WEAK TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF WALSH-KACZMARZ-MARCINKIEWICZ MEANS

The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.

Numerical Methods for Solving Turbulent Flows by Using Parallel Technologies

Parallel implementation of algorithm of numerical solution of Navier-Stokes equations for large eddy simulation (LES) of turbulence is presented in this research. The Dynamic Smagorinsky model is applied for sub-grid simulation of turbulence. The numerical algorithm was worked out using a scheme of splitting on physical parameters. At the first stage it is supposed that carrying over movement amount takes place only due to convection and diffusion. Intermediate field of velocity is determined by method of fractional steps by using Thomas algorithm (tridiaginal matrix algorithm). At the second stage found intermediate field of velocity is used for determination of the field of pressure. Three dimensional Poisson equation for the field of pressure is solved using upper relaxation method. Moreover various ways of geometrical decomposition for parallel numerical solution of three dimensional Poisson equations are investigated.

Inverse Problem of Astrodynamics

We consider the problem of determining the center of mass of an unknown gravitational body, using the disturbances in the motion of observed celestial bodies. In this paper an universal approach to obtain the approximate and stable estimate of problem solution is suggested. This approach can be used in other fields of Science. For example, it can be applied for investigation of interactions between fields of forces and elementary particles using known trajectories of elementary particles motions.

Uniform and L-convergence of Logarithmic Means of Walsh-Fourier Series

The （NSrlund） logarithmic means of the Fourier series of the integrable function f is：1/lnn-1∑k=1Sk（f）/n-k, where ln：=n-1∑k=11/k.In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L^1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm.

A necessary and sufficient condition for a surface sum of two handlebodies to be a handlebody

The main results of the paper are that we give a necessary and sufficient condition for a surface sum of two handlebodies along a connected surface to be a handlebody as follows:(1)The annulus sum H=H1∪AH2 of two handlebodies H1 and H2 is a handlebody if and only if the core curve of A is a longitude for either H1 or H2;(2)Let H=H1∪Sg,b H2 be a surface sum of two handlebodies H1 and H2 along a connected surface S=Sg,b,b 1,ni=g(Hi)2,i=1,2.Suppose that S is incompressible in both H1 and H2.Then H is a handlebody if and only if there exists a basis J={J1,...,Jm}with a partition(J1,J2)of J such that J1 is primitive in H1 and J2 is primitive in H2.

On the Local Solvability and Stability for the Inverse Spectral Problem of the Generalized Dirichlet–Regge Problem

For the generalized Dirichlet–Regge problem with complex coefficients,we prove the local solvability and stability for the inverse spectral problem,which indicates an improved result of the previous work([Journal of Geometry and Physics,159,103936(2021)]).

A NUMERICAL METHOD FOR THE SIMULATION OF FREE SURFACE FLOWS OF VISCOPLASTIC FLUID IN 3D

In this paper we study a numerical method for the simulation of free surface flows of viscoplastic （Herschel-Bulkley） fluids. The approach is based on the level set method for capturing the free surface evolution and on locally refined and dynamically adapted octree cartesian staggered grids for the discretization of fluid and level set equations. A regu- larized model is applied to handle the non-differentiability of the constitutive relations. We consider an extension of the stable approximation of the Newtonian flow equations on staggered grid to approximate the viscoplastic model and level-set equations if the free boundary evolves and the mesh is dynamically refined or coarsened. The numerical method is first validated for a Newtonian case. In this case, the convergence of numerical solutions is observed towards experimental data when the mesh is refined. Further we compute several 3D viscoplastic Herschel-Bulkley fluid flows over incline planes for the dam-break problem. The qualitative comparison of numerical solutions is done versus experimental investigations. Another numerical example is given by computing the freely oscillating viscoplastic droplet, where the motion of fluid is driven by the surface tension forces. Altogether the considered techniques and algorithms （the level-set method, compact discretizations on dynamically adapted octree cartesian grids, regularization, and the surface tension forces approximation） result in efficient approach to modeling viscoplastic free-surface flows in possibly complex 3D geometries.

On the Divergence of N(?)rlund Logarithmic Means of Walsh-Fourier Series

It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.

Chaotic Driven Tunneling in Rectangular Double-Well

We consider a charged particle confined in a one-dimensional rectangular doublewell potential,driven by an external periodic excitation at frequencyΩand with amplitude A.We find that there is the regime of the parametric resonance due to the modulation of the amplitude A at the frequencyωprm,which results in the change in the population dynamics of the energy levels.The analysis relies on the Dirac system of Hamiltonian equations that are equivalent to the Schr¨odinger equation.Considering a finite dimensional approximation to the Dirac system,we construct the foliation of its phase space by subsets F_(ab)given by constraints a≤N_(0)≤b on the occupation probabilities N0 of the ground state,and describe the tunneling by frequenciesνab of the system’s visiting subsets F_(ab).The frequenciesνab determine the probability density and thus the Shannon entropy,which has the maximum value at the resonant frequencyω=ωprm.The reconstruction of the state-space of the system’s dynamics with the help of the Shaw-Takens method indicates that the quasi-periodic motion breaks down at the resonant valueωprm.