Applied Mathematics

In this article, the phenomenon of fingero-imbibition in a particular displacement method concerning two immiscible fluids through a dipping homogeneous porous media with a magnetic field effect has been discussed analytically under certain conditions. This phenomenon provides a nonlinear partial differential equation as a governing equation, which can be solved by Homotopy Perturbation Sumudu transform method (HPSTM). The numerical and graphical results are discussed using MATLAB.

In this paper fuzzy soft connectedness on fuzzy soft topological spaces are defined. Some related properties regarding the newly defined concepts are proved.

In this work, the Adomian decomposition (ADM) and Picards Iterative Methods were used to solve nonlinear ordinary differential equations analytically and numerically using the Trapezoidal rule approach, and the results are compared for accuracy and rate of convergence. Though a little modification by the use of contraction principle was made to the Picard Iteration Method in order to accelerate the convergence of the method it was found out that the ADM converges faster than the Picard’s method.

The proof will demonstrate the non-existence of a 3x3 magic square of squares. I remember reading a Scientific America article and at the bottom of the article was the link to an article which described this problem. To me it seemed bizarre that a problem that had such a clear start point and was based on a concept so simple to understand could have no proof. I decided then that I would prove that such a square could never exist. I was inspired that the problem had been unresolved such it was first asked in 1984 and that it could be dated back to great mathematicians such as Leonhard Euler. Like many people interested in maths I am in awe of much of the the work that Leonhard Euler did so to be able to solve a problem whose roots can be traced back to him was exciting. People have been working with magic squares for centuries and yet nobody has presented a proof showing why a 3x3 magic square comprised entirely of square numbers cannot exist. I decided that night that I would provide such a proof. I was unaware how complex the problem was and how complex the tools I would need to solve the problem were but it was the start of the most wonderful journey that I wish I could relive. For hundreds of years people have been constructing magic squares. The definition of a magic square which I will refer to extensively throughout this proof states the following. The sum of all the elements in the rows, columns and diagonals must be equal. Each element must be unique in any square and must be a natural number. Therefore when I say something has been proven false through the defintion of a magic square this is the definition I am referrring to. Well reading an article in Scientific America I came across something that rather astounded me. The article claimed that no one had found an example of a 3x3 magic square that contains only magic square numbers. Furthermore no onw has proven that such a square cannot exist. This type of problem can be traced back all the way to Leonhard Euler who is the first person known to construct a 4x4 magic square of squares. I have always been fascinated in mathematical mysteries as the world is written in the mathematics to understand mathematics is to understand the world. Therefore by proving something in maths I am making the world a little more interesting. In the proof that follows I will show why a 3x3 magic square of squares can never exist. I will do this in 10 parts. The first part will be a general proof as to why the lowest element must be the middle or the corner for any magic square of squares to exist. I will then show that the lowest element can never occupy the middle or the corner of any square without violating the definition of what a magic square is.

In this paper we have studied the range of Hankel type and extended Hankel type transforms on some spaces of functions. Further the Paley-Wiener type theorem for the Hankel type transforms is also established.

A Goodman-Ronning type class of multivalent harmonic functions involving Dziok-Srivastava operators with respect to k-symmetric points is studied. An equivalent convolution class condition and a sufficient coefficient condition for this class is obtained. It is proved that this coefficient condition is necessary for its subclass. As an application of coefficient condition, a necessary and sufficient hypergeometric inequality is also given. Further, results on bounds, extreme points, a convolution property and a result based on the integral operator are obtained.

This paper is concerned with the controllability of impulsive functional differential equations with infinite delay in a Banach space. Sufficient conditions for controllability are obtained by using the measures of noncompactness and Monch fixed point therem under the assumption of noncompactness of the evolution system.

The main objective of the present paper is to obtain certain new results in the aspects of Hypergeometric function. The results presented here are presumably new.

A set of vertices D in a graph G = ( V, E ) is a dominating set if every vertex of V – D is adjacent to some vertex of D. If D has the smallest possible cardinality of any dominating set of G, then D is called a minimum dominating set. A graph G is said to be Just excellent (JE), if it to each u ? V, there is a unique ? - set of G containing u. In this paper we have obtained the domatic number of the subdivision graph of a just excellent graph.

Harmonic eccentric indices were proposed analogously to Harmonic indices already known and used for many years. We defined Harmonic eccentric index as HEI (G)= ?_(uv?E (G))?2/(e_u+e_v ) .In his paper we have calculated Harmonic eccentric index for some particular chains which are fused with different types of fusing namely ?-type fusing,?-type fusing and ?-type fusing . In future we will on various Eccentric indices with the Hexagonal chain.