Diagrammatic approach to gas-liquid phase transition in statistical theory

The lattice gas system is studied. In frameworks of statistical mechanics, it is proposed the analytic algorithm of approximations construction when pressure calculating. Algorithm is built on the basis of virial expansion using special small parameter ν. The parameter is introduced by the prescription of the corresponding ν-power weight to each Mayer diagram without contact vertexes. The obtained formulas describe the gas-liquid phase transitio

Isotropic covariant tensors in Rn

Statements about the dimension d(r,n) of L(n)r and basis tensors in them are proved. It is shown that multiplicative δ-tensors are linear dependent at sufficiently large value of difference r−2n and in this case dimL(n)r<(r−1)!! is valid when r is eve

Graphs and algebras of symmetric functions

We describe an algebraic technique for operating with power series whose coefficients arerepresented by integrals of symmetric functions fn defined on the Cartesian powers Ωⁿ of a set Ω with a measure

Probability distributions unimodality of nite sample extremes of independent Erlang random variables

The theory of probability distributions of extremes of random variables samples and the theory of the probability distributions of extreme values of trajectories of stationary random processes which is connected with it have arisen on the basis of the necessity to find some answers of quite practical questions. Now, this theory has extracted into a separate direction of research in the probability theory. In the framework of this scientific direction, the theory of probability distributions of extremes of independent random variables sequences occupies a special plac