One of the central problems of mathematics in the second half of the 19th century and at the beginning of the 20th century was the problem of uniformization of Riemann surfaces. The classics, Klein [1] and Poincaré [2], associated it with studying second-order ordinary differential equations with regular singular points. Poincaré proposed another approach to the uniformization problem [3]. It c...

We develop a level set method for the computation of multi-valued physical observables (density, velocity, energy, etc.) for the high frequency limit of symmetric hyperbolic systems in any number of space dimensions. We take two approaches to derive the method. The first one starts with a decoupled system of an eikonal eikonal for phase S and a transport equations for density ρ: ∂t S+H(x,∇S) = ...

Starting from the known expression for the three-point correlation functions for Liouville exponentials with generic real coefficients at we can prove the Liouville equation of motion at the level of three-point functions. Based on the analytical structure of the correlation functions we discuss a possible mass shell condition for excitations of noncritical strings and make some observations co...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

The quantum-classical Liouville equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville e...

In this paper, we obtain a suitable mathematical model for the seismic response of dams. By using the shear beam model (SB model), we give a mathematical formulation that it is a partial differential equation and transform it to the Sturm-Liouville equation.

Abstract: New physical principle for Monte-Carlo simulations has been introduced. It is based upon coupling of dynamical equations and the corresponding Liouville equation. The proposed approach does not require a random number generator since randomness is generated by instability of dynamics triggered and controlled by the feedback from the Liouville equation. Direct simulation of evolutionar...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix deformation. The corresponding deformed density matrix, which is called density pro-matrix is given explicitly. It properties have been investigated as well as som...

In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix deformation. The corresponding deformed density matrix, which is called density pro-matrix is given explicitly. It properties have been investigated as well as som...