Applied Mathematics

In this paper we have the space and some properties of this space are studied. It is shown that the conventional Hankel type transform is an automorphism of The generalized Hankel type transform of Gevrey ultradistributions is defined and it is established that the generalized Hankel type transform is an automorphism of . Multiplication on and convolution on are investigated.

In this paper we introduce some classes of p-valent analytic functions involving repeated Erdelyi-Kober fractional integral operators and investigate some of their properties specially inclusion relations for these classes. Some class preserving properties of an integral operator are also discussed.

Soret and Dufour effects on unsteady heat and mass transfer of an incompressible chemically reacting, electrically conducting memory fluid over a continuously moving horizontal non-conducting surface embedded in a porous medium in the presence of transverse magnetic field and volumetric rate of heat generation/ absorption are investigated. The governing non linear partial differential equations are transformed into coupled non dimensional non linear ordinary differential equations by using separation of variables and series expansion methods and are solved numerically by using MATLAB’s built in solver bvp4c. The influence of the Dufour number, Soret number, porosity parameter, heat source parameter and dimensionless chemical reaction parameter on temperature and concentration profiles as well as on local Nusselt number and Sherwood number are illustrated graphically. It is concluded that the Soret number, Dufour number and the chemical reaction parameter play a crucial role on the heat and mass transfer.

A b-vertex coloring of a graph[15] G is a proper vertex coloring of G such that each color class contains a vertex that has at least one vertex in every other color class in its neighborhood. The b-chromatic number of a graph G is the largest integer?(G) for which G has a b-vertex coloring with?(G) colors. This concept was introduced in [2] by Irving and Manlove by a certain partial ordering on all proper colorings in contrast to chromatic number ? (G),namely? (G) is the minimum of colors used among all minimal elements of this partial ordering, while ?(G) is the maximum of colors used among all minimal elements of the same partial ordering. The b-chromatic number has been considered with respect to subgraphs in [10,11], while the b-chromatic number under graph operations was considered in [15] for the Cartesian product and in [8] for the other three standard products. Operations on graphs produce new ones from older ones. Here the paper deals with the b-chromatic number of adding parallel chords in Cycle, Union of Path with Cycle and its complement, deletion and addition of vertices and edges in a Cycle.

The problem of generating epsilon of room is drawing the attention of the reliability analyst. Amongst those approaches, the characterization approach and the modelling approach are very appealing. In fact characterization approach is of interest to both theoreticians and applied workers. Here we have created an epsilon of room for application through characterization approach. In our application we have considered days of Menstrual Cycle with Melatonin hormone as variable compared with both control group and experimental group as women stress effects. Here we have used epsilon room (soft analysis) in the pineal gland. We have further discussed the main important point for saving energy to fight with the stress effects. The Hormones like Melatonin in the night time will be regulated as Melatonin is the night hormone which secretes in the pineal gland. If it secretes uniformly all other hormones like serotonin will be regulated in the day time.

A graph G=(V,E) with n vertices is said to be admitted prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the label of each pair of adjacent vertices are relatively prime. Some previous work on prime labeling includes prime labeling of bipartite graphs and ladder graphs. In this work, a new graph called Snow graph which is a union of wheel and star graphs is introduced. A theorem is given to obtain a prime labeling for this graph and an algorithm for prime labeling is given.

Abdollahi, Akbari, and Maimani put forward a conjecture named AAM's Conjecture as follows. If is a finite nonabelian simple group and is a group such that, then .In this note, we prove that if is a finite nonabelian simple group with, then ,where is the alternating group of degree 16.

In this paper, we expanded the application of Shehu transformation to obtained the solution for system of ordinary differential equations that subjected to known or unknown initial conditions, which applies in calculation for the cost of activity.

The group B(m,n) satis?es identity relation x^n = 1. Moreover, sinceF_m^n is a verbal subgroup of group F^m generated with word x^n, the group B(m,n) is free in the variety of all n-periodic groups, i.e. all groups, where the identical relationx^n = 1holds. The group B(m,n) is free in the variety of all n-periodical groups and is called free-periodical or free Burnside group of the period n and rank m.

In 2019, Matiama presented a new integral transformation called Shehu transformation, which used to solve many types of differential equations. In this article, we obtained the derivation and integration of Shehu transformation with its applications.