Authors:Mohammed M. Matar Pages: 959 - 973 Abstract: Abstract We are concerned with the existence of solutions of a class of fractional differential equations with anti-periodic and integral boundary conditions involving the Caputo fractional derivative with order \(\alpha \in (0,3]\) . We give three results based on Banach fixed-point theorem, and Schauder fixed-point theorems. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0332-4 Issue No:Vol. 40, No. 3 (2017)

Authors:A. Shidfar; Z. Darooghehgimofrad Pages: 1149 - 1158 Abstract: Abstract In this paper, a meshless numerical scheme for solving an inverse source problem is considered. The proposed scheme is based on approximating the solution employing the thin plate spline (TPS) radial basis function (RBF). Applying this radial basis function results in a badly ill-condition system of equations. The Tikhonov regularization method is employed for solving this system of equations. Determination of regularization parameter is based on generalized cross-validation (GCV) technique. Some numerical examples are presented to demonstrate the accuracy and ability of this method. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0358-7 Issue No:Vol. 40, No. 3 (2017)

Authors:Young Jae Sim; Oh Sang Kwon; Nak Eun Cho Pages: 1291 - 1306 Abstract: Abstract In the present paper, we derive a property of analytic functions \(p(z) = 1 + p_{n}z^{n} + \cdots \) with fixed initial coefficients in their series expansion, which satisfy the condition \( -\pi \beta /2 < \arg p(z_{1}) < \arg p(z) < \arg p(z_{2}) = \pi \alpha /2\) , for some \(z_{1}\) and \(z_{2}\) with \( z_{1} = z_{2} =r<1\) and for all z with \( z <r\) , where \(0<\alpha \le 2\) and \(0<\beta \le 2\) . Using this property, we obtain some sufficient conditions for normalized analytic functions \(f(z) = z + a_{n+1}z^{n+1} + \cdots \) by considering the fixed initial coefficients to satisfy \(-\pi \beta /2 < \arg \left\{ zf'(z)/f(z) - \gamma \right\} < \pi \alpha /2\) for all z in the unit disk \({\mathbb {U}}\) on the complex plane, where \(0 \le \alpha , \beta < 1\) , and \(\gamma =0\) or 1 / 2. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0369-4 Issue No:Vol. 40, No. 3 (2017)

Authors:Adolfo Ballester-Bolinches; Luis M. Ezquerro; A. A. Heliel; M. M. Al-Shomrani Pages: 1341 - 1351 Abstract: Abstract Subgroups \(A\) and \(B\) of a finite group are said to be mutually permutable (respectively, M-permutable and \({{\mathrm{sn}}}\) -permutable) if \(A\) permutes with every subgroup (respectively, every maximal subgroup and every subnormal subgroup) of \(B\) and viceversa. If every subgroup of \(A\) permutes with every subgroup of \(B\) , then the product is said to be totally permutable. These kinds of products have received much attention in the last twenty years. The aim of this paper is to analyse the behaviour of finite pairwise mutually permutable, mutually M-permutable, mutually \({{\mathrm{sn}}}\) -permutable and totally permutable products with respect to certain classes of groups including the supersoluble groups, widely supersoluble groups, and also the classes of \(PST\) -, \(PT\) - and \(T\) -groups. PubDate: 2017-07-01 DOI: 10.1007/s40840-015-0111-7 Issue No:Vol. 40, No. 3 (2017)

Authors:Jihong Zhao Abstract: Abstract In this paper, we study the three-dimensional dissipative fluid-dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the Navier–Stokes/Poisson–Nernst–Planck system. It is proved that the local smooth solution can be continued beyond the time T provided that the vorticity \(\omega \) satisfies $$\begin{aligned} \int _{0}^{T}\frac{\Vert \omega (\cdot ,t)\Vert _{\dot{B}^{-\alpha }_{\infty ,\infty }}^{\frac{2}{2-\alpha }}}{1+\ln \left( e+\Vert \omega (\cdot ,t)\Vert _{\dot{B}^{-\alpha }_{\infty ,\infty }}\right) }\mathrm{d}t<\infty \quad \text {for} \,\, 0<\alpha <2. \end{aligned}$$ Moreover, two regularity criteria for the marginal cases \(\alpha =0\) and \(\alpha =2\) are also established, respectively. PubDate: 2017-08-07 DOI: 10.1007/s40840-017-0537-1

Authors:Fengwei Li; Qingfang Ye; Juan Rada Abstract: Abstract The augmented Zagreb index (AZI index) of a graph \(G=(V,E)\) , which is a valuable predictive index in the study of the heat of formation in octanes and heptanes, is defined as $$\begin{aligned} \hbox {AZI}(G)=\sum _{uv\in E(G)}\left( \frac{d_{u}d_{v}}{d_{u}+d_{v}-2}\right) ^{3}{,} \end{aligned}$$ where \(d_{u}\) and \(d_{v}\) are the degrees of the terminal vertices u and v of edge uv, respectively. In this paper, we give the expressions for computing the augmented Zagreb indices of fluoranthene-type benzenoid systems, and we determine the extremal values of augmented Zagreb index in f-benzenoid systems with h hexagons. Especially, we give the extremal values of augmented Zagreb index in cata-catacondensed fluoranthene-type benzenoid systems with h hexagons. PubDate: 2017-08-06 DOI: 10.1007/s40840-017-0536-2

Authors:Ivy Carol B. Lomerio; Editha C. Jose Abstract: Abstract In this paper, we consider a time-dependent semilinear parabolic problem modeling the heat diffusion in a two-component composite. The domain has an \(\varepsilon \) -periodic interface, where the flux of the temperature is proportional to the jump of the temperature field by a factor of order \(\varepsilon ^\gamma \) . We determine the existence and uniqueness of the weak solution of the problem and use the periodic unfolding method to find the homogenization results. PubDate: 2017-08-05 DOI: 10.1007/s40840-017-0532-6

Authors:Hua Wang; Cai Wu; Junjie Huang Abstract: Abstract In this note, we investigate the existence of the Drazin inverse for the anti-triangular operator matrix \(M= \left( {\begin{matrix} A &{} B \\ C &{} 0 \end{matrix}}\right) \) with \(A^2=A\) and \( CAB=0\) , and the explicit representation of \(M^D\) is given in term of \(A, A^D, B,C \) and \((CB)^D\) . In addition, it is shown that \(\mathrm {ind} (M)\le 2 \ \mathrm {ind} (CB)+2\) , which is important to prove the existence and representation of the Drazin inverse for M. PubDate: 2017-08-02 DOI: 10.1007/s40840-017-0533-5

Authors:Zaihong Jiang; Mingxuan Zhu Abstract: Abstract This paper deals with the asymptotic behavior, regularity criterion and global existence for the generalized Navier–Stokes equations. Firstly, an upper bound for the difference between the solution of our equation and the generalized heat equation in \(L^2\) space is proved. We optimize the upper bound of decay for the solutions and obtain the algebraic lower bound by using Fourier splitting method. Then, a new scaling invariant regularity criterion on the fractional derivative is established. Finally, global existence is obtained provided that the initial data are small enough. PubDate: 2017-08-01 DOI: 10.1007/s40840-017-0531-7

Authors:M. Afkhami; S. Bahrami; K. Khashyarmanesh Abstract: Abstract Let \((P,\le )\) be a partially ordered set with a least element 0. The regular digraph of ideals of P, denoted by \(\overrightarrow{\Gamma }(P)\) , is a digraph whose vertex-set is the set of all nontrivial ideals of P and, for every two distinct vertices I and J, there is an arc from I to J whenever I contains a nonzero zero-divisor on J. Also, the undirected regular graph of ideals of P, denoted by \(\Gamma (P)\) , is a graph with all nontrivial ideals of P being the vertex-set, and for two distinct vertices I and J, I is adjacent to J if and only if I contains a nonzero zero-divisor on J or J contains a nonzero zero-divisor on I. In this paper, we study some basic properties of \(\overrightarrow{\Gamma }(P)\) . Also we completely characterize all posets P with planar regular graph. PubDate: 2017-07-31 DOI: 10.1007/s40840-017-0530-8

Authors:László Horváth; Đilda Pečarić; Josip Pečarić Abstract: Abstract The Jensen’s inequality plays a crucial role to obtain inequalities for divergences between probability distributions. In this paper, we introduce a new functional, based on the f-divergence functional, and then, we obtain some estimates for the new functional, the f-divergence and the Rényi divergence by applying a cyclic refinement of the Jensen’s inequality. Some inequalities for Rényi and Shannon entropies are obtained too. Zipf–Mandelbrot law is used to illustrate the results. PubDate: 2017-07-28 DOI: 10.1007/s40840-017-0526-4

Authors:Leilei Wei Abstract: Abstract In this paper, the numerical approximation of the distributed-order time-fractional reaction–diffusion equation is proposed and analyzed. Based on the finite difference method in time and local discontinuous Galerkin method in space, we develop a fully discrete scheme and prove that the scheme is unconditionally stable and convergent with order \(O\left( h^{k+\frac{1}{2}}+(\Delta t)^2+\Delta \alpha ^4\right) \) , where \(h,k,\Delta t\) and \(\Delta \alpha \) are the space-step size, piecewise polynomial degree, time-step size, step size in distributed-order variable, respectively. Numerical examples are presented to show the effectiveness and the accuracy of the numerical scheme. PubDate: 2017-07-27 DOI: 10.1007/s40840-017-0525-5

Authors:Hongbo Hua; Zhengke Miao Abstract: Abstract Classical topological indices, such as Zagreb indices ( \(M_{1}\) and \(M_2\) ) and the well-studied eccentric connectivity index ( \(\xi ^{c}\) ) directly or indirectly consider the total contribution of all edges in a graph. By considering the total degree sum of all non-adjacent vertex pairs in a graph, Ashrafi et al. (Discrete Appl Math 158:1571–1578, 2010) proposed two new Zagreb-type indices, namely the first Zagreb coindex ( \(\overline{M}_{1}\) ) and second Zagreb coindex ( \(\overline{M}_{2}\) ), respectively. Motivated by Ashrafi et al., we consider the total eccentricity sum of all non-adjacent vertex pairs, which we call the eccentric connectivity coindex ( \(\overline{\xi }^{c}\) ), of a connected graph. In this paper, we study the extremal problems of \(\overline{\xi }^{c}\) for connected graphs of given order, connected graphs of given order and size, and the trees, unicyclic graphs, bipartite graphs containing cycles and triangle-free graphs of given order, respectively. Additionally, we establish various lower bounds for \(\overline{\xi }^{c}\) in terms of several other graph parameters. PubDate: 2017-07-27 DOI: 10.1007/s40840-017-0528-2

Authors:Leyla Bugay; Melek Yağcı; Hayrullah Ayık Abstract: Abstract For \(n\in \mathbb {N}\) , let \(O_{n}\) be the semigroup of all order-preserving transformations on the finite chain \(X_{n}=\{1,\ldots ,n\}\) , under its natural order. For any non-empty subset A of \(X_{n}\) , let \(O_{n}(A)\) and \(O_{n}^+(A)\) be the subsemigroups of all order-preserving and A-decreasing, and of all order-preserving and A-increasing transformations on \(X_{n}\) , respectively. In this paper we obtain formulae for the number of elements and for the number of idempotents in \(O_{n}(A)\) . Moreover, we show that \(O_{n}(A)\) contains a zero element if and only if \(1\in A\) , and then we obtain the number of nilpotents in \(O_{n}(A)\) when \(1\in A\) . PubDate: 2017-07-26 DOI: 10.1007/s40840-017-0529-1

Authors:Shiqi Xing; Fanggui Wang Abstract: Abstract Let R be a commutative ring. The Gorenstein super finitely presented dimension of R is defined as \(G\hbox {-}\text{ s.gl. }\dim (R)=\sup \{\text{ Gpd }_{R}{M}\, \,M\) is a super finitely presented R-module}. In this paper, we give a series of characterizations of the ring with \(G\text{- }\text{ s.gl }.\dim (R)=0\) . We show that R is a ring with \(G\text{- }\text{ s.gl }.\dim (R)=0\) if and only if R is self-weak injective and R is a generalized coherent ring (i.e., R is a GFC-ring), where an R-module M is called weak injective if \(\mathrm{Ext}_{R}^{1}(N,M)=0\) for every super finitely presented R-module N, and R is called a generalized coherent ring if \(M^{*}\) is super finitely presented for any super finitely presented R-module M. Further, comparing with FGF-question, we give an example to show that a ring R is not necessarily a QF-ring if every (super) finitely presented R-module can embedded in a free R-module. PubDate: 2017-07-25 DOI: 10.1007/s40840-017-0527-3

Authors:Qianqian Cui; Qiang Zhang; Zhipeng Qiu; Xiaomin Yang Abstract: Abstract This paper focuses on the global stability of an epidemic model with vaccination, treatment and isolation. The basic reproduction number \({\mathcal {R}}_0\) is derived. By constructing suitable Lyapunov functions, sufficient conditions for the global asymptotic stability of equilibria are obtained. Numerical simulations are performed to verify and complement the theoretical results. Furthermore, we consider the uncertainty and sensitivity analysis of the basic reproduction number \({\mathcal {R}}_0\) . The results show that the transmission rate, the fraction of infected receives treatment, vaccination rate, the isolation rate are crucial to prevent the spread of infectious diseases. These suggest that public health workers design the control strategies of disease should consider the influence of vaccination, treatment and isolation. PubDate: 2017-07-11 DOI: 10.1007/s40840-017-0519-3

Authors:Zu Yao Teoh; Wen Chean Teh Abstract: Abstract Carlson introduced the notion of a Ramsey space as a generalization to the Ellentuck space. When a Ramsey space is induced by an algebra, Carlson suggested a study of its purely combinatorial version now called Ramsey algebra. Some basic results for homogeneous algebras have been obtained. In this paper, we introduce the notion of a Ramsey algebra for heterogeneous algebras and derive some basic results. Then, we study the Ramsey-algebraic properties of vector spaces. PubDate: 2017-07-10 DOI: 10.1007/s40840-017-0524-6

Authors:Wei Jin Abstract: Abstract It was previously shown that there is a bijection between the family of locally disconnected 2-geodesic transitive graphs \(\Gamma \) and a certain family of partial linear spaces \({\mathcal {S}}(\Gamma )\) . In this paper, we first determine a relationship between the 2-geodesic transitivity of \(\Gamma \) and the local s-arc transitivity of the incidence graph of \({\mathcal {S}}(\Gamma )\) . Next, we give a reduction theorem for the family of locally disconnected s-geodesic transitive graphs. PubDate: 2017-07-07 DOI: 10.1007/s40840-017-0523-7

Authors:Gang Li; K. P. Shum Abstract: Abstract We first study the structure of a special generalized regular semigroup, namely the B-semiabundant semigroup which can be expressed as the join of the pseudo-varieties of finite groups and finite aperiodic groups. In the literature, the weakly B-semiabundant semigroups have recently been thoughtfully investigated and considered by Wang. One easily observes that the class of good B-semiabundant semigroups is a special class of semigroups embraces all abundant (and hence regular) semigroups. In particular, a super B-quasi-Ehresmann semigroup is an analogy of an orthodox semigroup within the class of B-semiabundant semigroups. Thus, the class of super B-quasi-Ehresmann semigroups is obviously a subclass of the class of good B-quasi-Ehresmann semigroups which contains all orthodox semigroups. Thus, the super B-quasi-Ehresmann semigroup behaves similarly as the Clifford subsemigroups within the class of regular semigroups. Consequently, a super B-quasi-Ehresmann semigroup is now recognized as an important generalized regular semigroup. Our aim in this paper is to describe the properties and intrinsic structure of a super B-quasi-Ehresmann semigroup whose band of projections is right regular, right normal, left semiregular, left seminormal, regular, left quasinormal or normal, respectively. Hence, our representation theorem of the super B-quasi-Ehresmann semigroups improves, strengthens and generalizes the well-known “standard representation theorem of an orthodox semigroup” established by He et al. (Commun. Algebra 33:745–761, 2005). Finally, a general representation theorem in the category of Ehresmann semigroups is given. PubDate: 2017-07-04 DOI: 10.1007/s40840-017-0521-9