Abstract: In this paper, we study \((1+\lambda u)\) -constacyclic codes of length \(2^k\) over the ring \(\mathrm {R}={\mathbb {F}}_2+u{\mathbb {F}}_2+v{\mathbb {F}}_2+uv{\mathbb {F}}_2\) , where \(u^2=v^2=0,\ uv=vu\) , k is a positive integer and \(\lambda \) is a unit in \(\mathrm {R}\) . We classify all \((1+\lambda u)\) -constacyclic codes of length \(2^k\) over \(\mathrm {R}\) . We also completely classify the structure of \((1+\lambda u)\) -constacyclic codes of length \(2^k\) over \(\mathrm {R}\) that are contained in their annihilators as well as equal to their annihilators. We enumerate these codes and present mass formulas for them. Some optimal codes are obtained as the Gray images of these codes. In addition, we also study the structure of 1-generator generalized quasi-cyclic codes over the ring \(\mathrm {R}\) . A minimal spanning set for these codes is determined. A BCH-type bound on the minimum distance of these codes is also presented. PubDate: 2019-03-20
Abstract: Let \(\mathcal {X}\) , \(\mathcal {U}\) and \(\mathcal {Z}\) be classes of left R-modules, \(\mathcal {W}\) be a class of right R-modules and \(\mathcal {X}\subseteq \mathcal {U}\) . In this paper, we investigate the relationship between \(\mathcal {Z}\) -proper (resp. \(\mathcal {Z}\) -coproper, \(\mathcal {W}\) -pure) \(\mathcal {U}\) -(co)resolutions and \(\mathcal {Z}\) -proper (resp. \(\mathcal {Z}\) -coproper, \(\mathcal {W}\) -pure) \(\mathcal {X}\) -(co)resolutions. As applications, we give an affirmative answer to the stability question on Gorenstein classes of modules, which unify the corresponding results possessed by some known Gorenstein classes of modules. PubDate: 2019-03-18
Abstract: In this paper, we consider the asymptotic stability of the solutions near a constant equilibrium state to the Cauchy problem for the compressible full Hall-MHD equations in \(\mathbb {R}^3\) . We employ the energy estimate and introduce the negative Sobolev and Besov spaces to get the global existence and decay rates of the solution under the assumption that the \(H^3\) norm of the initial perturbation is small. As an immediate byproduct, the \(L^p-L^2\) \((1\leqslant p\leqslant 2)\) type of the decay rates follows without requiring the smallness for \(L^p\) norm of initial data. PubDate: 2019-03-14
Abstract: In this work, we consider a one-dimensional porous thermoelastic system with memory effects. We prove a general decay result, for which exponential and polynomial decay results are special cases, depending only on the kernel of the memory effects. Our result is established irrespective of the wave speeds of the system. The result obtained is new and improves previous results in the literature. PubDate: 2019-03-14
Abstract: The present paper deals with various recurrence relations, generating functions and series expansion formulas for two families of orthogonal polynomials in two variables, given Laguerre–Laguerre Koornwinder polynomials and Laguerre–Jacobi Koornwinder polynomials in the limit cases. Several families of bilinear and bilateral generating functions are derived. Furthermore, some special cases of the results presented in this study are indicated. PubDate: 2019-03-14
Abstract: In this paper, we consider the boundary value problem for the one-dimensional Dirac system with spectral parameter in the boundary condition. We completely study the oscillatory properties of components of the eigenvector functions of this problem. PubDate: 2019-03-12
Abstract: This paper considers properties of the spectrum of q-Sturm–Liouville operator derived from the q-Sturm–Liouville expression $$\begin{aligned} Ly:=-\frac{1}{q}D_{q^{-1}}\left( p(x)D_{q}y(x)\right) +r\left( x\right) y(x),\quad 0<x<a\le \infty . \end{aligned}$$ We prove that the regular symmetric q-Sturm–Liouville operator is semi-bounded from below. Using splittings technique, we will give some conditions for the self-adjoint operator associated with the singular q-Sturm–Liouville expression to have a discrete spectrum. We also investigate the continuous spectrum of this operator. PubDate: 2019-03-12
Abstract: This paper focuses on the multidimensional spherically symmetric full compressible Euler equations and constructs rigorously a family of global self-similar bounded weak solutions for all positive time to its initial value problem with constant initial data. The main approach is to reduce the full compressible Euler equations to an autonomous system of ordinary differential equations under the spherically symmetric and self-similar assumptions. We establish the detailed structures of solutions as well as their existence by analyzing carefully the properties of the integral curves of the autonomous ODE system. PubDate: 2019-03-08
Abstract: We obtain a result on Ulam stability and on the best Ulam constant for the linear difference equation \(x_{n+2}=ax_{n+1}+bx_n,\) where \(\mathbb {K}\) is one of the fields \(\mathbb {R}\) or \(\mathbb {C},\) \(a,b \in \mathbb {K}\) and \((x_n)_{n\ge 0}\) is a sequence in a Banach space X over the field \(\mathbb {K}.\) In this way, we improve and complement some recent results on Ulam stability of the second-order linear difference equation with constant coefficients. PubDate: 2019-02-22
Abstract: The 2-periodic function, \(W^*\in C^2({\mathbb {R}})\) is constructed in such a way that the sum \(\sum _{k=1}^n(-1)^{k+1}f(k)\) can be efficiently estimated for any \(n\in {\mathbb {N}}\cup \{\infty \} \) and for every \(f\in C^4[1,\infty )\) having \(\int _1^{\infty }\big f^{(4)}(x)\big \,\mathrm {d}\,x<\infty \) . PubDate: 2019-02-21
Abstract: We present a survey of various variants of fixed point results for single- and multivalued mappings, under conditions of the type first used by Pata (J Fixed Point Theory Appl 10:299–305, 2011). A number of examples are given, showing the effectiveness of these results. Some recent misinterpretations of the use of Pata-type conditions are commented. PubDate: 2019-02-19
Abstract: An approximation of statistical moments of solutions to exterior Dirichlet and Neumann problems with random boundary surfaces is investigated. A rigorous shape calculus approach has been used to approximate these statistical moments by those of the corresponding shape derivatives, which are computed by boundary integral equation methods. Examples illustrate our theoretical results. PubDate: 2019-02-18
Abstract: We prove that the Green function of the generator of symmetric unimodal Lévy process with the weak lower scaling order bigger than one and the Green functions of its gradient perturbations are comparable for bounded \(C^{1,1}\) subsets of the real line if the drift function is from an appropriate Kato class. PubDate: 2019-02-18
Abstract: This article shows the existence of weak solutions of a resonant problem for a fractional p-Laplacian equation in a bounded domain in \({\mathbb {R}}^N\) . Our arguments are based on the Minimum principle, saddle point theorem and rely on a generalization of the Landesman–Lazer-type condition. PubDate: 2019-02-18
Abstract: Let V be a sums of independent nonnegative integer-valued random variables and \(h_z\) be a call function defined by \(h_{z}(v)=(v-z)^+\) for \(v\ge 0, z \ge 0\) where \((v-z)^+=\max \{v-z,0\}\) . In this paper, we give bounds of Poisson approximation for \({E}[h_{z}(V)]\) . These bounds improve the results of Jiao and Karoui (Finance Stoch 13(2):151–180, 2009). The technique used is Stein–Chen method with the zero bias transformation. One example of applications for a call function in finance is the standard collateralized debt obligation (CDO) tranche pricing. The CDO is a security backed by a diversified pool of debt obligation such as bounds, loans and credit default swaps. PubDate: 2019-02-13
Abstract: Let \(I\subset K[x_1,\ldots ,x_n]\) be a squarefree monomial ideal generated in one degree. Let \(G_I\) be the graph whose nodes are the generators of I, and two vertices \(u_i\) and \(u_{ j}\) are adjacent if there exist variables x, y such that \(xu_i = yu_j\) . We show that if I is generated in degree \(n-2\) , then the following are equivalent: \(G_I\) is a connected graph; I has a \((n-2)\) -linear resolution; I has linear quotients; I is a variable-decomposable ideal. We also prove that if I has linear relations and \(\overline{G_I}\) is chordal, then I has linear quotients. PubDate: 2019-02-07
Abstract: A doubleRoman dominating function of a digraph D is a function \(f:V\longrightarrow \{0,1,2,3\}\) such that every vertex u for which \(f(u)=0\) has an in-neighbor v for which \(f(v)=3\) or at least two in-neighbors assigned 2 under f, while if \(f(u)=1\) , then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value \(f(V)=\sum _{u\in V}f(u)\) . The minimum weight of a double Roman dominating function of a digraph D is called the double Roman domination number of D, denoted by \(\gamma _{dR}\left( D\right) \) . This paper gives a descriptive characterization for some classes of digraphs satisfying \(\gamma _{dR}(D)=2\left( n-\Delta ^{+}(D)\right) +1\) . Also, a descriptive characterization for digraphs D of order \(n\ge 4\) for which \(\gamma _{dR}(D)+\gamma _{dR}({\overline{D}})=2n+3\) holds where \({\overline{D}}\) is the complement of D. PubDate: 2019-02-05
Abstract: We calculate Fréchet derivatives of the mapping \(a\mapsto f(a)\) , where a is a member of a complex unital Banach algebra and f is a complex analytic function in a neighborhood of the spectrum of a. Thus, the connection between the Fréchet derivative and the analytic functional calculus is established. PubDate: 2019-01-30
Abstract: In this paper, we characterize the graded post-Lie algebra structures and a class of shifting post-Lie algebra structures on the Witt algebra. As an application, the homogeneous Rota–Baxter operators and a class of non-homogeneous Rota–Baxter operators of weight 1 on the Witt algebra are studied. PubDate: 2019-01-29
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