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## On Necessary Conditions of Finite-Valued Random Variable Algebraic Approximation

Lobachevskii Journal of Mathematics. 2021. Vol. 42. No. 1. P. 217-221.

Yashunsky A.

We consider transformations of random variables on finite sets by algebraic operations. A system of operations is said to be approximation complete if any random variable may be approximated with arbitrary precision by applying the given operations to mutually independent identically distributed random variables whose distributions have no zero components. We establish some necessary conditions for a function system to be approximation complete and construct examples of approximation incomplete systems.

Yashunsky A., Journal of Applied and Industrial Mathematics 2020 Vol. 14 No. 3 P. 581-591

We consider the transformations of independent random variables over a linearly ordered finite set (a chain) by the join and meet operations. We investigate the possibility of approximating an arbitrary probability distribution on a chain by means of a (possibly iterated) application of the join and meet operations to independent random variables with distributions from ...

Added: July 6, 2021

Yashunsky A., Algebra Universalis 2019 Vol. 80 No. 1 (5) P. 1-16

We consider the problem of approximating distributions of Bernoulli random variables by applying Boolean functions to independent random variables with distributions from a given set. For a set B of Boolean functions, the set of approximable distributions forms an algebra, named the approximation algebra of Bernoulli distributions induced by B. We provide a complete description ...

Added: September 9, 2020

Yashunsky A., Doklady Mathematics 2020 Vol. 102 No. 1 P. 301-303

We consider the conditions for a finite set with a given system of operations (a finite algebra) to be subject to a probability limit theorem, i.e., arbitrary computations with mutually independent random variables have value distributions that tend to a certain limit (limit law) as the number of random variables used in the computation grows. ...

Added: July 6, 2021

Polyakov N. L., Шамолин М. В., Вестник Самарского государственного университета. Естественнонаучная серия 2013 № 6(107) С. 61-73

We give an effective description of symmetric closed classes of discrete functions preserving any unary predicate. ...

Added: October 5, 2018

Shvedov A. S., Математика в высшем образовании 2020 Т. 18 С. 109-114

It is clear how to tell students of mathematical specializations what an expectation of a random variable is. These students know Lebesgue integral and Stieltjes integral. Other students know only Riemannian integral often. It is generally accepted to give two different definitions in this case. An expectation of a discrete random variable is defined as ...

Added: January 12, 2021

Averboukh Y., SIAM Journal on Control and Optimization 2016 Vol. 54 No. 5 P. 2629-2649

The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a model game. The dynamics of the model game differs from the original one. The general result applied ...

Added: April 17, 2020

Silvanovich O. V., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2018 Vol. 51 No. 3 P. 267-275

For more than a century, the constructive description of functional classes in terms of the possible rate of approximation of its functions by means of functions chosen from a certain set remains among the most important problems of approximation theory. It turns out that the nonuniformity of the approximation rate due between the points of ...

Added: November 26, 2018

Ulyanov V.V., Theory Probability and its Applications 2016 Vol. 60 No. 2 P. 325-336

This paper deals with different properties of polynomials in random elements: bounds for characteristic functionals of polynomials, a stochastic generalization of the Vinogradov mean value theorem, the characterization problem, and bounds for probabilities to hit the balls. These results cover the cases when the random elements take values in finite as well as infinite dimensional ...

Added: March 12, 2017

Polyakov N. L., Шамолин М. В., Итоги науки и техники. Современная математика и ее приложения. Тематические обзоры 2020 Т. 174 С. 46-51

In the paper, combinatorial theorems relating to the theory of social choice are obtained.These theorems describe general conditions under which theproblem on the preserving the preferencesetDby an arbitrary aggregation rulefand the problem on the compatibility of the preference setDwith a pair(f,C)can be reduced to similar problems for two specific aggregation rules: the majority rulemaj and ...

Added: October 13, 2020

Victor M. Buchstaber, Nikolay Yu. E., Structural Chemistry 2016 Vol. 28 No. 1 P. 225-234

We study the well-known problem of combinatorial classification of fullerenes. By a (mathematical) fullerene we mean a convex simple three-dimensional polytope with all facets pentagons and hexagons. We analyse approaches of construction of arbitrary fullerene from the dodecahedron (a fullerene C 20). A growth operation is a combinatorial operation that substitutes the patch with more facets and ...

Added: June 17, 2021

Polyakov N. L., Shamolin M. V., Doklady Mathematics 2014 Vol. 89 No. 3 P. 290-292

A complete classification of symmetric sets of choice functions with the Arrow property is obtained. ...

Added: October 5, 2018

Zhuk D., Journal of Multiple-Valued Logic and Soft Computing 2015 Vol. 24 No. 1-4 P. 251-316

The lattice of all clones of self-dual functions in three-valued logic is described in the paper. Even though this lattice contains a continuum of clones, a simple description was found. Using this description different properties of the lattice and of the clones were derived. Pair wise inclusion of the clones into each other was described, ...

Added: June 15, 2020

Protasov V., Conti C., Charina M. et al., Numerische Mathematik 2017 Vol. 135 No. 3 P. 639-678

In this paper, we study scalar multivariate non-stationary subdivision
schemes with integer dilation matrix M and present a unifying, general approach
for checking their convergence and for determining their Hölder regularity (latter in
the case M = mI,m ≥ 2). The combination of the concepts of asymptotic similarity
and approximate sum rules allows us to link stationary and non-stationary ...

Added: February 7, 2018

Polyakov N. L., Working papers by Cornell University. Series math "arxiv.org" 2018 P. 1-22

We propose a classification of symmetric conservative clones with a finite carrier. For the study, we use the functional Galois connection (Inv_Q,Pol_Q), which is a natural modification of the connection (Inv,Pol) based on the preservation relation between functions f on a set A (of all finite arities) and sets of functions h∈AQ for an arbitrary ...

Added: October 9, 2018

Yashunsky A., Вестник Московского университета. Серия 1: Математика. Механика 2019 № 4 С. 3-9

We consider systems of Boolean functions inducing algebras of Bernoulli distributions, whose universal set has a single limit point. We establish a criterion for an algebra generated by a given set of distributions to have a unique limit point. ...

Added: September 9, 2020

Yashunsky A., Discrete Mathematics and Applications (Netherlands) 2019 Vol. 29 No. 4 P. 267-276

The paper is concerned with sets of Bernoulli distributions which are closed under substitutions of independent random variables into Boolean functions from a given set (an algebra of Bernoulli distributions). A description of all finite algebras of Bernoulli distributions is given. ...

Added: September 9, 2020

Puzino Y. A., Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния 2014 № 22 С. 46-52

The increasing of the efficiency of technological modes of steel products manufacturing requires simulation of metal forming during hot deformation. To obtain correct results, one should set the correct initial and boundary conditions, including the mechanical properties of materials, which represent the dependence of the stress-strain and strain rate at maintained temperature.
In the experiments one ...

Added: January 19, 2015

Ivanov A. I., Стрекопытова М. В., Зубов И. В. et al., СПб. : Издательский дом СПбГУ, 2011

Added: February 8, 2013

Yashunsky A., Доклады Российской Академии наук. Математика, информатика, процессы управления 2020 Т. 493 № 1 С. 47-50

Рассматриваются условия, при которых в конечном множестве с заданной системой операций (конечной алгебре) выполняется предельная вероятностная теорема, а именно, произвольные вычисления с независимыми случайными величинами имеют распределения значений, стремящиеся к некоторому предельному распределению (предельному закону) с ростом количества случайных величин, участвующих в вычислении. Подобное поведение можно рассматривать как одно из обобщений центральной предельной теоремы, имеющей ...

Added: June 29, 2021

191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016

Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624

Added: February 27, 2013

Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013

Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...

Added: February 5, 2014

Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70

A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...

Added: July 19, 2014

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020