Skew-symmetric differential forms possess properties that enable one to carry out a qualitative investigation of the equations of mathematical physics and the foundations of field theories. In the paper we call attention to a unique role in field theory of closed exterior skew-symmetric differential forms, which correspond to conservation laws for physical fields (to conservative quantities). At the same time, it was shown that such closed exterior forms can be derived from skew-symmetric differential forms, which follow from the mathematical physics equations describing material media such as thermodynamic, gas-dynamic, cosmic media. This points a connection the field theory equations with the mathematical physics equations. Such connection discloses the properties and specific features of field theory.Full article

In this paper we present a new classes of solutions for the Einstein-Maxwell system of field equations in a spherically symmetric spacetime under the influence of an electric field considering the MIT bag model equation of state with a particular form the metric potential that depends on an adjustable parameter. The obtained solutions can be written in terms of elementary functions, namely polynomials and algebraic functions. The obtained models satisfy all physical properties expected in a realistic star. The results of this research can be useful in the development and description of new models of compact structures.Full article

With respect to the exciton moving in the two-dimensional quantum well, the paper presents a scheme which can rigorously calculate out the binding energy of the exciton in the two-dimensional semiconductor quantum well by simply using the relation $\left|z_e-z_h\right|=\rho \tan \alpha$, which is much simpler than the complex calculation of Ref.[1-2]. Concerning the calculation result eq.(13), the paper discusses the results for two significant cases of $\left|z_e-z_h\right|$<<$\rho$and $\left|z_e-z_h\right|\to \infty$.Full article

The convection-diffusion equation is of primary importance in understanding transport phenom-ena within a physical system. However, the currently available methods for solving unsteady convection-diffusion problems are generally not able to offer excellent accuracy in both time and space variables. A procedure was given in detail to solve the one-dimensional unsteady convec-tion-diffusion equation through a combination of Runge-Kutta methods and compact difference schemes. The combination method has fourth-order accuracy in both time and space variables. Numerical experiments were conducted and the results were compared with those obtained by the Crank-Nicolson method in order to check the accuracy of the combination method. The anal-ysis results indicated that the combination method is numerically stable at low wave numbers and small CFL numbers. The combination method has higher accuracy than the Crank-Nicolson method.Full article