Authors:Mohammed M. Matar Pages: 959 - 973 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:Kwok-Pun Ho Pages: 995 - 1010 Abstract: We establish the boundedness of vector-valued intrinsic square function on Morrey and block spaces with variable exponents. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0330-6 Issue No:Vol. 40, No. 3 (2017)

Authors:Hong Xiang; Yong-Lu Tang; Hai-Feng Huo Pages: 1011 - 1023 Abstract: In this paper, a classical of virus dynamics model with intracellular delay and humoral immunity is introduced. By using suitable Lyapunov functionals and the Lasalle invariant principle, the global stability of the equilibria is proved. Numerical simulations are presented to illustrate our results. The effect of delay and humoral immunity is also discussed. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0326-2 Issue No:Vol. 40, No. 3 (2017)

Authors:J. M. Casas; E. Khmaladze; N. Pacheco Rego Pages: 1035 - 1054 Abstract: Non-abelian tensor product of Hom–Lie algebras is constructed and studied. This tensor product is used to describe universal ( \(\alpha \) )-central extensions of Hom–Lie algebras and to establish a relation between cyclic and Milnor cyclic homologies of Hom-associative algebras satisfying certain additional condition. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0352-0 Issue No:Vol. 40, No. 3 (2017)

Authors:Qaiser Mushtaq; Abdul Razaq Pages: 1115 - 1133 Abstract: Each conjugacy class of actions of \(PGL\left( {2,{\mathbb {Z}}} \right) \) on the projective line over a finite field \(F_q \) denoted by \(PL\left( {F_q } \right) \) , can be represented by a coset diagram \(D\left( {\theta ,q} \right) \) , where \(\theta \in F_q \) and q is a prime power. The coset diagrams are composed of fragments, and the fragments are further composed of two or more circuits at a certain common point. Professor Graham Higman raised a question: for what values of q and \(\theta \) , can a fragment \(\gamma \) be found in \(D\left( {\theta ,q} \right) '\) Mushtaq in 1983 found that the condition for the existence of a fragment in \(D\left( {\theta ,q} \right) \) is a polynomial f in \({\mathbb {Z}}\left[ z \right] \) . In this paper, we answer the question: how many polynomials are obtained from the fragments, composed by joining the circuits \(\left( {n_1 ,n_2 } \right) \) and \(\left( {m_1 ,m_2 } \right) \) , where \(n_2 <n_1 <m_2 <m_1\) , at all points of connection. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0357-8 Issue No:Vol. 40, No. 3 (2017)

Authors:José Antonio Cuenca Mira Pages: 1135 - 1148 Abstract: This paper deals with pairs of nonzero idempotents e and f of a third-power associative absolute valued algebra A satisfying \((ef)e= e(fe)\) and \((fe)f=f(ef)\) (pairwise flexible idempotents), and the role that they play on the structure of A. We show that if g is a nonzero idempotent of A such that the nonzero idempotents commuting with g are pairwise flexible, then the subalgebra that they generate \(B_g\) is isometrically isomorphic to \({\mathbb {R}}\) , \(\mathop {{\mathbb {C}}}\limits ^{\star }\) , \(\mathop {{\mathbb {H}}}\limits ^{\star }\) , or \(\mathop {{\mathbb {O}}}\limits ^{\star }\) . Our main theorem proves the equivalence of the following assertions: (i) for every two different nonzero idempotents e and f, the nonzero idempotents of A that commute with \((e-f)^2\) are pairwise flexible; (ii) each pair of nonzero idempotents of A generates a finite-dimensional subalgebra; and (iii) either A is isometrically isomorphic to \({\mathbb {R}}\) , \({\mathbb {C}}\) , \({\mathbb {H}}\) , \({\mathbb {O}}\) , \(\mathop {{\mathbb {C}}}\limits ^{\star }\) , \(\mathop {{\mathbb {H}}}\limits ^{\star }\) or \(\mathop {{\mathbb {O}}}\limits ^{\star }\) , or A contains a subalgebra B, which contains all idempotents of A and is isometrically isomorphic to the division absolute valued algebra \({\mathbb {P}}\) of the Okubo pseudo-octonions. More consequences on the structure of A related with the presence of pairwise flexible idempotents are given, among them several generalizations of some well-known theorems. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0351-1 Issue No:Vol. 40, No. 3 (2017)

Authors:A. Shidfar; Z. Darooghehgimofrad Pages: 1149 - 1158 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:Rakesh Batra; Sachin Vashistha Pages: 1159 - 1174 Abstract: Fixed point results for generalized weak contractions under w-distance are proved using discontinuous control functions that are more relaxed than functions used in related work for metric spaces. Later, we apply our theory to coupled coincidence point problems and existence of solution of Fredholm type integral equation. We present examples to justify our claims. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0347-x Issue No:Vol. 40, No. 3 (2017)

Authors:Yizhuo Wang; Zhenlai Han; Shurong Sun; Ping Zhao Pages: 1187 - 1217 Abstract: We establish some oscillation criteria for the third-order Emden–Fowler neutral delay dynamic equations of the form: $$\begin{aligned} (a(t)(x(t)+r(t)x(\tau (t)))^{\Delta \Delta })^\Delta +p(t)x^\gamma (\delta (t))=0 \end{aligned}$$ on a time scale \(\mathbb {T}\) , where \(\gamma >0\) is a quotient of odd positive integers, and a and p are real-valued positive rd-continuous functions defined on \(\mathbb {T}\) . Due to the different values of \(\gamma \) , we give not only the oscillation criteria for superlinear neutral delay dynamic equations, but also the oscillation criteria for sublinear neutral delay dynamic equations based on the Hille and Nehari-type oscillation criteria. Our results extend and improve some known results in the literature and are new even for the corresponding third-order differential equations and difference equations as our special cases. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0354-y Issue No:Vol. 40, No. 3 (2017)

Authors:Hossain Chizari; Farzad Ismail Pages: 1231 - 1264 Abstract: This paper presents an analytical and numerical approach in studying accuracy deterioration of residual distribution and cell-vertex finite volume methods on triangular grids. Results herein demonstrate that both methods preserve the order-of-accuracy reasonably well for uniformly skewed triangular grids and the \(L_2\) errors of both second-order accurate methods behave similarly with values of the same magnitude. On the other hand, the first-order finite volume method has an \(L_2\) error of about an order of magnitude higher than its residual distribution counterpart. Both first-order methods are unable to preserve the order-of-accuracy for high-frequency data when the grids are highly skewed although the residual distribution approach has a slightly better performance. Both second-order methods perform quite decently for high-frequency data on uniformly skewed grids. However, the order-of-accuracy of finite volume methods excessively deteriorate when the grids are skewed non-uniformly unlike the residual distribution methods which preserve the order-of-accuracy. PubDate: 2017-07-01 DOI: 10.1007/s40840-015-0292-0 Issue No:Vol. 40, No. 3 (2017)

Authors:Gek Ling Chia; Ta Sheng Tan Pages: 1265 - 1275 Abstract: In this paper, we are interested in the brush number of a graph—a concept introduced by McKeil, Messinger, Nowakowski and Pralat. Our main aim in this paper is to study the brush number of the Cartesian product of a tree with a path, and a tree with a cycle. Based on an optimal cleaning process of a tree, we describe cleaning processes that give upper bounds to the brush number of \(T\times P_n\) and \(T\times C_n\) . We also show that these bounds are tight if T is a star, a double star and some generalisation of a star. PubDate: 2017-07-01 DOI: 10.1007/s40840-016-0337-z Issue No:Vol. 40, No. 3 (2017)

Authors:Young Jae Sim; Oh Sang Kwon; Nak Eun Cho Pages: 1291 - 1306 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:M. De la Sen Pages: 1321 - 1340 Abstract: This paper investigates some properties of boundedness and convergence of distances of \(p\) - cyclic \(C\) -quasi contractions and \(C\) -contractions in probabilistic complete metric spaces and uniformly convex Banach spaces as well as the existence and uniqueness of fixed points and best proximity points. PubDate: 2017-07-01 DOI: 10.1007/s40840-015-0112-6 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: 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:Qingping Zeng; Huaijie Zhong Pages: 1363 - 1376 Abstract: For nonnegative integers \(n\) and \(k\) , we introduce in this paper a new class of \((n,k)\) -quasi- \(*\) -paranormal operators satisfying $$\begin{aligned} T^{1+n}(T^{k}x) ^{1/(1+n)} T^{k}x ^{n/(1+n)} \ge T^*(T^{k}x) \text { for all } x \in H. \end{aligned}$$ This class includes the class of \(n\) - \(*\) -paranormal operators and the class of \((1,k)\) -quasi- \(*\) -paranormal operators contains the class of \(k\) -quasi- \(*\) -class \(A\) operators. We study the basic properties of \((n,k)\) -quasi- \(*\) -paranormal operators, like relations of this new class of operators with other classes known in the literature, their matrix representation, and properties of their spectra. PubDate: 2017-07-01 DOI: 10.1007/s40840-015-0119-z Issue No:Vol. 40, No. 3 (2017)

Authors:Qianqian Cui; Qiang Zhang; Zhipeng Qiu; Xiaomin Yang 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: 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: 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: 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