Journal of Mathematics The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. An Interesting Property of a Class of Circulant Graphs Mon, 27 Feb 2017 00:00:00 +0000 Suppose that and are two Cayley graphs on the cyclic additive group , where is an even integer, , , and are the inverse-closed subsets of . In this paper, it is shown that is a distance-transitive graph, and, by this fact, we determine the adjacency matrix spectrum of . Finally, we show that if and is an even integer, then the adjacency matrix spectrum of is , , , (we write multiplicities as exponents). Seyed Morteza Mirafzal and Ali Zafari Copyright © 2017 Seyed Morteza Mirafzal and Ali Zafari. All rights reserved. A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem Tue, 21 Feb 2017 00:00:00 +0000 In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a discontinuous Galerkin method for the hyperbolic part of the state equation. The control variable is approximated by variational discretization approach. A priori error estimates of the state, adjoint state, and control are derived for both semidiscrete scheme and fully discrete scheme. Numerical example is given to show the effectiveness of the numerical scheme. Qingjin Xu and Zhaojie Zhou Copyright © 2017 Qingjin Xu and Zhaojie Zhou. All rights reserved. The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures Mon, 30 Jan 2017 00:00:00 +0000 One of the goals of this article is to describe a setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure and of the concentration property on metric measured spaces, inspired from classical examples of means. In some cases, we get a linear extension of the limit at infinity. Then, the mean value on an infinite product is defined, first for cylindrical functions and secondly taking the uniform limit. Finally, the mean value for the heuristic Lebesgue measure on a separable infinite dimensional topological vector space (e.g., on a Hilbert space) is defined. This last object, which is not the classical infinite dimensional Lebesgue measure but its “normalized” version, is shown to be invariant under translation, scaling, and restriction. Jean-Pierre Magnot Copyright © 2017 Jean-Pierre Magnot. All rights reserved. A Generalization of the Krätzel Function and Its Applications Thu, 26 Jan 2017 00:00:00 +0000 In this paper, we introduce new functions as a generalization of the Krätzel function. We investigate recurrence relations, Mellin transform, fractional derivatives, and integral of the function . We show that the function is the solution of differential equations of fractional order. Neşe Dernek, Ahmet Dernek, and Osman Yürekli Copyright © 2017 Neşe Dernek et al. All rights reserved. Differential Calculus on -Graded Manifolds Tue, 17 Jan 2017 06:52:23 +0000 The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over -graded commutative rings and on -graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on -graded manifolds. We follow the notion of an -graded manifold as a local-ringed space whose body is a smooth manifold . A key point is that the graded derivation module of the structure ring of graded functions on an -graded manifold is the structure ring of global sections of a certain smooth vector bundle over its body . Accordingly, the Chevalley–Eilenberg differential calculus on an -graded manifold provides it with the de Rham complex of graded differential forms. This fact enables us to extend the differential calculus on -graded manifolds to formalism of nonlinear differential operators, by analogy with that on smooth manifolds, in terms of graded jet manifolds of -graded bundles. G. Sardanashvily and W. Wachowski Copyright © 2017 G. Sardanashvily and W. Wachowski. All rights reserved. Approximate Solution of Perturbed Volterra-Fredholm Integrodifferential Equations by Chebyshev-Galerkin Method Thu, 12 Jan 2017 09:31:33 +0000 In this work, we obtain the approximate solution for the integrodifferential equations by adding perturbation terms to the right hand side of integrodifferential equation and then solve the resulting equation using Chebyshev-Galerkin method. Details of the method are presented and some numerical results along with absolute errors are given to clarify the method. Where necessary, we made comparison with the results obtained previously in the literature. The results obtained reveal the accuracy of the method presented in this study. K. Issa and F. Salehi Copyright © 2017 K. Issa and F. Salehi. All rights reserved. Different Characterizations of Large Submodules of QTAG-Modules Tue, 03 Jan 2017 07:07:55 +0000 A module over an associative ring with unity is a -module if every finitely generated submodule of any homomorphic image of is a direct sum of uniserial modules. The study of large submodules and its fascinating properties makes the theory of QTAG-modules more interesting. A fully invariant submodule of is large in if , for every basic submodule of The impetus of these efforts lies in the fact that the rings are almost restriction-free. This motivates us to find the necessary and sufficient conditions for a submodule of a QTAG-module to be large and characterize them. Also, we investigate some properties of large submodules shared by -modules, summable modules, -summable modules, and so on. Fahad Sikander, Alveera Mehdi, and Sabah A. R. K. Naji Copyright © 2017 Fahad Sikander et al. All rights reserved. Mathematical Analysis of a Reactive Viscous Flow through a Channel Filled with a Porous Medium Tue, 27 Dec 2016 09:50:46 +0000 An investigation has been carried out to study entropy generation in a viscous, incompressible, and reactive fluid flowing steadily through a channel with porous materials. Approximate solutions for both velocity and temperature fields are obtained by using a rapidly convergent Adomian decomposition method (ADM). These solutions are then used to determine the heat irreversibility and Bejan number of the problem. Variations of other important fluid parameters are conducted, presented graphically, and discussed. Samuel O. Adesanya, J. A. Falade, J. C. Ukaegbu, and K. S. Adekeye Copyright © 2016 Samuel O. Adesanya et al. All rights reserved. Fuzzy Soft Compact Topological Spaces Sun, 25 Dec 2016 13:27:25 +0000 In this paper, we have studied compactness in fuzzy soft topological spaces which is a generalization of the corresponding concept by R. Lowen in the case of fuzzy topological spaces. Several basic desirable results have been established. In particular, we have proved the counterparts of Alexander’s subbase lemma and Tychonoff theorem for fuzzy soft topological spaces. Seema Mishra and Rekha Srivastava Copyright © 2016 Seema Mishra and Rekha Srivastava. All rights reserved. Graphs Generated by Measures Mon, 19 Dec 2016 09:32:32 +0000 In this paper, a graph is assigned to any probability measure on the -algebra of Borel sets of a topological space. Using this construction, it is proved that given any number (finite or infinite) there exists a nonregular graph such that its clique, chromatic, and dominating number equals . A. Assari and M. Rahimi Copyright © 2016 A. Assari and M. Rahimi. All rights reserved. Classifying Quadratic Forms Over in Three Variables Tue, 13 Dec 2016 08:40:35 +0000 The quadratic forms in three variables over the field are classified. Some remarks are made about the group of equivalences of the quadratic forms. Gerard Thompson Copyright © 2016 Gerard Thompson. All rights reserved. A Generalized Hermite-Hadamard Inequality for Coordinated Convex Function and Some Associated Mappings Tue, 13 Dec 2016 07:28:35 +0000 We have discussed the generalization of Hermite-Hadamard inequality introduced by Lupaş for convex functions on coordinates defined in a rectangle from the plane. Also we define that mappings are related to it and their properties are discussed. Atiq Ur Rehman, Gulam Farid, and Sidra Malik Copyright © 2016 Atiq Ur Rehman et al. All rights reserved. Some Relations between Isologic and Varietal Perfect Groups Mon, 12 Dec 2016 14:50:17 +0000 In 1940, Hall introduced the notion of -isologism, with respect to a given variety of groups . In the present article, we study the concepts of -perfect groups, -subgroup, and -quotient irreducible groups, with respect to a given variety of groups . Also we prove and obtain some results. Shokufeh Lotfi and S. Mostafa Taheri Copyright © 2016 Shokufeh Lotfi and S. Mostafa Taheri. All rights reserved. Differentiation Theory over Infinite-Dimensional Banach Spaces Thu, 08 Dec 2016 10:25:18 +0000 We study, for any positive integer and for any subset of , the Banach space of the bounded real sequences and a measure over that generalizes the -dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables’ formula for the integration of the measurable real functions on . This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms. Claudio Asci Copyright © 2016 Claudio Asci. All rights reserved. Sectional and Ricci Curvature for Three-Dimensional Lie Groups Sun, 04 Dec 2016 11:09:39 +0000 Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined. Gerard Thompson and Giriraj Bhattarai Copyright © 2016 Gerard Thompson and Giriraj Bhattarai. All rights reserved. Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces Mon, 28 Nov 2016 13:31:02 +0000 We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry. Arnon Ploymukda and Pattrawut Chansangiam Copyright © 2016 Arnon Ploymukda and Pattrawut Chansangiam. All rights reserved. Presic Type Fixed Point Theorem for Four Maps in Metric Spaces Tue, 22 Nov 2016 06:27:48 +0000 We obtained a Presic type fixed point theorem for two pairs of jointly -weakly compatible maps in metric spaces. We also have given an example to illustrate our main theorem. K. P. R. Rao, Sk. Sadik, and S. Manro Copyright © 2016 K. P. R. Rao et al. All rights reserved. Multiple-Term Refinements of Young Type Inequalities Wed, 16 Nov 2016 13:34:34 +0000 Recently, a multiple-term refinement of Young’s inequality has been proved. In this paper, we show its reverse refinement. Moreover, we will present multiple-term refinements of Young’s inequality involving Kantorovich constants. Finally, we will apply scalar inequalities to operators. Daeshik Choi Copyright © 2016 Daeshik Choi. All rights reserved. Stability Analysis of the Periodic Solutions of Some Kinds of Predator-Prey Dynamical Systems Thu, 10 Nov 2016 06:49:40 +0000 Analysis of predator-prey dynamical systems that have the functional response which generalizes the other types of functional responses in two dimensions is mainly studied in this paper. The main problems for this study are to detect the if and only if conditions for attaining the periodic solution of the considered system and to find the condition for global asymptotic stability of this solution for some different types of predator-prey systems that are obtained from that system. To get the desired results, some aspects of semigroup theory for stability analysis and coincidence degree theory are used. Neslihan Nesliye Pelen Copyright © 2016 Neslihan Nesliye Pelen. All rights reserved. On Parametric -Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings Mon, 07 Nov 2016 06:46:50 +0000 We introduce the notion of a parametric -metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametric -metric space. It is important to obtain new fixed-point theorems on a parametric -metric space because there exist some parametric -metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametric -metric space. Nihal Taş and Nihal Yılmaz Özgür Copyright © 2016 Nihal Taş and Nihal Yılmaz Özgür. All rights reserved. A Study on Characteristic Roots of Lattice Matrices Mon, 31 Oct 2016 08:56:30 +0000 This paper deals with the characteristic roots of different types of lattice matrices and proves that a matrix and its transpose have the same characteristic roots. Also this paper introduces the concept of similar lattice matrices and proves that similar lattice matrices have the same characteristic roots. Kapiarumalayil Varkey Thomas and Geena Joy Copyright © 2016 Kapiarumalayil Varkey Thomas and Geena Joy. All rights reserved. End Point Results in Metric Spaces Endowed with a Graph Sun, 30 Oct 2016 13:12:30 +0000 We introduce the notion of end point of multivalued mappings in the setting of metric space endowed with a graph and prove some existence results in this context. The mappings are assumed to satisfy certain generalized multivalued almost -contractive type inequalities. Further, the consequences of the corresponding results in the cases of single-valued mappings are also discussed with examples. Binayak S. Choudhury, Nikhilesh Metiya, and Pradip Debnath Copyright © 2016 Binayak S. Choudhury et al. All rights reserved. On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs Tue, 25 Oct 2016 09:25:47 +0000 Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy ( energy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from its energy. S. R. Jog and Raju Kotambari Copyright © 2016 S. R. Jog and Raju Kotambari. All rights reserved. Nonsolvable Subalgebras of Tue, 18 Oct 2016 13:55:56 +0000 All the simple and then semisimple subalgebras of are found. Each such semisimple subalgebra acts by commutator on . In each case the invariant subspaces are found and the results are used to determine all possible subalgebras of that are not solvable. Ryad Ghanam and Gerard Thompson Copyright © 2016 Ryad Ghanam and Gerard Thompson. All rights reserved. Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces Mon, 10 Oct 2016 05:58:44 +0000 This article proves some theorems to approximate fixed point of Zamfirescu operators on normed spaces for some two-step iterative schemes, namely, Picard-Mann iteration, Ishikawa iteration, S-iteration, and Thianwan iteration, with their errors. We compare the aforementioned iterations using numerical approach; the results show that S-iteration converges faster than other iterations followed by Picard-Mann iteration, while Ishikawa iteration is the least in terms of convergence rate. These results also suggest the best among two-step iterative fixed point schemes in the literature. O. T. Wahab, R. O. Olawuyi, K. Rauf, and I. F. Usamot Copyright © 2016 O. T. Wahab et al. All rights reserved. Multivalued Fixed Point Theorems for Generalized Contractions and Their Applications Wed, 05 Oct 2016 14:00:48 +0000 We give common hybrid fixed point results for generalized weak contraction satisfying and properties in the framework of metric spaces. An application to functional equations is also discussed. Muhammad Shoaib and Muhammad Sarwar Copyright © 2016 Muhammad Shoaib and Muhammad Sarwar. All rights reserved. Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi Wed, 05 Oct 2016 07:58:17 +0000 In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods. Ali Özyapıcı, Zehra B. Sensoy, and Tolgay Karanfiller Copyright © 2016 Ali Özyapıcı et al. All rights reserved. Slightly Regular Measures and Measureable Sets Mon, 03 Oct 2016 11:46:57 +0000 Outer and inner measures of a measure are defined and used to prove results involving them on a lattice and its complement . The results concern slightly regular measures and sets such as which is the collection of -measureable sets. James Camacho Jr. Copyright © 2016 James Camacho Jr. All rights reserved. On a Special Form of -Torsion Tensor in Finsler Space Thu, 29 Sep 2016 12:11:52 +0000 A special form of () -torsion tensor was introduced which may be considered generalization of -Finsler space and -reducible Finsler space and then some properties of this space were studied. We also introduce connection and give some case and condition of torsion tensor Brijesh Kumar Tripathi and K. B. Pandey Copyright © 2016 Brijesh Kumar Tripathi and K. B. Pandey. All rights reserved. One Form of Lyapunov Operator for Stochastic Dynamic System with Markov Parameters Thu, 29 Sep 2016 07:15:19 +0000 The form of weak infinitesimal operator of Lyapunov type on solutions of stochastic dynamic systems of random structure with constant delay which exist under the action of Markov perturbations is obtained. Taras Lukashiv Copyright © 2016 Taras Lukashiv. All rights reserved.