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Решение проблемы оптимального управления запасом непрерывного продукта при постоянно происходящем потреблении в стохастической полумарковской модели
Информатика и ее применения. 2018. Т. 12. № 2. С. 83–89.
Shnourkoff P. V., Егоров А. Ю.
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Shnourkoff P. V., Адамова К. А., Системы и средства информатики 2021 Т. 31 № 3 С. 36–47
The paper proposes and analyzes a new stochastic model of regeneration of continuous product stock control. The volume of stock at an arbitrary moment of time is the status of the system. The control parameters are a maximum deterministic allowable stock volume and a random time from replenishment until the next order. For a stationary value indicator of ...
Added: February 2, 2023
Shnourkoff P. V., Информатика и ее применения 2022 Т. 16 № 2 С. 75–84
The present author investigates the analytical structure of three kinds of functionals from a controllable semi-Markov process with a finite set of states. It is proved that all these mathematical objects can be represented in the form of a fractional-linear integral functional defined on a finite set of probability measures that determine the control strategy of the corresponding semi-Markov ...
Added: February 2, 2023
Arbuzova A., В кн.: Статистические методы анализа экономики и общества. 12-я Международная научно-практическая конференция студентов и аспирантов (11–14 мая 2021 г.).: М.: Национальный исследовательский университет "Высшая школа экономики", 2021. С. 48–51.
В данной работе исследуется задача оптимального управления непрерывным запасом в модели регенерации. Параметром управления является случайная длительность периода от момента пополнения до момента заказа следующей поставки. Эффективность управления системы описывается стационарным интегральным дробно-линейным функционалом средней удельной прибыли. Установлено, что оптимальное управление определяется точкой, доставляющей экстремум основной функции функционала средней удельной прибыли. Особенностью рассматриваемой модели являются ...
Added: December 7, 2022
Shnourkoff P. V., Адамова К. А., Информатика и ее применения 2020 Т. 14 № 2 С. 98–103
The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral expressions in the numerator and the denominator in the problem under consideration depend on a real optimization parameter vector. ...
Added: November 10, 2020
Shnourkoff P. V., Егоров А. Ю., Информатика и ее применения 2018 Т. 12 № 1 С. 109–117
Проводится построение и предварительное исследование дискретной стохастической полумарковской модели, описывающей функционирование некоторой системы управления запасом непрерывного продукта при постоянно происходящем потреблении. Модель представляет собой пару случайных процессов (x(t),z(t)), где основной процесс x(t) описывает объем запаса в системе в момент времени t, а сопровождающий полумарковский случайный процесс z(t) определяется по состояниям основного непосредственно после пополнений. Задача ...
Added: April 13, 2018
P. V. Shnurkov, Doklady Mathematics 2016 Vol. 94 No. 2 P. 550–554
A new, generalized and strengthened, form of an assertion about an extremum of a linear-fractional integral functional given on a set of probability measures is presented. It is shown that the solution of the extremal problem for such a functional is completely determined by the extremal properties of the so-called test function, which is the ratio of the ...
Added: February 8, 2018
Shnourkoff P. V., Пименова Е. Ю., Системы и средства информатики 2017 Т. 27 № 4 С. 80–94
Исследуется задача оптимального управления запасом в стохастической модели регенерации. Данная проблема формализуется в виде экстремальной задачи для некоторого стационарного стоимостного показателя, зависящего от функции распределения времени от момента очередного пополнения запаса до момента заказа на следующее пополнение. Найден явный вид этого показателя в форме дробно-линейного интегрального функционала, для которого получены представления подынтегральных функций числителя и ...
Added: December 13, 2017
Shnourkoff P. V., Горшенин А. К., Белоусов В. В., Информатика и ее применения 2016 Т. 10 № 4 С. 72–88
Настоящее исследование посвящено теоретическому обоснованию нового метода нахождения оптимальной стратегии управления полумарковским процессом с конечным множеством состояний. Рассматриваются марковские рандомизированные стратегии управления, определяемые конечным набором вероятностных мер, соответствующих каждому состоянию. Характеристикой качества управления служит стационарный стоимостной показатель. Данный показатель представляет собой дробно-линейный интегральный функционал от набора вероятностных мер, задающих стратегию управления. Для этого функционала известны ...
Added: January 18, 2017
Shnourkoff P. V., Доклады Академии наук 2016 Т. 470 № 4 С. 387–392
Представлена новая обобщенная и усиленная форма утверждения об экстремуме дробно-линейного интегрального функционала, заданного на множестве вероятностных мер. Доказано, что решение экстремальной проблемы для функционала полностью определяется экстремальными свойствами так называемой основной функции, которая представляет собой отношение подынтегральных функций числителя и знаменателя. На основе указанного утверждения доказана теорема об оптимальной стратегии управления полумарковским процессом с конечным ...
Added: September 20, 2016