Journal of Mathematics
http://www.i-scholar.in/index.php/JMaTh
Journal of Mathematics is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of mathematics.Hindawi Limiteden-USJournal of Mathematics2314-4629Generalized Fractional Integral Operators and <i>M</i>-Series
http://www.i-scholar.in/index.php/JMaTh/article/view/98644
Two 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.A. M. KhanR. K. KumbhatAmit ChouhanAnita Alaria2016Automorphisms and Inner Automorphisms
http://www.i-scholar.in/index.php/JMaTh/article/view/98698
Let <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.Ameer JaberMoh’D Yasein2016Improving Genetic Algorithm with Fine-Tuned Crossover and Scaled Architecture
http://www.i-scholar.in/index.php/JMaTh/article/view/98700
Genetic 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.Ajay ShresthaAusif Mahmood2016Product of the Generalized <i>L</i>-Subgroups
http://www.i-scholar.in/index.php/JMaTh/article/view/98703
We 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>Dilek BayrakSultan Yamak2016Inner Product over Fuzzy Matrices
http://www.i-scholar.in/index.php/JMaTh/article/view/98705
The 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.A. Nagoor GaniK. KannanA. R. Manikandan2016Hermite-Hadamard-Fejer Type Inequalities for Quasi-Geometrically Convex Functions via Fractional Integrals
http://www.i-scholar.in/index.php/JMaTh/article/view/98707
Some Hermite-Hadamard-Fejer type integral inequalities for quasi-geometrically convex functions in fractional integral forms have been obtained.Imdat IscanMehmet Kunt2016Herd Behavior and Financial Crashes: An Interacting Particle System Approach
http://www.i-scholar.in/index.php/JMaTh/article/view/98709
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 CrescimannaLuca Di Persio2016Applications of Cesaro Submethod to Trigonometric Approximation of Signals (Functions) Belonging to Class Lip(α, p) in <i>L</i><sub><i>p</i></sub>-Norm
http://www.i-scholar.in/index.php/JMaTh/article/view/98720
We 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.M. L. MittalMradul Veer Singh2016