Journal of Mathematics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . 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. Computation of New Degree-Based Topological Indices of Graphene Mon, 26 Sep 2016 11:35:31 +0000 Graphene is one of the most promising nanomaterials because of its unique combination of superb properties, which opens a way for its exploitation in a wide spectrum of applications ranging from electronics to optics, sensors, and biodevices. Inspired by recent work on Graphene of computing topological indices, here we propose new topological indices, namely, Arithmetic-Geometric index ( index), SK index, SK1 index, and SK2 index of a molecular graph and obtain the explicit formulae of these indices for Graphene. V. S. Shigehalli and Rachanna Kanabur Copyright © 2016 V. S. Shigehalli and Rachanna Kanabur. All rights reserved. On the Composition Ideals of Schatten Class Type Mappings Sun, 14 Aug 2016 08:29:57 +0000 We study the composition ideals of multilinear and polynomial mappings generated by Schatten classes. We give some coincidence theorems for Cohen strongly 2-summing multilinear operators and factorization results like that given by Lindenstrauss-Pełczński for Hilbert Schmidt linear operators. Abdelaziz Belaada, Khalil Saadi, and Abdelmoumen Tiaiba Copyright © 2016 Abdelaziz Belaada et al. All rights reserved. Improving Genetic Algorithm with Fine-Tuned Crossover and Scaled Architecture Tue, 05 Apr 2016 13:37:24 +0000 Genetic Algorithm (GA) is a metaheuristic used in solving combinatorial optimization problems. Inspired by evolutionary biology, GA uses selection, crossover, and mutation operators to efficiently traverse the solution search space. This paper proposes nature inspired fine-tuning to the crossover operator using the untapped idea of Mitochondrial DNA (mtDNA). mtDNA is a small subset of the overall DNA. It differentiates itself by inheriting entirely from the female, while the rest of the DNA is inherited equally from both parents. This unique characteristic of mtDNA can be an effective mechanism to identify members with similar genes and restrict crossover between them. It can reduce the rate of dilution of diversity and result in delayed convergence. In addition, we scale the well-known Island Model, where instances of GA are run independently and population members exchanged periodically, to a Continental Model. In this model, multiple web services are executed with each web service running an island model. We applied the concept of mtDNA in solving Traveling Salesman Problem and to train Neural Network for function approximation. Our implementation tests show that leveraging these new concepts of mtDNA and Continental Model results in relative improvement of the optimization quality of GA. Ajay Shrestha and Ausif Mahmood Copyright © 2016 Ajay Shrestha and Ausif Mahmood. All rights reserved. Generalized Fractional Integral Operators and -Series Wed, 30 Mar 2016 09:24:38 +0000 Two fractional integral operators associated with Fox -function due to Saxena and Kumbhat are applied to -series, which is an extension of both Mittag-Leffler function and generalized hypergeometric function . The Mellin and Whittaker transforms are obtained for these compositional operators with -series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms of -function, which are in compact form suitable for numerical computation. Special cases of the results are also pointed out in the form of lemmas and corollaries. A. M. Khan, R. K. Kumbhat, Amit Chouhan, and Anita Alaria Copyright © 2016 A. M. Khan et al. All rights reserved. Applications of Cesàro Submethod to Trigonometric Approximation of Signals (Functions) Belonging to Class in -Norm Sun, 06 Mar 2016 14:00:39 +0000 We prove two Theorems on approximation of functions belonging to Lipschitz class in -norm using Cesàro submethod. Further we discuss few corollaries of our Theorems and compare them with the existing results. We also note that our results give sharper estimates than the estimates in some of the known results. M. L. Mittal and Mradul Veer Singh Copyright © 2016 M. L. Mittal and Mradul Veer Singh. All rights reserved. Product of the Generalized -Subgroups Thu, 03 Mar 2016 06:11:18 +0000 We introduce the notion of -product of -subsets. We give a necessary and sufficient condition for --subgroup of a product of groups to be -product of --subgroups. Dilek Bayrak and Sultan Yamak Copyright © 2016 Dilek Bayrak and Sultan Yamak. All rights reserved. Inner Product over Fuzzy Matrices Sun, 21 Feb 2016 14:20:38 +0000 The purpose of this study was to introduce the inner product over fuzzy matrices. By virtue of this definition, -norm is defined and the parallelogram law is proved. Again the relative fuzzy norm with respect to the inner product over fuzzy matrices is defined. Moreover Cauchy Schwarz inequality, Pythagoras, and Fundamental Minimum Principle are established. Some equivalent conditions are also proved. A. Nagoor Gani, K. Kannan, and A. R. Manikandan Copyright © 2016 A. Nagoor Gani et al. All rights reserved. Hermite-Hadamard-Fejér Type Inequalities for Quasi-Geometrically Convex Functions via Fractional Integrals Thu, 18 Feb 2016 11:30:04 +0000 Some Hermite-Hadamard-Fejér type integral inequalities for quasi-geometrically convex functions in fractional integral forms have been obtained. İmdat İşcan and Mehmet Kunt Copyright © 2016 İmdat İşcan and Mehmet Kunt. 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.