A generalized Dilworth and Gleason theorem

The theorem of R.P. Dilworth and A.M. Gleason is a generalization of a Cantor theorem. We propose and proof the generalized Dilworth and Gleason theorem for functors with codomain $K/D$.

The estimates of the Schatten-Neumann norms of one class of integral operators

The article considers an integral operator acting from Lebesque spaces to Lorentz spaces. The conditions are found under which the compact operator belongs to the Shatten-Neumann classes.

Tropical sequences associated with the Gale-Robinson sequences

In this paper, tropical sequences associated with some Gale-Robinson sequences are calculated.

Covariant hydrodynamics of Hamiltonian systems

The theory of hydrodynamic reduction of non-autonomous Hamiltonian mechanics (V. Kozlov, 1983) is presented in the geometric formalism of bundles over the time axis R. In this formalism, time is one of the coordinates, not a parameter; the connections describe reference frames and velocity fields of mechanical systems. The equations of the theory are presented in a form that is invariant with respect to time-dependent coordinate transformations and the choice of reference frames.

Parallel computing of Edwards–Anderson model

An algorithm for parallel exact calculation of the ground state of a two-dimensional Edwards–Anderson model with free boundary conditions is given. The running time of the algorithm grows exponentially as the side of the lattice square increases. If one side of the lattice is fixed, the running time grows polynomially with increasing size of the other side. The method may find application in the theory of spin glasses, in the field of quantum computing. Performance data for the bimodal distribution is given. The distribution of spin bonds can be either bimodal or Gaussian. The method makes it possible to compute systems up to a size of 40x40.

Periodic ultradiscrete plane transformation with a period of 12

V.A. Bykovskii constructed a new periodic ultradiscrete plane transformation with a period of 12. In his work only the idea of proving this periodicity was proposed. We provide a complete and detailed proof of this statement.

The Fekete-Szego problem by a variational method

The article is devoted to the well-known Fekete and Szego problem. The paper investigate the problem in sufficient detail using some new observations by the classical method of internal variations, developed at the Tomsk School of Complex Analysis. One particular case is considered. We carried out complete qualitative analysis of the functional-differential equation relative boundary mapping. We completely solved the problem for the real parameter.

Heat flux structure for Ornstein–Uhlenbeck particles of a one-dimensional harmonic chain

A one-dimensional harmonic chain of N particles is considered, located between two thermal reservoirs (Ornstein–Uhlenbeck particles). An exact solution is constructed for the system of equations describing the dynamics of the system.

Approximate solution of the Signorini problem by the finite element method in three-dimensional space

The finite element method is usually used for two-dimensional space. The paper investigates the finite element method for solving the Signorini problem in three-dimensional space.

On two relations characterizing the golden ratio

V.G. Zhuravlev found two relations associated with the golden ratio: $\tau=\frac{1+\sqrt{5}}{2}$: $[([i\tau]+1)\tau]=[i\tau^2]+1$ and $[[i\tau]\tau]+1=[i\tau^2]$. We give a new elementary proof of these relations and show that they give a characterization of the golden ratio. Further we consider satisfability of our relations for finite sets of $i$-s and establish some forcing property for this situation.