Physical Mathematics

We propose a classical analogue of the vertex algebra in the context of classical integrable field theories. We use this fundamental notion to describe the auxiliary function of the linear auxiliary problem as a classical vertex operator. Then using the underlying algebra satisfied by the auxiliary function together with the linear auxiliary problem we identify the local integrals of motion, which by construction are in involution. The time components of the Lax pair are also identified in terms of the classical vertex operators. Systems in the presence of point like defects as well as systems on the semi-infinite line are investigated. Specific examples associated to the classical Yangian and twisted Yangian are also presented

The diesel generator is the only way used for the production of energy in isolated sites and remote areas, Saharan Africa of the paid Algeria. Our goal is study and designs a power plant Production of mobile autonomous electricity, hybrid plant, which combines two renewable energy sources (wind, photovoltaic) and a diesel engine backup with storage. The objective of the work is the first step in our goal. We have simulated the conversion wind turbine by adopting the continuous model Converters. To control the DC bus voltage and the exchange of active and reactive powers, we have implanted proportional correctors integral.

In this paper the behaviour of the cumulative number distribution and the maximum values of cumulative number in an event of all charged particles (protons,π±-mesons) produced in p12C-interctions at 4.2 A GeV/c from experimental and simulation data has been analysed. One could see four different regions in the cumulative number distributions for protons in which the last region has cumulative number greater than one which correspond to cumulative region. Similarly one could see two and three different regions for negative and positive pions respectively but there is totally absence of the cumulative area for negative pions but there are few positive pions in the cumulative area. The simulation data obtained from Cascade code cannot describe satisfactorily the distributions of the cumulative number for protons and positive and negative pions but in case of particles with maximum values of cumulative number cascade code can describe the behaviour of cumulative number distribution well.

This paper, I have made an investigation on a stellar model with Kramer’s Opacity and negligible abundance of heavy elements. I have determined the structure of a star with mass 2.5⊗ M, i.e., the physical variables like pressure, density, temperature and luminosity at different interior points of the star. Discussed about some equation of structure, mechanism of energy production in a star and energy transports in stellar interior and then I solved radiative envelope and convective core by the matching or fitting point method by C Programming language.

In this paper, convergence analysis of a finite difference method for the linear second order boundary value ordinary differential equation is determined by investigating basic key concepts such as consistency and stability by using the maximum norm

The steady flow of an incompressible second grade viscoelastic fluid above a rotating disk that is stretching in radial direction is studied. The Coriolis and centrifugal forces are taking into account. The constitutive non-linear partial differential equations are transformed to system of ordinary differential equations. For analysis Homotopy Analysis Metod (HAM) BVPh2.0 package is used. The effects of viscoelastic parameter α, rotating parameter β, stretching parameter γ, Coriolis and centrifugal forces on the velocity component are discussed.

In this work, we are compared between the theory of thermoelasticity with two relaxation times and the theory of thermoelasticity without energy dissipation. To a half-space overlaid by a thick layer of a different material. The upper surface of the layer is taken to be traction free and is subjected to a constant thermal shock. We are used Laplace transform to eliminate the time variable t. The inverses Laplace transforms are obtained by using a numerical method based on Fourier expansion techniques comparison between the predictions of both theories are discussed. Numerical results are computed for the temperature, displacement and stress distributions. The numerical results are represented graphically

The paper emphasizes an approach to solve complex q-exponential integrals by an implication of Binomial expansion along with some specific conditions on the integral limits and sets a relation between the limits which were used such as the maximum energy of the electrons and the chemical potential. The integral results which yielded the average energy and the effective electron concentration which proved out to be essential in order to calculate the average velocity of the electrons and the electrical conductivity of a metallic wire while taking consideration of the Drude’s model. The dependency on temperature of these parameters with the variation of Tsallis factor renders anomalous results depicting the Nonextensive Critical Temperature value to be 20 K and its importance has been mentioned in this paper along with the dependency of these parameters on certain regions consisting of Tsallis factor which follows subextensivity and superextensivity and infers a point known to be as Maximum Entropy Limiting Factor.

In this paper, the stability region of the 2-point diagonally implicit super class of block backward differentiation formula with off-step points is to obtain and demonstrate its suitability for solving stiff ODEs. The stability region must cover the entire negative half-plane for the method to be suitable for solving stiff differential equations, analysis also shows that the method is zero stable.