Applied Mathematics

Primes are the building blocks of integer universe. Prime numbers plays a major role in number theory. This paper is a detailed survey on prime numbers.This describes different types of primes and some testing methods. In addition to that, we have constructed MATLAB programs using popular primality tests to determine a given positive integer is prime or not. Further, this concises the definitions regarding prime numbers, history of prime numbers, distribution of prime numbers, some mathematical occurrences and open questions concerning prime numbers. Moreover, the usage of primes in nature and in the real life has been considered.

Dufour effect on unsteady free convection MHD flow past a moving vertical plate through porous medium with variable temperature and constant mass diffusion is studied here. The Laplace transform technique has been used to find the solutions for the velocity, temperature and concentration. The results obtained are discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof number, Prandtl number, permeability parameter, the Hartmann number, Schmidt number, Dufour number, time and inclination of magnetic field. The numerical values of Skin-friction have been tabulated.

This paper is mainly concerned with the existence of mild solutions for some partial neutral functional integrodifferential equations with state-dependent delay in Banach spaces. The results are obtained by using resolvent operators and Krasnoselski-Schaefer’s type fixed point theorem.

The Fourier-Finite Mellin transform is a variant of the Fourier transform; however, it certainly does not have as glorious or as predominant a history as the Fourier transform. This Fourier-Finite Mellin transform is used to correct various optical distortions, including noise in lenses, it is also used in radar classification of ships. Theoretically, the Fourier-Finite Mellin transform should provide a truly translation, rotation and scale invariant measure of an image. Fourier-Finite Mellin transform is frequently used in content-based image retrieval and digital image watermarking.The Object of the present paper is to prove an Inversion theorem for distributional Fourier-Finite Mellin transform with the help of two lemmas which are also given in this paper.

A numerical analysis is carried out to study the effects of mass transfer and thermal radiation on a steady boundary layer flow of a viscous incompressible electrically conducting fluid with uniform transverse magnetic field and variable free stream near a stagnation point on a non-conducting stretching sheet through a porous medium in presence of variable thermal conductivity, heat generation and viscous dissipation. The equations of continuity, momentum, energy and mass are transformed into ordinary differential equations and solved numerically using shooting method. The velocity, temperature and concentration distributions are discussed numerically and presented through graphs. Skin-friction coefficient, Nusselt number and Sherwood number at the sheet are derived, discussed numerically and their numerical values for various values of physical parameters are presented through tables.

In this paper, properties of fuzzy extremally disconnected spaces and fuzzy submaximal spaces are discussed.

We study composition operators between higher order weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Under a mind condition we show that a composition operators Cj is compact on the higher order weighted Bergman spaces and Hardy spaces of the open unit ball in n C if and only.

The paper presented a method with an improvement crossover operation, reserve policy and Niche technology to adjust the algorithm, which made algorithm be avoided to converge prematurely, and prevented algorithm falling into best local solutions. Through case emulates, it was found that it had good performance. Finally, the principle of convergence was proved.

Let G (V, E) be a simple, finite, undirected connected graph. A dominating set S Í V is called a locating dominating set, if for any two vertices v, w Î V – S, N(v) Ç S ¹ N(w) Ç S. A locating dominating set S Í V is called a co – isolated locating dominating set, if there exists atleast one isolated vertex in . gDcild is the number of minimum co – isolated locating dominating set of a graph G. The co – isolated locating domination number gcild is the minimum cardinality of a co – isolated locating dominating set. In this paper average co – isolated domination number ?agcild(G) is defined and, ?cild and ?agcild are obtained for binomial trees, binary trees, ternary trees and complete c – ary trees. Also the bounds for ?agcild(G) are found.

An exact solution of unsteady flow past a parabolic starting motion of an infinite vertical plate with variable temperature and uniform mass diffusion, in the presence of homogeneous chemical reaction of first order has been studied. The plate temperature is raised linearly with time and the concentration level near the plate is raised uniformly. The solutions for the velocity, temperature and concentration fields are solved using Laplace-transform technique. The effect of velocity profiles are studied for the physical parameters like chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time. It is observed that the velocity increases with increasing values the thermal Grashof number or mass Grashof number. The trend is just reversed with respect to the chemical reaction parameter or the Schmidt number.