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

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

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

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

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

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

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

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

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

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

Abstract: We establish the boundedness of vector-valued intrinsic square function on Morrey and block spaces with variable exponents. PubDate: 2017-07-01

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

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

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

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

Abstract: In this paper, we unify previous definitions of weakened open subsets in a given topological space. We felt necessary to make this unification since we observed recently too many definitions, actually, more or less significant. We also show that our new framework is more general than the known supra-topological structure. Finally we show that, in our new framework, we can define well several standard topologies like concepts such as convergence, continuity, and compactness. We expect that our new framework could find application in images processing. PubDate: 2017-07-01

Abstract: In this paper, we considered Ricci semi-symmetric real hypersurface in complex two-plane Grassmannians. Then we prove the non-existence of Ricci semi-symmetric Hopf hypersurfaces in complex two-plane Grassmannians by using the method of simultaneous diagonalization for pairwise commutative matrices. PubDate: 2017-07-01

Abstract: In this paper we establish some fixed point results for the sum of two multivalued mappings with weakly sequentially closed graph under weak topology features in a Banach space. An application to illustrate our theory is included. PubDate: 2017-07-01

Abstract: We introduce a special kind of almost geodesic mappings of the first type \(\pi _1^*\) of spaces with non-symmetric affine connections. Also, we investigate a special class of equitorsion almost geodesic mappings of type \(\pi _1^*\) and find some invariant geometric objects of these mappings. PubDate: 2017-07-01