Realizing Quasiordered Sets by Subspaces of ‘Continuum-Like’ Spaces

Given an ordered set E and a topological space X, we say that E can be realized within X if there is an injection j from E into the class of (homeomorphism classes of) subspaces of X such that, for x, y in E, x y if and only if j(x) is homeomorphically embeddable into j(y). It is known, for instance, that transfinite induction demonstrates that every partially-ordered set of cardinality c (and some larger ones) can be realized within the real line. We explore aspects of the realizability problem, indicating, in particular, how to weaken the hypothesis on E from partial- to quasi-order, and seeking to isolate the characteristics of the real line that are relevant here.     

Construction of non-Gaussian surface measures by Malliavin’s method

We generalize the Airault-Malliavin theorem on the existence of surface measures on infinite-dimensional spaces with Gaussian measures on surfaces. We prove that the sets of capacities generated by Sobolev classes on infinite-dimensional spaces are dense. Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 377–388, March, 1999.     

Call for Paper The 6th International Conference on Fuzzy Information and Engineering (ICFIE’ 2012)

Short Communication

Call for Paper The 6th International Conference on Fuzzy Information and Engineering (ICFIE’ 2012) University of Mazandaran on 25–26 October 2012, Iran     

Numerical solutions of two-dimensional Burgers’ equations by lattice Boltzmann method

In this paper, the two-dimensional Burgers’ equations with two variables are solved numerically by the lattice Boltzmann method. The lattice Bhatnagar–Gross–Krook model we used can recover the macroscopic equation with the second order accuracy. Numerical solutions for various values of Reynolds number, computational domain, initial and boundary conditions are calculated and validated against exact solutions or other published results. It is concluded that the proposed method performs well.     

On the Stability of Eaton’s Characterization by the Properties of Linear Forms

We consider a population and a sample X ₁,X ₂,…,X _n of n independent observations drawn from this population. We assume that two suitably chosen linear statistics of X ₁,X ₂,…,X _n are given. The assumption that these statistics are identically distributed or have the same distribution as the monomial X ₁ can be used to characterize various populations. This is an object of the so-called characterization theorems. But if the assumptions of a characterization theorem are fulfilled only approximately, then can we state that the conclusion of this characterization is also fulfilled approximately? Theorems concerning problems of this type are called stability theorems. By Eaton’s theorem, if, under additional conditions, two linear statistics $(X_{1}+\cdots +X_{k_{1}})/k_{1}^{1/\alpha}We consider a population and a sample X ₁,X ₂,…,X _n of n independent observations drawn from this population. We assume that two suitably chosen linear statistics of X ₁,X ₂,…,X _n are given. The assumption that these statistics are identically distributed or have the same distribution as the monomial X ₁ can be used to characterize various populations. This is an object of the so-called characterization theorems. But if the assumptions of a characterization theorem are fulfilled only approximately, then can we state that the conclusion of this characterization is also fulfilled approximately? Theorems concerning problems of this type are called stability theorems. By Eaton’s theorem, if, under additional conditions, two linear statistics and have the same distribution as the monomial X ₁, then this monomial has a symmetric stable distribution of order α. The stability estimation in this theorem is investigated in the λ ₀-metric.      

Preface of the Special Issue on Symplectic Geometry and Mathematical Physics

<正>Symplectic geometry is a branch of differential geometry and differential topology and has its origins in the Hamiltonian formulation of classical mechanics. In the last few decades, symplectic geometry has experienced enormous progress and has had interactions with many other branches of mathematics, including enumerative geometry, low-dimensional topology, mathematical physics, Hamiltonian dynamics,     

Hypercyclicity and chaotic character of generalized convolution operators generated by Gel’fond-Leont’ev operators

Mathematical Notes - We consider generalized convolution operators generated by operators of Gel’fond-Leont’ev generalized differentiation. In this paper, we prove that any such...     

Approximation of almost Sahoo–Riedel’s points by Sahoo–Riedel’s points

In this paper, we present an extention of Hyers–Ulam stability of Sahoo–Riedel’s points for real-valued differentiable functions on [a, b] and then we obtain stability results of Flett’s points for functions in the class of continuously differentiable functions on [a, b] with f′(a) = f′(b).     

Numerical solution of the Burgers’ equation by local discontinuous Galerkin method

In this paper, the Burgers’ equation is transformed into the linear diffusion equation by using the Hopf–Cole transformation. The obtained linear diffusion equation is discretized in space by the local discontinuous Galerkin method. The temporal discretization is accomplished by the total variation diminishing Runge–Kutta method. Numerical solutions are compared with the exact solution and the numerical solutions obtained by Adomian’s decomposition method, finite difference method, B-spline finite element method and boundary element method. The results show that the local discontinuous Galerkin method is one of the most efficient methods for solving the Burgers’ equation. Even with small viscosity coefficient, it can get the satisfied solution.     

On solving systems of linear algebraic equations by Gibbs’s method

The paper presents an algorithm of approximate solution of a system of linear algebraic equations by the Monte Carlo method superimposed with ideas of simulating Gibbs and Metropolis fields. A solution in the form of a Neumann series is evaluated, the whole vector of solutions is obtained. The dimension of a system may be quite large. Formulas for evaluating the covariance matrix of a single simulation run are given. The method of solution is conceptually linked to the method put forward in a 2009 paper by Ermakov and Rukavishnikova. Examples of 3 × 3 and 100 × 100 systems are considered to compare the accuracy of approximation for the method proposed, for Ermakov and Rukavishnikova’s method and for the classical Monte Carlo method, which consists in consecutive estimation of the components of an unknown vector.     

Investigation of saddle-node and pitchfork bifurcations by Magnitskii’s stabilization method

We consider Magnitskii’s method in almost original form and prove a property of it, on the basis of which we suggest a way to use the method for stabilizing saddle cycles and cycles passing through a pitchfork bifurcation. By way of example, we consider some solutions of the four-dimensional Yang-Mills equations in the presence of the Higgs mechanism.