Features of mappings leading to a central field

For a mechanical system with two degrees of freedom, it is shown that the condition of zeroing the Jacobian map depended on the interaction potential selects a central field that ensures this condition fulfillment. It has been hypothesized that, in the general case, the features of coordinate mappings lead to potentials that admit the existence of an motion integral additional to the energy.

Integration methods of mixed-type stochastic differential equations with fractional Brownian motions

In the present, article new methods of exact integration of mixed-type stochastic differential equations with standard Brownian motion, fractional Brownian motion with the Hurst exponent H> 1/2 and the drift term have been constructed. Solutions of these equations are understood in integral sense where, in turn, the standard Brownian motion integral is the Ito integral and the fractional Brownian motion integral is the pathwise Young integral. The constucted integration methods can be attributed to two types. The first-type methods are based on reducing the equations to simpler equations, in particular – to the simplest equations and the linear inhomogeneous equations. In the article, necessary and sufficient conditions of reducing the equations applicable to one-dimensional equations have been obtained and the examples particularly covering the stochastic Bernoulli-type equations have been given. The second-type method is based on going to the Stratonovich equation and is applicable to multidimensional equations. In addition to the mentioned integration methods, the analogues of the differential Kolmogorov equation have been obtained for mathematical expectations and the solution probability density, assuming that coefficients of the mixed-type stochastic differential equation generate commuting flows.

Komunikasi Politik Mohammad Natsir

This study aims to reveal aspects of political communication made by M. Natsir when formulating, socialize, until the date of the adoption by MPRS integral motion. This study uses qualitative descriptive approach, so as to reveal the fact that more comprehensive. This study has revealed a struggle that is not simply how a motion integral before being accepted and confirmed by parliament. M. Natsir when trusted to formulate make the concept of unification of Indonesia in response to the threat of disintegration, he conducted political lobbies are quite long, before finally when dipidatokan no interruptions and obstacles of other MPs. These findings make clear that aspects of political communication becomes very important in reading a historical fact related to the socialization integral motion Natsir.

CORRELATION IDENTITIES AND APPLICATION

General correlation identities are derived in a unified way using the quantum analysis,1–4 which include the well-known classical correlation identities5–7 such as the Ising correlation identities.5,6 In particular, quantum correlation identities are applied to the Heisenberg models and the transverse Ising model with local constants of motion. Integral identities are also presented in the spirit of the Gauss–Manin connection and they are applied to derive the generalized Bernoulli equation on the pressure and energy of ideal quantum gasses. There are many applications to condensed matter physics, which will be summarized in the present article together with an integrated list of papers on such applications in order to show how useful these correlation identities are.