Abstract: Abstract It is shown that two Levi–Tanaka and infinitesimal CR automorphism algebras, associated with a totally nondegenerate model of CR dimension one are isomorphic. As a result, the model surfaces are maximally homogeneous and standard. This gives an affirmative answer in CR dimension one to a certain question formulated by Beloshapka. PubDate: 2019-10-14

Abstract: Abstract Let R be a standard graded algebra over an infinite field \(\mathbb {K}\) and M a finitely generated \({\mathbb Z}\) -graded R-module. Let \(I_1,\ldots I_m\) be graded ideals of R. The functions \(r(M/I_1^{a_1}\ldots I_m^{a_m}M)\) and \(r(I_1^{a_1}\ldots I_m^{a_m}M)\) are investigated and their asymptotical behaviours are given. Here, \(r(\bullet )\) stands for the reduction number of a finitely generated graded R-module \(\bullet \) . PubDate: 2019-10-14

Abstract: Abstract An independent double Roman dominating function (IDRDF) on a graph \(G=(V,E)\) is a function \(f{:}V(G)\rightarrow \{0,1,2,3\}\) having the property that if \(f(v)=0\) , then the vertex v has at least two neighbors assigned 2 under f or one neighbor w assigned 3 under f, and if \(f(v)=1\) , then there exists \(w\in N(v)\) with \(f(w)\ge 2\) , such that the set of vertices with positive weight is independent. The weight of an IDRDF is the value \(\sum _{u\in V}f(u)\) . The independent double Roman domination number \(i_\mathrm{dR}(G)\) of a graph G is the minimum weight of an IDRDF on G. We continue the study of the independent double Roman domination and show its relationships to both independent domination number (IDN) and independent Roman \(\{2\}\) -domination number (IR2DN). We present several sharp bounds on the IDRDN of a graph G in terms of the order of G, maximum degree and the minimum size of edge cover. Finally, we show that, any ordered pair (a, b) is realizable as the IDN and IDRDN of some non-trivial tree if and only if \(2a + 1 \le b \le 3a\) . PubDate: 2019-10-11

Abstract: Abstract This paper concerns with a class of fractional integro-differential equations in the space of continuous functions which defined on interval \( \left[ 0,a\right] \) and take values in a Banach space E. Using a generalized Darbo fixed-point theorem associated with measure of noncompactness, the existence of solutions has been established. Also an example which shows that the main result is applicable is given. PubDate: 2019-10-11

Abstract: Abstract In this paper, we give some sufficient conditions for the algebraic dependence of three meromorphic mappings from Kähler manifold into \({\mathbb {P}}^n({\mathbb {C}})\) sharing hyperplanes in subgeneral position, where all zeros with multiplicities more than certain values do not need to be counted. PubDate: 2019-10-11

Abstract: This paper is concerned with bistable wave fronts in a class of nonlocal reaction diffusion model for a single species with stage structure and distributed maturation delay. By choosing the strong and weak kernel functions to transform system with delays to a two- or three-dimensional system without any delays, the existence of traveling wave fronts is established by abstract results. Then we prove the asymptotic stability (up to translation) of bistable wave fronts and the uniqueness of wave speeds by spectral analysis and upper and lower solution technique, respectively. At last, we apply these results to a single species model with special nonlinearity. PubDate: 2019-10-08

Abstract: Abstract Let \(P_t(\mu )\) be the matrix power mean of a compactly supported probability measure \(\mu \) on the set of positive definite matrices \(\mathbb {P}_n\) . We present an inequality involving the matrix power mean \(P_t(\mu )\) and its adjoint \(P_{-t}(\mu )\) . Our result gives in particular a comparison of the quasi arithmetic mean \(\sharp _{\omega ,t}\) and its adjoint \(\sharp _{\omega ,-t}\) . PubDate: 2019-10-08

Abstract: Abstract This paper introduces a noninstantaneous impulsive Lasota–Wazewska model with pure delay. We establish existence and uniqueness of positive almost periodic solutions and show any solution converges exponentially to this positive almost periodic solution. An example is given to illustrate our theoretical results. PubDate: 2019-10-08

Abstract: Abstract In this paper, by using the notion of convolution types we introduce symmetric and non-symmetric convolution type \(\hbox {C}^*\) -algebras. It is shown that any (exact) convolution type induces a (an exact) functor on the category of \(\hbox {C}^*\) -algebras. In particular, any group induces a convolution type and a functor on the category of \(\hbox {C}^*\) -algebras. It is also shown that discrete crossed product of \(\hbox {C}^*\) -algebras and discrete inverse semigroup \(\hbox {C}^*\) -algebras can be considered as convolution type \(\hbox {C}^*\) -algebras. PubDate: 2019-10-08

Abstract: Abstract In this paper, we use the Gauss–Jacobi quadrature formula to get an approximate solution for a finite part singular integral equation. The zeros of Jacobi polynomials and Jacobi functions of the second kind are used to construct a square system of algebraic equations which yield an interpolating function for the regular part of the solution of the singular integral equation. In a special case, another approach consists in converting the finite part singular integral equation to a Fredholm integral equation of the second kind using the analytical solution of a simple finite part singular integral equation. To simplify the calculation of kernel and right-hand side of the obtained Fredholm equation, we use the new polynomials \(J_n(x)\) , which admit a recurrence relation. The equivalent form of the integral equation in the last case is used to investigate the error bound of the approximated solution. PubDate: 2019-09-23

Abstract: Abstract Abaffy, Broyden and Spediacto (ABS) introduced a class of the so-called ABS methods to solve systems of linear equations. The ABS approach was specialized to solve linear Diophantine systems by Esmaeili, Mahdavi-Amiri and Spedicato. The method was extended to systems of certain linear inequalities to provide all solutions. Here, we mainly focus on the theoretical research into rank reduction processes for solving linear Diophantine systems and computing integer factorizations. Basic integer ABS algorithm, integer extended ABS (IEABS) algorithm, rank one perturbed problem, the generalized Rosser’s approach (GRA), the extended integer rank reduction process, the integer Wedderburn rank reduction formula and the associated integer biconjugation process are studied. We present an integrated integer rank reduction process, develop various integer factorizations and show their use in solving Diophantine equations. PubDate: 2019-09-16

Abstract: Abstract For a graph \(G = (V, E)\) , a double Roman dominating function (DRDF) on G is a function \(f : V \rightarrow \{0, 1, 2, 3\}\) having the property that if \(f(v) = 0\) , then vertex v has at least two neighbors assigned 2 under f or one neighbor w with \(f(w)=3\) , and if \(f(v)=1\) , then vertex v has at least one neighbor w with \(f(w)\ge 2\) . A DRDF f is called an independent double Roman dominating function (IDRDF) if the set of vertices with positive weight is independent. The weight of an IDRDF is the sum \(f (V) =\sum _{v\in V} f (v)\) . The independent double Roman domination number \(i_{dR}(G)\) is the minimum weight of an IDRDF on G. In this paper, we initiate the study of independent double Roman domination. We first show that the decision problem associated with \(i_{dR}(G)\) is NP-complete for bipartite graphs and then we present some sharp bounds on the independent double Roman domination number. PubDate: 2019-09-04

Abstract: Abstract Assume that G is a finite non-Dedekind p-group, where p is an odd prime. Passman introduced the following concept: we say that \(H_{1}<H_{2}<\cdots <H_{k}\) is a chain of nonnormal subgroups of G if each \(H_{i}\ntrianglelefteq G\) and if \( H_i:H_{i-1} =p\) for \(i=2,3,\dots , k\) . k is called the length of the chain. \(\mathrm{chn}(G)\) denotes the maximum of the lengths of the chains of nonnormal subgroups of G. In this paper, finite p-groups G with \(\mathrm{chn}(G)\le 2\) are completely classified up to isomorphism. PubDate: 2019-09-04

Abstract: Abstract Let R be a commutative Noetherian ring and M, N be two finitely generated R-modules. In this note, we prove the cofiniteness of generalized local cohomology modules \(H^{i}_{I}(M,N)\) with respect to I for all \(i<t\) and the finiteness of \((0:_{H^{t}_{I}(M,N)}I)\) provided \(H^{i}_{I}(M,N)_{\mathfrak {p}}\) is finitely generated for all \(i<t\) and all \(\mathfrak {p}\in \bigcup _{j<t}{{\,\mathrm{Supp}\,}}_{R}(H^{j}_{I}(M,N))\) with \(\dim R/\mathfrak {p}>1\) , where t is a given non-negative integer. This extends the results of Bahmanpour and Naghipour (J Algebra 321:1997–2011, 2009), Bahmanpour et al. (Commun Algebra 41:2799–2814, 2013), and Cuong et al. (Kyoto J Math 55(1):169–185, 2015). This also provides a partially affirmative answer to Hartshorne’s question in Hartshorne (Invent Math 9:145–164, 1970) for the case of generalized local cohomology modules. PubDate: 2019-08-29

Abstract: Abstract Let k be a positive integer. A k-tuple (total) dominating set in a graph G is a subset S of its vertices such that any vertex v in G has at least k vertices inside S among its neighbors and v itself (resp. among its neighbors only). The minimum size of a k-tuple (total) dominating set for G is called the k-tuple (total) domination number of G. It is shown in this article that the k-tuple total domination number of a connected \((k+1)\) -regular graph with n vertices is at most \(\frac{k^2+k-1}{k^2+k}n\) , unless it is the incident graph of a finite projective plane of order k, where this number is \(\frac{k^2+k}{k^2+k+1}n\) . We also show that the k-tuple domination number of a connected k-regular graph with n vertices is at most \(\frac{k^2-1}{k^2}n\) , unless it is a Moore graph of diameter 2, where this number is \(\frac{k^2}{k^2+1}n\) . PubDate: 2019-08-27

Abstract: Abstract Let \({\mathcal {R}}\) be a 2-torsion-free commutative ring with unity, X a locally finite pre-ordered set with a finite number of connected components and \(I(X,{\mathcal {R}})\) the incidence algebra of X over \({\mathcal {R}}\) . In this paper, we give a sufficient and necessary condition for a commuting map on \(I(X,{\mathcal {R}})\) to be proper. PubDate: 2019-08-26

Abstract: Abstract In this letter, we propose a continuous-time dynamics for social network that represents patterns of both amity and enmity through directed signed graphs. The introduction of discrepancies between true and perceived sentiments gives rise to a non-autonomous system and distinguishes itself from the prior models. We show that for almost all initial configurations, the system will evolve into at most four factions. Under some mild assumptions on the initial conditions, structural balance with at most two factions can be achieved, which extends the previous results for symmetric or normal initial configurations without considering the effect of perceived sentiment. PubDate: 2019-08-26

Abstract: Abstract Let G be a finite group and H a subgroup of G. We say that H: is generalized S-quasinormal in G if \(H=\left\langle A,B\right\rangle \) for some modular subgroup A and S-quasinormal subgroup B of G; m-S-complemented in G if there are a generalized S-quasinormal subgroup S and a subgroup T of G such that \(G=HT\) and \(H\cap T\le S\le H\) . In this paper, we study finite groups with given systems of m-S-complemented subgroups. In particular, we prove that if \({\mathfrak {F}}\) is a saturated formation containing all supersoluble groups and E is a normal subgroup of a finite group G such that \(G/E\in {\mathfrak {F}}\) and for every non-cyclic Sylow subgroup P of E every maximal subgroup of P not having a nilpotent supplement in G is m-S-complemented in G, then \( G\in {\mathfrak {F}}\) . PubDate: 2019-08-24