Journal of Mathematics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Herd Behavior and Financial Crashes: An Interacting Particle System Approach Thu, 11 Feb 2016 12:08:48 +0000 We provide an approach based on a modification of the Ising model to describe the dynamics of stock markets. Our model incorporates three different factors: imitation, the impact of external news, and private information; moreover, it is characterized by coupling coefficients, static in time, but not identical for each agent. By analogy with physical models, we consider the temperature parameter of the system, assuming that it evolves with memory of the past, hence considering how former news influences realized market returns. We show that a standard Ising potential assumption is not sufficient to reproduce the stylized facts characterizing financial markets; this is because it assigns low probabilities to rare events. Hence, we study a variation of the previous setting providing, also by concrete computations, new insights and improvements. Vincenzo Crescimanna and Luca Di Persio Copyright © 2016 Vincenzo Crescimanna and Luca Di Persio. All rights reserved. Automorphisms and Inner Automorphisms Sun, 07 Feb 2016 13:09:45 +0000 Let be a field of characteristic not and let be central simple superalgebra over , and let be superinvolution on . Our main purpose is to classify the group of automorphisms and inner automorphisms of (i.e., commuting with ) by using the classical theorem of Skolem-Noether. Also we study two examples of groups of automorphisms and inner automorphisms on even central simple superalgebras with superinvolutions. Ameer Jaber and Moh’D Yasein Copyright © 2016 Ameer Jaber and Moh’D Yasein. All rights reserved. A Fixed Point Theorem for Monotone Maps and Its Applications to Nonlinear Matrix Equations Thu, 24 Dec 2015 16:01:30 +0000 By using the fixed point theorem for monotone maps in a normal cone, we prove a uniqueness theorem for the positive definite solution of the matrix equation , where is a monotone map on the set of positive definite matrices. Then we apply the uniqueness theorem to a special equation and prove that the equation has a unique positive definite solution when and and . For this equation the basic fixed point iteration is discussed. Numerical examples show that the iterative method is feasible and effective. Dongjie Gao Copyright © 2015 Dongjie Gao. All rights reserved. New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators Tue, 22 Dec 2015 11:22:25 +0000 We discuss new approaches to handling Fokker Planck equation on Cantor sets within local fractional operators by using the local fractional Laplace decomposition and Laplace variational iteration methods based on the local fractional calculus. The new approaches maintain the efficiency and accuracy of the analytical methods for solving local fractional differential equations. Illustrative examples are given to show the accuracy and reliable results. Hassan Kamil Jassim Copyright © 2015 Hassan Kamil Jassim. All rights reserved. An Extension of Wright Function and Its Properties Tue, 08 Dec 2015 05:50:05 +0000 The paper is devoted to the study of the function , which is an extension of the classical Wright function and Kummer confluent hypergeometric function. The properties of including its auxiliary functions and the integral representations are proven. Moustafa El-Shahed and Ahmed Salem Copyright © 2015 Moustafa El-Shahed and Ahmed Salem. All rights reserved. Coefficient Bounds for Certain Subclasses of -Fold Symmetric Biunivalent Functions Wed, 25 Nov 2015 14:06:04 +0000 We consider two new subclasses and of consisting of analytic and -fold symmetric biunivalent functions in the open unit disk . Furthermore, we establish bounds for the coefficients for these subclasses and several related classes are also considered and connections to earlier known results are made. Şahsene Altınkaya and Sibel Yalçın Copyright © 2015 Şahsene Altınkaya and Sibel Yalçın. All rights reserved. Ordering Properties of the First Eigenvector of Certain Similarity Matrices Thu, 12 Nov 2015 11:52:01 +0000 It is shown for coefficient matrices of Russell-Rao coefficients and two asymmetric Dice coefficients that ordinal information on a latent variable model can be obtained from the eigenvector corresponding to the largest eigenvalue. Matthijs J. Warrens and Alexandra de Raadt Copyright © 2015 Matthijs J. Warrens and Alexandra de Raadt. All rights reserved. Symplectic Toric Geometry and the Regular Dodecahedron Wed, 11 Nov 2015 11:55:06 +0000 The regular dodecahedron is the only simple polytope among the platonic solids which is not rational. Therefore, it corresponds neither to a symplectic toric manifold nor to a symplectic toric orbifold. In this paper, we associate to the regular dodecahedron a highly singular space called symplectic toric quasifold. Elisa Prato Copyright © 2015 Elisa Prato. All rights reserved. Irreducible Modular Representations of the Reflection Group Mon, 09 Nov 2015 08:54:56 +0000 In an article published in 1980, Farahat and Peel realized the irreducible modular representations of the symmetric group. One year later, Al-Aamily, Morris, and Peel constructed the irreducible modular representations for a Weyl group of type . In both cases, combinatorial methods were used. Almost twenty years later, using a geometric construction based on the ideas of Macdonald, first Aguado and Araujo and then Araujo, Bigeón, and Gamondi also realized the irreducible modular representations for the Weyl groups of types and . In this paper, we extend the geometric construction based on the ideas of Macdonald to realize the irreducible modular representations of the complex reflection group of type . José O. Araujo, Tim Bratten, and Cesar L. Maiarú Copyright © 2015 José O. Araujo et al. All rights reserved. Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series Wed, 04 Nov 2015 09:39:10 +0000 New differences of integer orders, which are connected with derivatives of integer orders not approximately, are proposed. These differences are represented by infinite series. A characteristic property of the suggested differences is that its Fourier series transforms have a power-law form. We demonstrate that the proposed differences of integer orders are directly connected with the derivatives . In contrast to the usual finite differences of integer orders, the suggested differences give the usual derivatives without approximation. Vasily E. Tarasov Copyright © 2015 Vasily E. Tarasov. All rights reserved. On -Symmetric -Paracontact Metric Manifolds Thu, 29 Oct 2015 11:01:24 +0000 The notions of -symmetric, 3-dimensional locally -symmetric, -Ricci symmetric, and 3-dimensional locally -Ricci symmetric -paracontact metric manifolds have been introduced and properties of these structures have been discussed. D. G. Prakasha and K. K. Mirji Copyright © 2015 D. G. Prakasha and K. K. Mirji. All rights reserved. Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method Tue, 27 Oct 2015 10:47:03 +0000 We study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem by using Infeasible Newton’s method applied to the KKT system of equations which can be started from any point. We implement the method using backtracking line search technique and also study the effect of large weights on the method. We use numerical experiments to compare Infeasible Newton’s method with Standard Newton’s method. The results show that Infeasible Newton’s method moves in the interior of the feasible regions often very quickly, starting from any point. We recommend it as a method for finding an interior point by setting each weight to be 1. It appears to work better than Standard Newton’s method in finding the weighted analytic center when none of weights is very large relative to the other weights. However, we find that Infeasible Newton’s method is more sensitive than Standard Newton’s method to large variation in the weights. Shafiu Jibrin Copyright © 2015 Shafiu Jibrin. All rights reserved. Killing Vector Fields in Generalized Conformal -Change of Finsler Spaces Mon, 26 Oct 2015 08:29:36 +0000 We consider a Finsler space equipped with a Generalized Conformal β-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformal β-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformal β-change of metric. Mallikarjun Yallappa Kumbar, Narasimhamurthy Senajji Kampalappa, Thippeswamy Komalobiah Rajanna, and Kavyashree Ambale Rajegowda Copyright © 2015 Mallikarjun Yallappa Kumbar et al. All rights reserved. Two-Temperature Generalized Thermoviscoelasticity with Fractional Order Strain Subjected to Moving Heat Source: State Space Approach Wed, 21 Oct 2015 13:34:36 +0000 The theory of generalized thermoelasticity with fractional order strain is employed to study the problem of one-dimensional disturbances in a viscoelastic solid in the presence of a moving internal heat source and subjected to a mechanical load. The problem is in the context of Green-Naghdi theory of thermoelasticity with energy dissipation. Laplace transform and state space techniques are used to obtain the general solution for a set of boundary conditions. To tackle the expression of heat source, Fourier transform is also employed. The expressions for different field parameters such as displacement, stress, thermodynamical temperature, and conductive temperature in the physical domain are derived by the application of numerical inversion technique. The effects of fractional order strain, two-temperature parameter, viscosity, and velocity of internal heat source on the field variables are depicted graphically for copper material. Some special cases of interest have also been presented. Renu Yadav, Kapil Kumar Kalkal, and Sunita Deswal Copyright © 2015 Renu Yadav et al. All rights reserved. Some Theorems about -Contraction in Fuzzy Metric Spaces Sun, 18 Oct 2015 13:04:34 +0000 We previously proved a number of fixed point theorems for some kinds of contractions like -contraction and contraction in fuzzy metric spaces. In this paper, we discuss the problem of existence of fixed point for -contraction in fuzzy metric spaces in sense of George and Veeramani. Parvin Azhdari Copyright © 2015 Parvin Azhdari. All rights reserved. The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Order Mon, 12 Oct 2015 14:23:52 +0000 Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of order are obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski. Mengkun Zhu and Xinzhong Huang Copyright © 2015 Mengkun Zhu and Xinzhong Huang. All rights reserved. The Structure of Simple Modules of Birman-Murakami-Wenzl Algebras Mon, 12 Oct 2015 11:17:41 +0000 We study the restriction of simple modules of Birman-Murakami-Wenzl algebras with   being not a root of 1. Precisely, we study the module structure for the restriction of to and describe the socle and head of the restriction of each simple module completely. Xu Xu Copyright © 2015 Xu Xu. All rights reserved. Norm Estimates for Solutions of Polynomial Operator Equations Sun, 04 Oct 2015 16:08:26 +0000 We consider the equations and , where   , , are given linear bounded operators in a Banach space and is to be found. Representations of solutions are derived. In the cases of Euclidean and Hilbert spaces, norm estimates for the solutions are suggested. Michael Gil’ Copyright © 2015 Michael Gil’. All rights reserved. Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions Thu, 01 Oct 2015 12:02:20 +0000 We consider a problem of stability of fixed point sets for a sequence of multivalued mappings defined on a metric space converging to a limit function where the convergence is with respect to the Pompeiu-Hausdorff distance. The members of the sequence are assumed to be multivalued almost contractions. We show that the fixed point sets of this sequence of mappings are stable. Binayak S. Choudhury and Chaitali Bandyopadhyay Copyright © 2015 Binayak S. Choudhury and Chaitali Bandyopadhyay. All rights reserved. On a Theorem of Ziv Ran concerning Abelian Varieties Which Are Product of Jacobians Thu, 01 Oct 2015 09:45:36 +0000 We give a new proof for a theorem of Ziv Ran which generalizes some results of Matsusaka and Hoyt. These results provide criteria for an Abelian variety to be a Jacobian or a product of Jacobians. The advantage of our method is that it works in arbitrary characteristic. Cristian Anghel and Nicolae Buruiana Copyright © 2015 Cristian Anghel and Nicolae Buruiana. All rights reserved. The Partition Function of the Dirichlet Operator on a -Dimensional Rectangle Cavity Tue, 15 Sep 2015 06:16:23 +0000 We study the asymptotic behavior of the free partition function in the limit for a diffusion process which consists of -independent, one-dimensional, symmetric, -stable processes in a hyperrectangular cavity with an absorbing boundary. Each term of the partition function for this polyhedron in -dimensions can be represented by a quermassintegral and the geometrical information conveyed by the eigenvalues of the fractional Dirichlet Laplacian for this solvable model is now transparent. We also utilize the intriguing method of images to solve the same problem, in one and two dimensions, and recover identical results to those derived in the previous analysis. Agapitos N. Hatzinikitas Copyright © 2015 Agapitos N. Hatzinikitas. All rights reserved. Maps Preserving Idempotence on Matrix Spaces Wed, 09 Sep 2015 07:13:00 +0000 Suppose is an arbitrary field. Let be the number of the elements of . Let be the space of all matrices over , let be the subset of consisting of all symmetric matrices, and let be the subset of consisting of all upper-triangular matrices. Let ; a map is said to preserve idempotence if is idempotent if and only if is idempotent for any and . In this paper, the maps preserving idempotence on , , and were characterized in case . Yuqiu Sheng and Hanyu Zhang Copyright © 2015 Yuqiu Sheng and Hanyu Zhang. All rights reserved. Some Applications of Ordinary Differential Operator to Certain Multivalent Functions Tue, 18 Aug 2015 16:28:56 +0000 The aim of this paper is to apply the well-known ordinary differential operator to certain multivalent functions which are analytic in the certain domains of the complex plane and then to determine some criteria concerning analytic and geometric properties of the related complex functions. Müfit Şan, Hüseyin Irmak, and Ayhan Şerbetçi Copyright © 2015 Müfit Şan et al. All rights reserved. Locally Defined Operators in the Space of Functions of Bounded Riesz-Variation Mon, 06 Jul 2015 11:18:12 +0000 We study the locally defined operator on the spaces of bounded Riesz -variation functions and we prove that those operators are the Nemytskii operator. W. Aziz, J. A. Guerrero, K. Maldonado, and N. Merentes Copyright © 2015 W. Aziz et al. All rights reserved. Note on Quasi-Numerically Positive Log Canonical Divisors Sun, 31 May 2015 17:25:50 +0000 We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the ampleness in some elementary cases. Shigetaka Fukuda Copyright © 2015 Shigetaka Fukuda. All rights reserved. Nonexplosion and Pathwise Uniqueness of Stochastic Differential Equation Driven by Continuous Semimartingale with Non-Lipschitz Coefficients Sun, 17 May 2015 11:50:23 +0000 We study a class of stochastic differential equations driven by semimartingale with non-Lipschitz coefficients. New sufficient conditions on the strong uniqueness and the nonexplosion are derived for -dimensional stochastic differential equations on with non-Lipschitz coefficients, which extend and improve Fei’s results. Jinxia Wang Copyright © 2015 Jinxia Wang. All rights reserved. Boundedness of Marcinkiewicz Integrals on RBMO Spaces over Nonhomogeneous Metric Measure Spaces Sun, 19 Apr 2015 14:23:42 +0000 Let be a metric measures space satisfying the upper doubling conditions and the geometrically doubling conditions in the sense of Hytönen. Under the assumption that the dominating function satisfies the weak reverse doubling condition, the authors prove that Marcinkiewicz integral with kernel satisfying certain stronger Hörmander-type condition is bounded on RBMO space. Ji Cheng and Guanghui Lu Copyright © 2015 Ji Cheng and Guanghui Lu. All rights reserved. On the Range of the Radon Transform on and the Related Volberg’s Uncertainty Principle Mon, 02 Feb 2015 13:21:37 +0000 We characterize the image of exponential type functions under the discrete Radon transform R on the lattice of the Euclidean space . We also establish the generalization of Volberg's uncertainty principle on , which is proved by means of this characterization. The techniques of which we make use essentially in this paper are those of the Diophantine integral geometry as well as the Fourier analysis. Ahmed Abouelaz, Abdallah Ihsane, and Takeshi Kawazoe Copyright © 2015 Ahmed Abouelaz et al. All rights reserved. Inferior Mean of Measures on Curves and Subspaces Sun, 28 Dec 2014 11:16:42 +0000 We obtain new sharp upper bounds of the inferior mean for positive harmonic functions defined by finite boundary measures that lie on curves or subspaces of the boundary of the half-space. Yevgenya Movshovich Copyright © 2014 Yevgenya Movshovich. All rights reserved. Noninvariant Hypersurfaces of a Nearly Trans-Sasakian Manifolds Mon, 22 Dec 2014 11:17:26 +0000 The present paper focuses on the study of noninvariant hypersurfaces of a nearly trans-Sasakian manifold equipped with -structure. Initially some properties of this structure have been discussed. Further, the second fundamental forms of noninvariant hypersurfaces of nearly trans-Sasakian manifolds and nearly cosymplectic manifolds with -structure have been calculated provided is parallel. In addition, the eigenvalues of have been found and proved that a noninvariant hypersurface with -structure of nearly cosymplectic manifold with contact structure becomes totally geodesic. Finally the paper has been concluded by investigating the necessary condition for totally geodesic or totally umbilical noninvariant hypersurface with -structure of a nearly trans-Sasakian manifold. Satya Prakash Yadav and Shyam Kishor Copyright © 2014 Satya Prakash Yadav and Shyam Kishor. All rights reserved.