Journal of Advances in Mathematics and Computer Science

In this paper, the test of unit root for bounded AR (2) model with constant term and dependent errors has been derived. Asymptotic distributions of OLS estimators and t-type  statistics under different tests of hypotheses have been derived. A simulation study has been established to compare between different tests of the unit root. Mean squared error (MSE) and Thiel's inequality coefficient (Thiel’s U) have been considered as criteria of comparison.

An innovative approach that treats prime numbers as raw experimental data making use of experimental/computational mathematics and the approximation methods is presented in order to get advanced and more exact formulations of the canonical form  =    being the prime value and  its counter. The use of many different functions - such as the inverse of the modified chi-square function  with its three parameters ,  and , the function  with the ad-hoc  values being  , the function , the function , the harmonic series  and its approximation by Euler and so on - as fit functions of finite sets i.e. sequences of prime numbers leads to induction algorithms and to new relationships of the kind  though within the approximations of the calculations with all the estimations better than that of the standard formulation . In such a manner, refined formulations with higher precisions are got showing that there are many ways to treat the finite sequences of prime numbers. Comparisons among the various methods are made in order to find the best formulation of a new and more refined relationship in a closed form that can be valid to find the most approximate value of a prime starting from its counter in the finite case.

In this research introduces four different mathematical designs for the coordination and three-stage profit optimization models of agricultural products in Bangladesh. This research, we occupied that the three types of market players are coordinated by mutually sharing all kind of information related to their business. To enrich a Mixed Integer Linear Programming (MILP) model and explore the circumstance of production receptivity is inadequate for the manufacturer. The manufacturers will coverage these deficits by external sources, which decided very beginning of the business contract. This is very significant foreword in deciding so as to alleviate these challenges and to enlarge the method representation and distinct benefit of the Supply Chain Network (SCN). The coordinated system in alliance with the market players has been projected to realize the best result. The formulated MILP models optimize the maximum profit and also to optimize the best production distribution center which satisfy most of the customer demand. This paper, the formulated MILP model were solved by a mathematical programming language (AMPL) and we get the results by using appropriate solver MINOS. Analyzed a numerical example for some important parameters has been deployed to validate our proposed models. We get the results after coordination the individual profits could be increased, in the same time end user cost price decrease.

The inverse problem for determination of parameters related to the support and/or functions describing the intensity of coefficient and sources in models based strongly elliptic second order systems is posed with Cauchy data over specification at boundary. This stablish a set of various boundary value problems associated with the same group of unknown parameters. A Lipschitz boundary dissection is used for decomposing each Cauchy data into pairs of complementary mixed boundary values problems. The concept of Calderon projector is introduced as a tool to check the consistency of the Cauchy data and to demonstrate the equivalence of these two problems. This lets you define a discrepancy function to measure the distance between the solutions of problems obtained by dissecting Lipschitz Cauchy data. This discrepancy appears as a consequence of inadequate parameters values in the constitutive relations. For Cauchy noisy data, the difference between these solutions would be small if the parameters used in the solution are correct. The methodology we propose explores concepts as Lipschitz Boundary Dissection, Complementary Mixed Problems with trial parameters and Internal Discrepancy fields. Differentiable and non-differentiable optimizations algorithms can then be used in the reconstruction of these parameters simultaneously. Numerical experiments are presented.

After a careful study of some works of servaral authors on affine immersion of co-dimension one [1], co-dimension two [2], co-dimension three [3] and co-dimension four [4], we extend some of thier fundamental equations to affine immersion of genaral co-dimension p. Furthermore, we extend some theorem of Frank Dillen at el in [5] to affine immersion of general co-dimension and obtain the divisibility of the cubic forms by the second fundamental forms.