http://www.i-scholar.in/index.php/JMaTh/issue/feedJournal of Mathematics2016-05-04T05:42:49+00:00Dr. Huixiang Chenjmath@hindawi.comOpen Journal SystemsJournal of Mathematics is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of mathematics.http://www.i-scholar.in/index.php/JMaTh/article/view/98644Generalized Fractional Integral Operators and <i>M</i>-Series2016-05-04T05:42:15+00:00A. M. Khankhanarif76@gmail.comR. K. KumbhatAmit ChouhanAnita AlariaTwo fractional integral operators associated with Fox <em>H</em>-function due to Saxena and Kumbhat are applied to <em>M</em>-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric function <em><sub>p</sub>F<sub>q</sub></em>. The Mellin and Whittaker transforms are obtained for these compositional operators with <em>M</em>-series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms of <em>H</em>-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.http://www.i-scholar.in/index.php/JMaTh/article/view/98698Automorphisms and Inner Automorphisms2016-05-04T05:42:33+00:00Ameer Jaberameerj@hu.edu.joMoh’D YaseinLet <em>K</em> be a field of characteristic not 2 and let <em>A</em> = <em>A</em><sub>0</sub> + <em>A</em><sub>1</sub> be central simple superalgebra over K, and let * be superinvolution on A. Our main purpose is to classify the group of automorphisms and inner automorphisms of (<em>A</em>, *) (i.e., commuting with *) by using the classical theoremof Skolem-Noether. Also we study two examples of groups of automorphisms and inner automorphisms on even central simple superalgebras with superinvolutions.http://www.i-scholar.in/index.php/JMaTh/article/view/98700Improving Genetic Algorithm with Fine-Tuned Crossover and Scaled Architecture2016-05-04T05:42:34+00:00Ajay Shresthashrestha@my.bridgeport.eduAusif MahmoodGenetic Algorithm (GA) is ametaheuristic 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.http://www.i-scholar.in/index.php/JMaTh/article/view/98703Product of the Generalized <i>L</i>-Subgroups2016-05-04T05:42:48+00:00Dilek Bayrakdbayrak@nku.edu.trSultan YamakWe introduce the notion of (λ, μ)-product of <em>L<em>-subsets. We give a necessary and sufficient condition for (λ, μ)-<em>L<em>-subgroup of a product of groups to be (λ, μ)-product of (λ, μ)-<em>L<em>-subgroups.</em></em></em></em></em></em>http://www.i-scholar.in/index.php/JMaTh/article/view/98705Inner Product over Fuzzy Matrices2016-05-04T05:42:48+00:00A. Nagoor Ganiganijmc@yahoo.co.inK. KannanA. R. ManikandanThe purpose of this study was to introduce the inner product over fuzzy matrices. By virtue of this definition, α-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.http://www.i-scholar.in/index.php/JMaTh/article/view/98707Hermite-Hadamard-Fejer Type Inequalities for Quasi-Geometrically Convex Functions via Fractional Integrals2016-05-04T05:42:48+00:00Imdat IscanMehmet Kuntmkunt@ktu.edu.trSome Hermite-Hadamard-Fejer type integral inequalities for quasi-geometrically convex functions in fractional integral forms have been obtained.http://www.i-scholar.in/index.php/JMaTh/article/view/98709Herd Behavior and Financial Crashes: An Interacting Particle System Approach2016-05-04T05:42:48+00:00Vincenzo CrescimannaLuca Di Persiodipersioluca@gmail.comWe 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.http://www.i-scholar.in/index.php/JMaTh/article/view/98720Applications of Cesaro Submethod to Trigonometric Approximation of Signals (Functions) Belonging to Class Lip(α, p) in <i>L</i><sub><i>p</i></sub>-Norm2016-05-04T05:42:49+00:00M. L. MittalMradul Veer Singhmradul.singh@gmail.comWe prove two Theorems on approximation of functions belonging to Lipschitz class Lip(α, <em>p</em>) in <em>L</em><sub><em>p<em></em></em></sub>-norm using Cesaro 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.