Персона: Костин, Андрей Борисович
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Институт общей профессиональной подготовки (ИОПП)
Миссией Института является:
фундаментальная базовая подготовка студентов, необходимая для получения качественного образования на уровне требований международных стандартов;
удовлетворение потребностей обучающихся в интеллектуальном, культурном, нравственном развитии и приобретении ими профессиональных знаний; формирование у студентов мотивации и умения учиться; профессиональная ориентация школьников и студентов в избранной области знаний, формирование способностей и навыков профессионального самоопределения и профессионального саморазвития.
Основными целями и задачами Института являются:
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;
учебно-методическое руководство общеобразовательными кафедрами Института, осуществляющими подготовку бакалавров и специалистов по социо-гуманитарным, общепрофессиональным и естественнонаучным дисциплинам, обеспечение единства требований к базовой подготовке студентов в рамках крупных научно-образовательных направлений (областей знаний).
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Костин
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Андрей Борисович
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- 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 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 метаданныеApplication of the Hausdorff Metric in Model Problems with Discontinuous Functions in Boundary Conditions(2023) Kostin, A. B.; Sherstyukov, V. B.; Костин, Андрей БорисовичUsing an example of the Cauchy problem for the one-dimensional heat equation, we study the approximation of the solution to the initial condition in the Hausdorff metric. The simplest discontinuous function u0(x) = sgn x is taken for the initial condition. Based on the asymptotic behavior of the Lambert W function and its modification, we obtain a two-sided estimate and an asymptotics for the Hausdorff distance between the solution given by the Poisson formula and the function u0(x). Similar results are obtained for a similar model problem for the Laplace equation in the upper half-plane.
- ПубликацияТолько метаданныеEnveloping of the Values of an Analytic Function Related to the Number e(2023) Kostin, A. B.; Sherstyukov, V. B.; Костин, Андрей Борисович
- ПубликацияТолько метаданныеINTEGRAL REPRESENTATIONS OF QUANTITIES ASSOCIATED WITH GAMMA FUNCTION(2021) Kostin, A. B.; Sherstyukov, V. B.; Костин, Андрей БорисовичWe study a series of issues related with integral representations of Gamma functions and its quotients. The base of our study is two classical results in the theory of functions. One of them is a well-known first Binet formula, the other is a less known Malmsten formula. These special formulae express the values of the Gamma function in an open right half-plane via corresponding improper integrals. In this work we show that both results can be extended to the imaginary axis except for the point z = 0. Under such extension we apply various methods of real and complex analysis. In particular, we obtain integral representations for the argument of the complex quantity being the value of the Gamma function in a pure imaginary point. On the base of the mentioned Malmsten formula at the points z not equal 0 in the closed right half-plane, we provide a detailed derivation of the integral representation for a special quotient expressed via the Gamma function: D(z) Gamma(z + 1/2)/Gamma(z + 1). This fact on the positive semi-axis was mentioned without the proof in a small note by Dusan Slavic in 1975. In the same work he provided two-sided estimates for the quantity D(x) as x > 0 and at the natural points D(x) coincided with the normalized central binomial coefficient. These estimates mean that D(x) is enveloped on the positive semi-axis by its asymptotic series. In the present paper we briefly discuss the issue on the presence of this property on the asymptotic series D(z) in a closed angle vertical bar arg z vertical bar <= pi/4 with a punctured vertex. By the new formula representing D(z) on the imaginary axis we obtain explicit expressions for the quantity vertical bar D(iy)vertical bar(2) and for the set Arg D(iy) as y > 0. We indicate a way of proving the second Binet formula employing the technique of simple fractions.
- ПубликацияТолько метаданныеTwo-Sided Estimates of the Analytic Function Associated with the Euler Number(2024) Kostin, A. B.; Sherstyukov, V. B.; Костин, Андрей Борисович