Персона: Костин, Андрей Борисович
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Институт общей профессиональной подготовки (ИОПП)
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обеспечение высококачественной (фундаментальной) базовой подготовки студентов бакалавриата и специалитета; поддержка и развитие у студентов стремления к осознанному продолжению обучения в институтах (САЕ и др.) и на факультетах Университета; обеспечение преемственности образовательных программ общего среднего и высшего образования; обеспечение высокого качества довузовской подготовки учащихся Предуниверситария и школ-партнеров НИЯУ МИФИ за счет интеграции основного и дополнительного образования;
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Костин
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Андрей Борисович
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17 results
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Теперь показываю 1 - 10 из 17
- ПубликацияТолько метаданныеRecovery of Multifactor Source in Parabolic Equation with Integral Type Observation(2020) Kamynin, V. L.; Kostin, A. B.; Камынин, Виталий Леонидович; Костин, Андрей Борисович© 2019, Springer Science+Business Media, LLC, part of Springer Nature.We consider the inverse multifactor source problem for a uniformly parabolic equation with integral overdetermination conditions and study the existence, uniqueness, and stability of a solution. We obtain two forms of sufficient conditions for the unique solvability and present examples of inverse problems satisfying the assumptions of the proved theorems.
- ПубликацияТолько метаданныеComputation of Sums of Natural Powers of the Inverses of Roots of an Equation Connected with a Spectral Problem(2020) Kostin, A. B.; Sherstyukov, V. B.; Костин, Андрей Борисович© 2019, Springer Science+Business Media, LLC, part of Springer Nature.We consider equations arising in the oblique derivative spectral problem of the formazJv′(z)+bJv(z)=0,z∈ℂ, where ν, a, b ∈ ℂ are parameters such that |a|+|b| > 0 and Jν(z) is the Bessel function. For roots of the equation we prove summation relations. The results obtained agree with the theory of Rayleigh sums which are calculated in terms of zeros of the Bessel functions.
- ПубликацияТолько метаданныеAsymptotic Behavior of Remainders of Special Number Series(2020) Kostin, A. B.; Sherstyukov, V. B.; Костин, Андрей Борисович© 2020, Springer Science+Business Media, LLC, part of Springer Nature.We consider a one-parameter family of number series involving the generalized harmonic series and study asymptotic properties of the remainders. Using R(Np)≡∑n=N∞1/np as an example, we describe the typical obtained results: we obtain the integral representation, find the complete asymptotic expansion with respect to the parameter 2N − 1 as N →∞, and prove that R(N, p) is enveloped by its asymptotic series. The possibilities of the proposed approach are demonstrated by the problem of exact two-sided estimates for the central binomial coefficient.
- ПубликацияТолько метаданныеBasis Property of the System of Root Functions of the Oblique Derivative Problem for the Laplace Operator in a Disk(2019) Kostin, A. B.; Sherstyukov, V. B.; Костин, Андрей Борисович© 2019, Pleiades Publishing, Ltd.We study the spectral oblique derivative problem for the Laplace operator in a disk D. The asymptotic properties of the eigenvalues are established, and the basis property with parentheses in the space L2(D) is proved for the system of root functions of the above problem.
- ПубликацияТолько метаданныеInverse source problem for the abstract fractional differential equation(2021) Piskarev, S. I.; Kostin, A. B.; Костин, Андрей Борисович© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.In a Banach space, the inverse source problem for a fractional differential equation with Caputo-Dzhrbashyan derivative is considered. The initial and observation conditions are given by elements from D (A) D(A), and the operator function on the right side is sufficiently smooth. Two types of the observation operator are considered: integral and at the final point. Under the assumptions that operator A is a generator of positive and compact semigroup the uniqueness, existence and stability of the solution are proved.
- ПубликацияТолько метаданныеTHE INVERSE PROBLEM OF DETERMINING THE LOWEST COEFFICIENT IN A HIGHER-ORDER PARABOLIC EQUATION WITH WEAK DEGENERACY(2021) Kamynin, V. L.; Kostin, A. B.; Камынин, Виталий Леонидович; Костин, Андрей БорисовичWe consider the inverse problem of finding the coefficient before u(t, x) in a higher-order parabolic equation, which is not assumed to be uniformly parabolic and can admit weak degeneracy. The required coefficient is considered to depend only on the spatial variable x is an element of [0, l]. Additional information is taken in the form of an integral over the variable t is an element of [0, T] of the solution with a given weight function (integral observation). The initial condition and m boundary conditions of the first kind (2m order of the equation) are specified in a standard way. It is assumed that the leading coefficient rho before u(t) in the equation is non-negative, and its reciprocal 1/rho belongs to the space L-q(Q) for some q > 1. For the considered inverse problem, existence and uniqueness theorems for the generalized solution are proved. In the course of its research, the corresponding theorems on the solvability of the direct problem were formulated and proved. In this case, the approaches and results of the well-known work of S. N. Kruzhkov(1979) were used. In the conclusion, we give an example of the inverse problem for which the conditions of the theorems proved are satisfied. It is shown that for all sufficiently large values of T > 0 its solution exists, is unique, and an estimate for the required coefficient is written out.
- ПубликацияТолько метаданныеEnveloping of Riemann’s Zeta Function Values and Curious Approximation(2022) Kostin, A. B.; Sherstyukov, V. B.; Tsvetkovich, D. G.; Костин, Андрей БорисовичIn this note, by the example of approximate calculation of $ pi
- ПубликацияТолько метаданныеON TAYLOR COEFFICIENTS OF ANALYTIC FUNCTION RELATED WITH EULER NUMBER(2022) Kostin, A. B.; Sherstyukov, V. B.; Костин, Андрей БорисовичWe consider a classical construction of second remarkable limit. We pose a question on asymptotically sharp description of the character of such approximation of the number e. In view of this we need the information on behavior of the coefficients in the power expansion for the function (Formula Presented) converging in the interval (Formula Presented). We obtain a recurrent rule regulating the forming of the mentioned coefficients. We show that the coefficients form a sign-alternating sequence of rational numbers (−1)nan, where n ∈ N ∪ {0} and a0 = 1, the absolute values of which strictly decay. On the base of the Faá di Bruno formula for the derivatives of a composed function we propose a combinatorial way of calculating the numbers an as n ∈ N. The original function f(x) is the restriction of the function f(z) on the real ray x andgt; −1 having the same Taylor coefficients and being analytic in the complex plane C with the cut along (−∞, −1]. By the methods of the complex analysis we obtain an integral representation for an for each value of the parameter n ∈ N. We prove that an → 1/e as n → ∞ and find the convergence rate of the difference an − 1/e to zero. We also discuss the issue on choosing the contour in the integral Cauchy formula for calculating the Taylor coefficients (−1)nan of the function f(z). We find the exact values of arising in calculations special improper integrals. The results of the made study allows us to give a series of general two-sided estimates for the deviation e−(1+x) 1/x consistent with the asymptotics s of f(x) as x → 0. We discuss the possibilities of applying the obtained statements © Kostin A.B., Sherstyukov V.B. 2022
- ПубликацияТолько метаданныеInverse Source and Coefficient Problems for Elliptic and Parabolic Equations in Holder and Sobolev Spaces(2019) Prilepko, A. I.; Kostin, A. B.; Solov'ev, V. V.; Костин, Андрей Борисович© 2019, Springer Science+Business Media, LLC, part of Springer Nature. We review some results obtained by the authors during the last 15 years. In particular, we present the existence and uniqueness theorems for linear and nonlinear inverse problems of reconstructing unknown coefficients in elliptic and parabolic equations.
- ПубликацияОткрытый доступЛинейные и нелинейные обратные задачи с нелокальным наблюдением для параболических уравнений в пространствах Соболева(НИЯУ МИФИ, 2015) Костин, А. Б.; Костин, Андрей Борисович; Фатьянов, А. А.