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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: 2021-10-15

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Abstract: In this paper, we introduce a new inertial subgradient projection algorithm for finding a solution of an equilibrium problem in a real Hilbert space. The algorithm combines subgradient projection methods with the self-adaptive and inertial techniques to generate an iteration sequence converging weakly to a solution of the equilibrium problem. Based on the proposed algorithm, we develop a modified algorithm for finding a common solution of the equilibrium problem and fixed point problems. Several of fundamental experiments are showed to illustrate our algorithms and compare with some others. PubDate: 2021-10-15

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Abstract: We introduce the conformally balanced condition on almost Hermitian manifolds. We show that a compact Kähler-like and G-Kähler-like almost Hermitian manifold with the conformally balanced condition becomes Kähler. PubDate: 2021-10-15

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Abstract: Two improved nonlinear conjugate gradient methods are proposed by using the second inequality of the strong Wolfe line search. Under usual assumptions, we proved that the improved methods possess the sufficient descent property and global convergence. By testing the unconstrained optimization problems which taken from the CUTE library and other usual test collections, some large-scale numerical experiments for the presented methods and their comparisons are executed. The detailed results are listed in tables and their corresponding performance profiles are reported in figures, which show that our improved methods are superior to their comparisons. PubDate: 2021-10-15

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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: 2021-10-13

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Abstract: In this paper, we analyze various classes of weighted Stepanov ergodic spaces, weighted Weyl ergodic spaces and weighted pseudo-ergodic spaces in \({{\mathbb {R}}}^{n}\) with the help of results from the theory of Lebesgue spaces with variable exponents \(L^{p(x)}\) . Several structural results of ours seem to be new even in the case of consideration of the constant exponents \(p(x)\equiv p\in [1,\infty ).\) We especially examine the Stepanov asymptotical almost periodicity at minus infinity and the Weyl asymptotical almost periodicity at minus infinity, providing also some interesting applications to the abstract Volterra integro-differential equations in Banach spaces. PubDate: 2021-10-11

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Abstract: To locate all C-eigenvalues of a piezoelectric-type tensor, a new C-eigenvalue inclusion interval is constructed. It is proved that the new interval is tighter than that proposed by Wang et al. (Appl Math Lett 100:106035, 2020). Numerical examples show the effectiveness of the new result. PubDate: 2021-10-11

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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: 2021-10-07

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Abstract: This article is devoted to studying the problem of multiobjective semi-infinite programming on Hadamard manifolds. We first establish both Karush–Kuhn–Tucker necessary and sufficient optimality conditions for some type of efficient solutions. Then, we propose Wolfe and Mond–Weir-type dual problems and examine duality relations under geodesic convexity assumptions. PubDate: 2021-10-07

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Abstract: Let \({\mathcal {A}}\) and \({\mathcal {B}}\) be two factors with dim \({\mathcal {A}}>4\) . In this article, it is proved that a bijective map \(\Phi : {\mathcal {A}}\rightarrow {\mathcal {B}}\) satisfies \(\Phi ([A\bullet B, C])=[\Phi (A)\bullet \Phi (B), \Phi (C)]\) for all \(A, B, C\in {\mathcal {A}}\) if and only if \(\Phi \) is a linear \(*\) -isomorphism, or a conjugate linear \(*\) -isomorphism, or the negative of a linear \(*\) -isomorphism, or the negative of a conjugate linear \(*\) -isomorphism. PubDate: 2021-10-01

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Abstract: In this paper, we introduce the irreducible \(\alpha \) -Nekrasov matrices and irreducible \(\alpha \) -S-Nekrasov matrices as the extended irreducible Nekrasov matrices and we analyze the relationships among the involved matrices and irreducible H-matrices. PubDate: 2021-10-01

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Abstract: Let \({\mathcal {R}}\) be a semiprime ring with center \(Z({\mathcal {R}})\) and with extended centroid C and let \(\sigma : {\mathcal {R}} \rightarrow {\mathcal {R}}\) be an automorphism. Assume that \(\tau : {\mathcal {R}} \rightarrow {\mathcal {R}} \) is an anti-homomorphism, such that the image of \(\tau \) has small centralizer. It is proved that the following are equivalent: (1) \(x^{\sigma }x^{\tau } = x^{\tau }x^{\sigma }\) for all \(x\in {\mathcal {R}};\) (2) \(x^{\sigma } + x^{\tau }\in Z({\mathcal {R}})\) for all \(x\in {\mathcal {R}};\) (3) \(x^{\sigma }x^{\tau }\in Z({\mathcal {R}})\) for all \(x\in {\mathcal {R}}.\) In this case, there exists an idempotent \(e \in C\) , such that \((1-e){\mathcal {R}}\) is a commutative ring and the semiprime ring \(e{\mathcal {R}}\) is equipped with an involution \(\widetilde{\tau }\) , which is induced canonically by \(\tau \) . Note that one can easily obtained the main result in Lee (Commun Algebra 46(3):1060–1065, 2018) when \(\sigma =id_{{\mathcal {R}}}.\) PubDate: 2021-10-01

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Abstract: Let \(G=(V,E)\) be a simple graph. A set \(M\subseteq E\) is a matching if no two edges in M have a common vertex. The matching number, denoted \(\beta (G)\) (or \(\beta \) ), is the maximum size of a matching in G. A double Roman dominating function (DRDF) on a graph G is a function f: \(V\longrightarrow \{0,1,2,3\}\) satisfying the conditions that for every vertex u of weight \(f(u)\in \left\{ 0,1\right\} \) : \(\left( i\right) \) if \(f(u)=0\) , then u is adjacent to either at least one vertex v with \(f(v)=3\) or two vertices \(v_{1}\) , \(v_{2}\) with \(f(v_{1})=f(v_{2})=2\) . \(\left( ii\right) \) if \(f(u)=1\) , then u is adjacent to at least one vertex v with \(f(v)\in \left\{ 2,3\right\} \) . The weight of a double Roman dominating function f is the value \(f(V)=\sum _{u\in V}f(u)\) . The minimum weight of a double Roman dominating function on a graph G is called the double Roman domination number of G, denoted by \(\gamma _{dR}\left( G\right) \) . In this paper, first, we note that \(\gamma _{dR}(G)\le 3\beta (G)\) , where G is a graph without isolated vertices. Moreover, we give a descriptive characterization of block graphs G satisfying \(\gamma _{dR}(G)=3\beta (G)\) . Finally, we show that the decision problem associated with \(\gamma _{dR}(G)=3\beta (G)\) is \(CO-\mathcal {NP}\) -complete for bipartite graphs. PubDate: 2021-10-01

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Abstract: Let \(S_{\cos }^{*}\) denote the class of normalized analytic functions f such that \(\frac{zf^{\prime }(z)}{f(z)}\prec \cos (z)\) . For this class, we obtain structural formula, inclusion results, differential subordinations and some radii problems such as radius of convexity, radius for the class of Janowski starlike functions and radius for some other subclasses of starlike functions. PubDate: 2021-10-01

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Abstract: Based on the Schur complements, two upper bounds for the infinity norm of the inverse of doubly strictly diagonally dominant (DSDD) matrices are presented. As applications, an error bound for linear complementarity problems of DB-matrices and a lower bound for the smallest singular value of matrices are given. PubDate: 2021-10-01

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Abstract: Let f be a transcendental meromorphic function of hyper-order strictly less than 1. In this paper, we deal with the uniqueness problem on f sharing two values with its nth order differences \(\Delta ^n f \) . And this research extends earlier results by Chen and Yi (Result Math 63:557–565, 2013), Gao et al. (Anal Math 45:321–334, 2019) and Lü and Lü (Comput Methods Funct Theory 17:395–403, 2017). PubDate: 2021-10-01

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Abstract: In this paper, we study rings with the property that every cyclic module is almost-injective (CAI). It is shown that R is an Artinian serial ring with \(J(R)^2=0\) if and only if R is a right CAI-ring with the finitely generated right socle (or I-finite) if and only if every semisimple right R-module is almost injective, \(R_R\) is almost injective and has finitely generated right socle. Especially, R is a two-sided CAI-ring if and only if every (right and left) R-module is almost injective. From this, we have the decomposition of a CAI-ring via an SV-ring for which Loewy (R) \(\le \) 2 and an Artinian serial ring whose squared Jacobson radical vanishes. We also characterize a Noetherian right almost V-ring via the ring for which every semisimple right R-module is almost injective. PubDate: 2021-10-01

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Abstract: Let \(f : A \longrightarrow B\) be a ring homomorphism and let J be an ideal of B. In this article, we study the possible transfer of the properties of being a \(\phi \) -ring, a \(\phi \) -chained ring, and a \(\phi \) -pseudo-valuation ring to the amalgamated algebra \(A\bowtie ^{f}J\) . Our aim is to provide examples of new classes of commutative rings satisfying the aforementioned properties. PubDate: 2021-10-01

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Abstract: In this paper, we study a generalized convex vector equilibrium problem with cone and set constraints in real Banach spaces. We provide some basic characterizations on generalized convexity for the first- and second-order directional derivatives. We obtain Kuhn–Tucker second-order necessary and sufficient optimality conditions for efficiency to such problem under suitable assumptions on the generalized convexity of objective and constraint functions. As an application, we present Kuhn–Tucker second-order necessary and sufficient optimality conditions to a generalized convex vector variational inequality problem and a generalized convex vector optimization problem with constraints. Some examples are also given to demonstrate the main results of the paper. PubDate: 2021-10-01

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Abstract: Let p be an analytic function defined on the open unit disc \(\mathbb {D}\) with \(p(0)=1\) and \(0< \alpha \le 1\) . The conditions on complex valued functions C, D, and E are obtained for p to be subordinate to \(((1+z)/(1-z))^{\alpha }\) when \(C(z) z^{2}p''(z)+D(z)zp'(z) + E(z)p(z)=0\) . Sufficient conditions for confluent (Kummer) hypergeometric function and generalized and normalized Bessel function of the first kind of complex order to be subordinate to \(((1+z)/(1-z))^{\alpha }\) are obtained as applications. The conditions on \(\alpha \) and \(\beta \) are derived for p to be subordinate to \(((1+z)/(1-z))^{\alpha }\) when \(1+\beta zp'(z)/p^{n}(z)\) with \(n=1,2\) is subordinate to \(1+4z/3+2z^{2}/3=:\varphi _{CAR}(z)\) . Similar problems were investigated for \({{\,\mathrm{Re}\,}}p(z)>0\) when the function \(p(z)+\beta zp'(z)/p^{n}(z)\) with \(n=0,2\) is subordinate to \(\varphi _{CAR}(z)\) . The condition on \(\beta \) is determined for p to be subordinate to \(((1+z)/(1-z))^{\alpha }\) when \(p(z)+\beta zp'(z)/p^{n}(z)\) with \(n=0,1,2\) is subordinate to \(((1+z)/(1-z))^{\alpha }\) . PubDate: 2021-10-01