Modern Scientific Press

ABSTRACT: Let P(z):= Σ ⁿ_j=0(a_jz^j) is a polynomial of degree n. In this paper we prove some generalizations and extensions of Eneström Kakeya theorem by relaxing the hypothesis, assuming that k+ a_n≥ a_n-1 ≥….≥ a₁ ≥ a₀.

ABSTRACT: : In this article, we suggest a new modified ratio estimator of population mean of the study variable using the linear combination of known values of Co-Efficient of Kurtosis and Quartile deviation of the auxiliary variable. Mean square error and bias of the proposed estimator is calculated and compared with Yan & Tian [5] estimator. By this comparison, we demonstrate theoretically and numerically that the proposed estimator is more efficient than the existing one in all conditions.

ABSTRACT: This paper deals with an inventory model with non-instantaneous receipt under trade credit and time dependent demand rate. The purpose of this paper is to determine optimal replenishment policies under conditions of non-instantaneous receipt and trade credits. Mathematical formulation has been given for two different cases to represent closed form solution for finding the optimal order quantity, optimal cycle time, optimal receipt period and total relevant cost. Numerical examples are given to illustrate the proposed model. Finally sensitivity analysis of variation of parameters is also mentioned to validate the proposed model.

ABSTRACT: Natural heat convection for the flow of a third grade fluid through two parallel vertical infinite flat plates is considered. Similarity transforms combined with conservation laws are used to obtain the set of coupled nonlinear ordinary differential equations that govern the flow. Variation of Parameters Method (VPM) is used to determine the semi-exact solution to the problem. A numerical solution is also sought using Runge-Kutta (RK-4) method. Both the solutions are compared and an excellent agreement has been found. Effects of different dimensionless physical parameters on the flow are demonstrated graphically coupled with comprehensive discussions at the end of the article.

ABSTRACT: Let f(z) be a polynomial of degree n, then Rahman and Schmeisser introduced B_n-operators preserving zeros of a polynomial in unit circle and proved that if f(z) be a polynomial of degree n having no zeros in |z|<1, then for any B_n-operator T,

 |T[f](z)|≤1/2 M{|T[1](z)|+|T[φ](z)|},                          (|z|≥1)  

 where φ(z)=zⁿ and M=max_|z|=1|f(z)|. 

In this paper, we improve upon the above inequality and generalize a result due to Aziz and Dawood.

ABSTRACT: The fundamental characteristics of soliton and chaos in nonlinear equation are completely different. But all nonlinear equations with a soliton solution may derive chaos. While only some equations with a chaos solution have a soliton. The conditions of the two solutions are different. When some parameters are certain constants, the soliton is derived; while these parameters vary in a certain region, the bifurcation-chaos appears. It connects a chaotic control probably. Some possible meanings on the double solutions are discussed in mathematics, physics, particle theory and neurobiology. We propose a new type of soliton equation, whose solutions may describe some statistical distributions, for example, Cauchy distribution, normal distribution and student’s t distribution, etc. Further, from an extension of this type of equation we may obtain the exponential distribution, and the Fermi-Dirac distribution in quantum statistics. Moreover, by using the method of the soliton-solution, the nonlinear Klein-Gordon equation and nonlinear Dirac equations may derive Bose-Einstein and Fermi-Dirac distributions, respectively, and both distributions may be unified by the nonlinear equation.