Journal of Applied & Computational Mathematics

This paper gives a proof of the following result: if η(ρ)=0 and R(ρ)>0, then: η is the Dirichlet eta function defined for R(s)>0 by with

In this paper, we analyse the problem of identification of the pollution term in a heat system when the dynamics of the state is governed by a parameterized operator. In this way, we introduce a notion of average sentinel. First, we prove the existence of such sentinels introduced by Lions by solving a problem of null average controllability given by Zuazua. Secondly, we identify the information for pollution terms by using the average sentinel.

Theory of artificial enabled social engineering attacking risk factors are employed in this study to determine the impact that disturbed the personal productivity of higher learning institute of the user towards the AI enable SoE attacking. Five independent variable which are threat, vulnerability, valuation, countermeasure and personal disturbance factors using in this paper. Moreover using as an indicator in determining disturbance of personal productivity in a higher learning institute. Since multiple regression by using Structural Equation Modelling –Partial Least Square (SEM-PLS) is used to examine the collection of data by a questionnaire which is relevant with AI enable SE attacking risk. And the resulting point out three independent variable significantly influences the personal productivity in higher learning institute. As a matter of fact this study concludes that the foremost influence factor on disturbance of personal productivity in higher learning institute towards the AI enables SoE attacking risk factors such as threat, vulnerability, valuation and countermeasure. This study contributes to introductory study but vibrant understanding in stimulating the higher learning institute to become a worldwide institution.

The main aim of this paper is to understand the information to numerical computing. In this paper we solve some examples of numerical computing. The numerical computational techniques are the technique by which mathematical problems are formulated and they can be solved with arithmetic operations. Those techniques are basically numerical methods. Numerical method supports the solution of almost every type of problem. The numerical methods are classified depending upon the type of the problem.

The normal distribution is one of the most popular probability distributions with applications to real life data. In this research paper, an extension of this distribution together with Weibull distribution called the Weimal distribution which is believed to provide greater flexibility to model scenarios involving skewed data was proposed. The probability density function and cumulative distribution function of the new distribution can be represented as a linear combination of exponential normal density functions. Analytical expressions for some mathematical quantities comprising of moments, moment generating function, characteristic function and order statistics were presented. The estimation of the proposed distribution’s parameters was undertaken using the method of maximum likelihood estimation. Two data sets were used for illustration and performance evaluation of the proposed model. The results of the comparative analysis to other baseline models show that the proposed distribution would be more appropriate when dealing with skewed data.

The problem of uncertainty claim pricing using distortion operators is considered in this research paper. This approach was first developed in insurance pricing, where the original distortion function was defined in terms of the normal probability distribution. This approach is generalized by using a distortion that is based on the Weibull distribution in this research paper. The Weibull family allows for heavier and skewed tail because it is so flexible that other statistical distributions can be recovered from it by change of parameters. The problem of uncertainty claims has been extensively studied for non-Gaussian model in which the formula was derived for the normal Inverse Gaussian distribution Asset pricing. It is shown in this paper how Weibull based distortion function can used to derive the formula for asset pricing of uncertainty future returns of a risky asset. The risk measure for the incurred risk modelled by the Weibull variables was derived and it was shown that it follows the power law.

The boundary element method is a numerical computational method of solving partial differential equations which have been formulated as integral equations. It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture mechanics. The method can be seen as a weighted residual method for solving partial differential equations, characterized by choosing an appropriate fundamental solution as a weighting function and by using the generalized Green’s formula for complete transfer of one or more partial differential operators on the weighting function. Time discretization approach requires replacing the partial derivative of the equation that involves time with a finite difference approximation, and the resulting equation now has one variable x with t becoming a constant. In this paper the advection-diffusion equation has been formulated using time discretization approach of the boundary element method. The fundamental solution of the elliptic operator has been constructed, and test examples provided.

General considerations about this (3-n)d algebra.

In this work we show that it is possible to calculate the fractional integrals and derivatives of order (using the Riemann-Liouville formulation) of power functions (t-*)β with β being any real value, so long as one pays attention to the proper choice of the lower and upper limits according to the original functions domain. We, therefore, obtain valid expressions that are described in terms of function series of the type (t-*)± α+k and we also show that they are related to the famous hypergeometric functions of the Mathematical-Physics.