Anderson’s theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. γ-matrices are the only absolute objects of the Dirac equation. There are two ways of the γmatrices transformation: (1) γi is a 4-vector and ψ is a scalar, (2) γi are scalars and ψ is a spinor. ...

An overview of methods of pseudo-analysis in applications on important classes of nonlinear partial differential equations, occurring in different fields, is given. Hamilton-Jacobi equations, specially important in the control theory, are for important models usually with non-linear Hamiltonian H which is also not smooth, e.g., the absolute value, min or max operations, where it can not apply t...

The Ostrovsky equation is a modification of the Korteweg-de Vries equation which takes account of the effects of background rotation. It is well known that then the usual Korteweg-de Vries solitary wave decays and is replaced by radiating inertia-gravity waves. Here we show through numerical simulations that after a long-time a localized wave packet emerges as a persistent and dominant feature....

prediction of available vapor pressure data in the case of compounds containing c-h-o led to derivations and recommendations of standard equations for this property. the accuracy of vapor pressure estimations is essential to use as a basis to calculate acentric factor, thermal and equilibrium properties. in this study, according to the previous work, an accurate equation to estimate vapor press...

background: understanding customers has become an urgent topic for increasing competitiveness. the purpopse of  the study was to develop a qualitative dynamic attribute value model which provides insight into the customers' value for healthcare institute managers by conducting the initial open-ended questionnaire survey to select participants purposefully. methods: a total number of 427 questio...

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173-1573 K) and strain rates (10-4-10-2 s-1) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard e...

Spatiotemporal chaos in the complex Ginzburg–Landau equation is known to be associated with a rapid increase in the density of defects, which are isolated points at which the solution amplitude is zero and the phase is undefined. Recently there have been significant advances in understanding the details and interactions of defects and other coherent structures, and in the theory of convective a...

In this work we generate the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. Absolute error of the present method is compared to the absolute error of the two existing methods for two test problems. The method is also analy...