Moscow University Mathematics Bulletin
Moscow University Mathematics Bulletin is an international peer-reviewed journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics. The journal welcomes manuscripts from all countries.
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Vol 74, No 6 (2019)
- Year: 2019
- Articles: 8
- URL: https://journals.rcsi.science/0027-1322/issue/view/10061
Article
The Set of Geometric Medians for Four-Element Subsets in Lindenstrauss Spaces
Abstract
The connections between the set of geometric medians for a four-element set and the set of Steiner points for its three-element subsets in L1-predual spaces are studied. A Lipschitz selection for the mapping from quadruples of continuous functions on a Hausdorff compact space to the set of their geometric medians is presented.
215-220
Solution of the Cauchy Problem for the Heat Equation on the Heisenberg Group and the Wiener Integral
Abstract
The issues related to applications of functional integrals to evolution equations are studied. In particular, this is the problem of representation of solutions to the Cauchy problem for the heat equation in the three-parameter Heisenberg group H3(ℝ) in terms of Wiener integral in the space of trajectories from C[0, t] × C[0, t].
221-226
Search for Zeros of Functionals, Fixed Points, and Mappings Coincidence in Quasi-Metric Spaces
Abstract
The cascade search principle for zeros of (α, β)-search functionals and consequent fixed point and coincidence theorems are proved for collections of single-valued and set-valued mappings of (b1, b2)-quasimetric spaces. These results are extensions of previous author’s results for metric spaces. In particular, a generalization is obtained for the recent result on coincidences of a covering mapping and a Lipschitz mappings of (b1, b2)-quasimetric spaces.
227-234
Spectral Characteristics of the Sturm-Liouville Operator under Minimal Restrictions on Smoothness of Coefficients
Abstract
In this paper we consider the Sturm-Liouville problem in general form with Dirichlet boundary conditions under the minimal smoothness assumptions for the coefficients. We obtain the asymptotics formulas for eigenvalues and eigenfunctions of this problem. Under the assumption that the Lp-norm of eigenfunctions is equal to 1, we get uniform estimates of the Chebyshev norm.
235-240
Brief Communication
Quasiuniversal Boolean Automaton with Four Constant States
Abstract
The problem of realization of Boolean functions by initial Boolean automata with constant states and n inputs is considered. Initial Boolean automaton with constant states and n inputs is an initial automaton with output such that in all states the output functions are n-ary constant Boolean functions 0 or 1. An example of an initial Boolean automaton with the minimum number of constant states and n inputs realizing the maximum possible number of n-ary Boolean fonctions, where n ≥ 3, is constructed.
241-245
Asymptotic Stability of Equilibrium States for Carleman and Godunov-Sultangazin Systems of Equations
Abstract
One-dimensional systems of Carleman and Godunov-Sultangazin are studied for two and three groups of particles, respectively. These systems are a special case of the discrete Boltzmann kinetic equation. Theorems on existence of global solution to these systems for perturbations in the weighted Sobolev space are presented. Thus, an exponential stabilization to the equilibrium state is obtained.
246-248
Local Power of Kolmogorov’s and Omega-Squared Type Criteria in Autoregression
Abstract
A stationary AR(p) model is considered. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parametric estimates, an analog of the empirical distribution function is defined and tests of Kolmogorov’s and ω2 type are constructed for testing hypotheses on the distribution of innovations. The asymptotic power of these tests under local alternatives is obtained.
249-252
253-255