spread throughout a network under certain conditions. Considering an example of propagation, we explain how to define an automaton on the network according to the propagation steps and the conditions under which the epidemic is transmitted. We call this automaton forcing automaton. Also, we call the language of this automaton an epidemic language. We describe how forcing automata and epidemic languages allow us to have a more accurate analysis of propagation in reality. Furthermore, we show that by knowing the epidemic language, it is possible to compare the spread of an epidemic in different networks. Finally, we present an algorithm that can predict a network in which the epidemic spreads, by only knowing its epidemic language. PubDate: 2022-10-01

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Abstract: Abstract We present two types of simple algorithms for numerical approximations of the two-dimensional shallow water equations with variable topography by a dimensional splitting approach. The scheme of the first type has two steps and the the one of the second type has three steps of splitting dimensions in each iteration. In each step, the component computation incorporates a well-balanced method on Cartesian mesh in one-dimensional space. Tests show that these schemes provide us with a reasonable accuracy. Furthermore, we also establish the well-balanced property for both types of schemes. PubDate: 2022-10-01

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Abstract: Abstract In this paper, we study a problem posed by Lasserre (Discrete Comput Geom 50(3):673–678, 2013). Namely, if \(G =\{x\in \mathbb {R}^n : g(x)\le 1\}\) is the compact sublevel set of a non-negative k-homogeneous polynomial g of n variables, we seek to find the minimum number of moments required to determine or to recover g. For polynomials of degree two, we can recover g computing eigenvalues and eigenvectors associated to a matrix \(M \in \mathbb R^{n \times n}\) . For polynomials of degree k, we only prove that g is determined by all its \(\left( {\begin{array}{c}n+k-1\\ k\end{array}}\right) \) moments of degree k PubDate: 2022-10-01

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Abstract: Abstract In this paper, we give some sufficient conditions for a weighted Orlicz space \(L^\Phi _w(G)\) to be a convolution Banach algebra, where G is a locally compact group and \(\Phi \) is a Young function. Also, we prove a hereditary property regarding the discrete subgroups of G. Furthermore, we show that if G be an abelian locally compact group with an open compact subgroup, \((\Phi ,\Psi )\) be a complementary pair of N-functions, and \(L^\Phi _w(G)\) be a convolution Banach algebra, then \(\frac{1}{w^*}\in L^\Psi (G)\) . PubDate: 2022-10-01

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Abstract: Abstract In this article, we study an extended split equality variational inclusion and fixed point problems which is an extension of the split equality variational inclusion problems and fixed point problems. We propose a simultaneous inertial type iterative algorithm with a self adaptive stepsizes such that there is no need for a prior information about the operator norm. We further stated and prove that the proposed algorithm weakly converges to a solution of the extended split equality variational inclusion and fixed point problems. Finally, we give some numerical examples to demonstrate the performance and the applicability of the proposed algorithm. The results of this paper complements and extends results on split equality variational inclusion and fixed point problems. PubDate: 2022-10-01