Editorial backlog

  1. Arabov M.K., Mukhamadiev E.M., Nurov I.D., Sobirov H.I. SIGNS OF EXISTENCE OF LIMITING CYCLES IN THE SECOND ORDER DIFFERENTIAL EQUATIONS
    Status: accepted в т.9 №2
    Abstract.
    This article takes consideration into the discovery of the limiting cycles in neighborhood of stationary point of the non - smooth second order differential equation. New conditions are found for coefficient of the equation which ensure the existence of a limiting cycle. On the basis of taken results was made sector division in a plane. Created a package of programs for drawing phase portraits in appropriate sectors.
    Date of submission: 19 Aprel 2016 г.


  2. Klyachin A.A. On continuity and differentiability of the maximum values of functions
    Status: reviewing
    Abstract.
    This article discusses the functions which are the maximum values of continuous functions on compact subsets of families. These functions are used, for example, in the study of the geometric structure of the equilibrium of different surfaces -- minimal surfaces, surfaces of constant mean curvature, etc. In this paper we find conditions under which such functions are continuous and differentiable.
    Date of submission: 17 May 2016 г.


  3. Oreshina M.N. Spectral decomposition of a normal operator in a real Hilbert space
    Status: reviewing
    Abstract.
    Unbounded normal operators acting in a real Hilbert space are considered. In this article we carry over the classic results of the spectral theory to the case of such operators. The questions connected with the complexification and decomplexification of normal operators are discussed. We present two real variants of the spectral decomposition and the real functional calculus theorems for unbounded normal operators acting in a real Hilbert space.
    Date of submission: 22 May 2016 г.


  4. Khasanov Yu.Kh., Shakiriv I.A. BILATERAL EVALUATION OF THE NORM OF THE FOURIER OPERATOR
    Status: reviewing
    Abstract.
    The lower and the upper uniform estimates of the Lebesgue constants of the classical Fourier operator are not final. A new and more simple integral representation received for it, then on the basis of which the problem of its top assessment is completely solved and the known lower assessment is improved.
    Date of submission: 14 July 2016 г.


  5. Salo T.M., Skaskiv O.B. The minimum modulus of gap power series and h-measure of exceptional sets
    Status: reviewing
    Abstract.
    For an entire function of the form $f(z)=\sum_{k=0}^{+\infty}f_kz^{n_k}$, where $(n_k)$ is a strictly increasing sequence of non negative integers, we establish conditions when the relations $$ M_f(r)=(1+o(1)) m_f(r),\quad M_f(r)=(1+o(1))\mu_f(r) $$ is true as $r\to+\infty$ outside some set $E$ such that $\text{\rm h-meas }(E)=\int_{E}\frac{dh(r)}{r}<+\infty$, where $h(r)$ is positive continuous function increasing to $+\infty$ on $[0,+\infty)$ with non-decreasing derivative, and $M_f(r)=\max\{|f(z)|\colon |z|=r\},\ m_f(r)=\min\{|f(z)|\colon |z|=r\},\ \mu_f(r)=\max\{|f_k|r^{n_k}\colon k\geq 0\} $ the maximum modulus, the minimum modulus and the maximum term of $f,$ respectively.
    Date of submission: 22 July 2016 г.


  6. Mitrokhin S.I. Об исследовании дифференциального оператора с суммируемым потенциалом с разрывной весовой функцией
    Status: reviewing
    Abstract.
    В работе предлагается новый подход к исследованию дифференциальных операторов с разрывной весовой функцией. Изучены спектральные свойства дифференциального оператора, заданного на конечном отрезке, с разделенными граничными условиями, с суммируемым потенциалом, с условиями <<сопряжения>> в точке разрыва весовой функции. При больших значениях спектрального параметра получена асимптотика фундаментальной системы решений соответствующего дифференциального уравнения, с помощью которой выведено уравнение на собственные значения изучаемого дифференциального оператора. Изучена индикаторная диаграмма и найдена асимптотика собственных значений исследуемого оператора.
    Date of submission: 25 Avgust 2016 г.


  7. Khushtova F.G. The first boundary value problem in the half-strip for a differential equation with Bessel operator and partial derivative of Riemann-Liouville
    Status: reviewing
    Abstract.
    We study the first boundary value problem in the half-strip for a differential equation with Bessel operator and partial derivative of Riemann-Liouville. The representation of the solution in the case of the zero side condition found in terms of the integral transform with the Wright's function at the kernel. Uniqueness of the solution is proved in the class of functions that satisfy the analogue of Tikhonov's condition.
    Date of submission: 16 September 2016 г.


  8. Khrystiyanyn A.Y., Lukivska D.V. Quasi-elliptic functions
    Status: reviewing
    Abstract.
    We investigate quasi-elliptic functions (i. e. certain generalization of elliptic functions). For this class of functions analogues of $\wp$, $\zeta$ and $\sigma$ Weierstrass functions are constructed and relation between quasi-elliptic and $p$-loxodromic functions is obtained.
    Date of submission: 27 September 2016 г.


  9. Nurmagomedov A.A., Rasulov N.K., Umalatov A.A. Estimations to Function Lebega of Fourier Sums by Polynomials Orthogonal on Non-uniform grids
    Status: reviewing
    Abstract.
    We study to function Lebega of Fourier private sums by polynomials forming orthonormal system on non-uniform grids from segments $[-1, 1]$ are investigated. In particular, we find a order of the growing for discrete function Lebega.
    Date of submission: 28 October 2016 г.


  10. Krivosheyeva O.A. Invariant subspaces with spectrum of zero density
    Status: reviewing
    Abstract.
    In the paper it is shown that every analytic solution of the homogeneous convolution equation with the characteristic function of a minimal exponential type in the domain of its existence is represented as the series of exponential polynomials which converges uniformly on compact subsets of this domain.
    Date of submission: 31 October 2016 г.


  11. Baizaev S., Rakhimova M.A. О некоторых функциональных уравнениях в пространствах Шварца и их приложениях
    Status: reviewing
    Abstract.
    В статье изучается вопросы нетривиальной разрешимости функциональных уравнений вида $$(B+r^{2}E)u(r,\theta)=0$$ где $B -$ постоянная комплексная матрица порядка $n$, $E -$ единичная матрица порядка $n$, $(r,\theta) -$ полярные координаты в пространствах Шварца. Получены многообразия всех решений из указанных пространств и даны приложения результатов к задачам нахождения решений полиномиального роста ряда классов эллиптических систем и переопределенных систем.
    Date of submission: 12 December 2016 г.


  12. Garifullin R.N., Yamilov R.I. On the integrability of a discrete analogue of the Kaup–Kupershmidt equation
    Status: accepted в т.0 №0
    Abstract.
    We study a new example of equation obtained as a result of a recent generalized symmetry classification of differential-difference equations defined on five points of one-dimensional lattice. We have established that in the continuous limit this new equation goes into the well-known Kaup–Kupershmidt equation. We have also proved its integrability by constructing an $L-A$ pair and conservation laws. Moreover, we present a possibly new scheme for deriving conservation laws from $L-A$ pairs.
    Date of submission: 12 December 2016 г.


  13. Ishkina Sh.Kh. Combinatorial bounds of overfitting for threshold classifiers
    Status: reviewing
    Abstract.
    Tightening generalization bounds is a fundamental objective of statistical learning theory. However, accurate and computationally efficient bounds are still unknown even for very simple cases. In~this paper, we consider one-dimensional threshold decision rules. We~use the framework of combinatorial theory of overfitting, which is based on a single probabilistic assumption that all partitions of a~set of objects into an observed training sample and a~hidden test sample can occur with equal probability. We~propose a~polynomial algorithm for computing both probability of overfitting and complete cross-validation.
    Date of submission: 21 December 2016 г.


  14. Kalyakin L.A. Adiabatic approximation for a model of resonance capture
    Status: accepted в т.9 №2
    Abstract.
    Две модельные задачи о захвате в резонанс анализируются методом усреднения, который приводит к адиабатическому приближению в главном члене асимптотики. Основной целью является приближенное описание области захвата в резонанс. Эта область зависит от дополнительного параметра, входящего в уравнения. Демонстрируется непригодность адиабатического приближения, когда область захвата становится узкой. В этом случае требуется значительное изменение метода усреднения.
    Date of submission: 26 December 2016 г.


  15. Galakhov E.I., Salieva O.A. Условия отсутствия решений некоторых неравенств и систем с функциональными параметрами и сингулярными коэффициентами на границе
    Status: accepted в т.0 №0
    Abstract.
    We obtain sufficient conditions for nonexistence of positive solutions of some nonlinear elliptic inequalities and systems that contain the $p(x)$-Laplace operators with variable power exponents and coefficients possessing singularity on the boundary.
    Date of submission: 28 December 2016 г.


  16. Belaidi B., Saidani M. On The Growth of Solutions of Some Higher Order Linear Differential Equations With Meromorphic Coefficients
    Status: reviewing
    Abstract.
    In this paper, we study the growth of meromorphic solutions of the differential equation ....
    Date of submission: 06 January 2017 г.


  17. Khan N.U., Usman T. CERTAIN GENERATING FUNCTIONS OF HERMITE-BERNOULLI-LEGENDRE POLYNOMIALS
    Status: reviewing
    Abstract.
    In this paper, we introduce a new class of generating functions for Hermite- Bernoulli-Legendre polynomials and investigate certain implicit summation formulas by using different analytical means and applying generating function. We also introduce bi- lateral series associated with the newly-introduced generating function by appropriately specializing a number of known or new partly unilateral and partly bilateral generating functions.
    Date of submission: 27 January 2017 г.


  18. Shukla I. Simultaneous Quadruple Series Equations Involving Konhauser Biorthogonal Polynomials
    Status: reviewing
    Abstract.
    Spencer and Fano [11] used the biorthogonal polynomials (for the case of k = 2) in carrying out calculations involving penetration of gamma rays through matter. In the present paper an exact solution of simultaneous quadruple series equations involving Konhauser – biorthogonal polynomials of first kind of different indices is obtained by multiplying factor technique due to Noble [13]. This technique has been modified by Thakare [12] to solve dual series equations involving orthogonal polynomials which led to disprove a possible conjecture of Askey [6] that dual series equations involving Jacobi polynomials of different indices cannot be solved. In this paper the solution of simultaneous quadruple series equations involving generalized Laguerre polynomials also have been discussed in a particular case.
    Date of submission: 28 January 2017 г.


  19. Salimov R.B. The study of the behavior of the singular integral with the Hilbert kernel near a point of the new weak continuity of the density
    Status: reviewing
    Abstract.
    We study the behavior of a singular integral with the Hilbert kernel near a fixed point, where the density vanishes as a negative exponent of the logarithm module of the distance from the fixed point to a variable one at the new conditions.
    Date of submission: 08 February 2017 г.


  20. Biswas T., Datta S.K. On some bounds involving relative Ritt type and relative Ritt weak type of entire functions represented by vector valued Dirichlet series
    Status: reviewing
    Abstract.
    In this paper we wish to study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of relative Ritt type and relative Ritt weak type.
    Date of submission: 13 February 2017 г.


  21. Murtazina S.A., Fazlytdinov M.F., Shevtsova T.V., Yumagulov M.G. Operator methods for computing Lyapunov quantities in the problems on the local bifurcations of dynamical systems
    Status: reviewing
    Abstract.
    This work proposes new formulas to calculate Lyapunov quantities in problems of major scripts of local bifurcations of dynamical systems. Considered a dynamical system, described by differential equations, and point mappings. The proposed formulas are obtained from the general operational method of the study of local bifurcations and do not require transition to normal forms and use theorems about the central diversity.
    Date of submission: 06 Mart 2017 г.


  22. Kononova A.A. On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio near infinity
    Status: reviewing
    Abstract.
    We consider perturbations of orthogonality measure of the system of polynomials that do not change (in some sense) the asymptotical behavior of the ratio of corresponding orthogonal polynomials. The support of the measure consists of the finite number of Jordan curves and may also contain a finite number of mass-points out of the polynomial convex hull of the support of the absolute continuous part of the measure. The problem is a generalization of the problem of compactness of the perturbation of Jacobi operator generated by the perturbation of its spectral measure. A condition, necessary (or necessary and sufficient under some additional restriction) for the stability of the asymptotical behavior of the corresponding orthogonal polynomials is found.
    Date of submission: 09 Mart 2017 г.


  23. Halder S., Sahoo P. UNIQUENESS OF MEROMORPHIC FUNCTIONS CONCERNING DIFFERENTIAL POLYNOMIALS SHARING A SET
    Status: reviewing
    Abstract.
    In this paper, we investigate the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a set of values with finite weight and obtain some results that generalize and improve the recent results due to H.Y. Xu [J. Computational Analysis and Applications, 16(2014), 942-954].
    Date of submission: 27 Mart 2017 г.


  24. Nuraliev F.A., Hayotov A.R., Shadimetov Kh.M. Optimal quadrature formulas with derivatives in Sobolev space
    Status: reviewing
    Abstract.
    In the present paper the problem of construction of optimal quadrature formulas in the sense of Sard in the space $L_2^{(m)}(0,1)$ is considered. Here the quadrature sum consists of values of the integrand at nodes and values of the first and the third derivatives of the integrand at the end points of the integration interval. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number $N\geq m-3$ and for any $m\geq 4$ using S.L. Sobolev method which is based on the discrete analogue of the differential operator $d^{2m}/dx^{2m}$. In particular, for $m=4,\ 5$ optimality of the classical Euler-Maclaurin quadrature formula is obtained. Starting from $m=6$ new optimal quadrature formulas are obtained. At the end of this work some numerical results are presented.
    Date of submission: 30 Mart 2017 г.


  25. Krivosheyev A.S., Kuzhaev A.F. On a Leontiev-Levin theorem
    Status: reviewing
    Abstract.
    In this work we investigate relations between different densities of a positive sequence and variables related to them. The results are used to generalise classical proposition on completeness of exponential monomials systems with positive exponents in a convex domain when these exponents haven't density. That proposition was obtained by A.Leontiev and B.Levin independently. This generalisation is given for sufficiently wide class of convex domains, for example, with vertical or horizontal symmetry axes.
    Date of submission: 30 Mart 2017 г.


  26. Rathod A. Nevanlinna’s Five-values Theorems for Algebroid Functions
    Status: reviewing
    Abstract.
    By using the second main theorem of the algebroid function, we inves- tigate the problem on two algebroid functions partially sharing five or more values and that improve and generalize the previous results given by Xuan and Gao.
    Date of submission: 06 Aprel 2017 г.


  27. Khashimov A.R. ЭНЕРГЕТИЧЕСКИЕ ОЦЕНКИ ДЛЯ РЕШЕНИЙ КРАЕВЫХ ЗАДАЧ УРАВНЕНИЯ ТРЕТЬЕГО ПОРЯДКА С КРАТНЫМИ ХАРАКТЕРИСТИКАМИ
    Status: reviewing
    Abstract.
    В статье рассмотрена первая краевая задача для уравнения третьего порядка с кратными характеристиками. Для обобщенного решения уравнения установлена энергетические оценки типа аналога принципа Сен-Венана. С помощью этой оценки выявлены наибольшее класс единственности решений краевых задач в зависимости от геометрических характеристик области.
    Date of submission: 07 Aprel 2017 г.


  28. Shabat A.B., Эфендиев M.H. О приложениях формулы Фаа-ди-Бруно
    Status: reviewing
    Abstract.
    Two new modifications of the classical Faa-di-Bruno formula are constructed and applications of the obtained formulas in the theory of integrability of nonlinear partial differential equations
    Date of submission: 08 Aprel 2017 г.


  29. Stepanova I.V. Symmetries of heat and mass transfer equations in viscous fluids
    Status: reviewing
    Abstract.
    The paper is devoted to description of results of application of classical Lie-Ovsyannikov theory to study of heat and mass transfer equations in viscous liquids. Group properties of equations of convective and molecular heat and mass transfer are under consideration. The author analyzed 124 papers and monographs be concerning to mentioned problem.
    Date of submission: 10 Aprel 2017 г.


  30. Singh D.K., Singh P. Wright Function Associated with Fractional Calculus
    Status: reviewing
    Abstract.
    With the marvelous light of fractional calculus, the study of this paper is based on Wright function and Raizada polynomial.
    Date of submission: 17 Aprel 2017 г.


  31. Zhukova N.I. The influence of stratification on groups of conformal transformations of pseudo-Riemannian orbifolds
    Status: reviewing
    Abstract.
    Groups of conformal transformations of $n$-dimensional pseudo-Riemannian orbifolds $({\mathcal N},g)$ are investigated for $n\geq 3$. It is shown that a conformal pseudo-Riemannian geometry is induced on each stratum of that orbifold. For $k\in\{0,1\}\cup\{3,...,n-1\}$ exact estimates of dimensions of the conformal transformation groups of $n$-dimensional pseudo-Rieman\-ni\-an orbifolds admitting $k$-dimensional strata with essential conformal trans\-for\-ma\-tion groups are obtained.
    Date of submission: 08 May 2017 г.


  32. Kachalov V.I. Pseudoholomorphic functions and their application
    Status: reviewing
    Abstract.
    An analysis of asymptotic methods for solving singularly perturbed problems shows that the solutions obtained by means of these solutions depend in two ways on the small parameter: regularly and singularly. This dependence is particularly clearly demonstrated by the method of regularization of S.A.\,Lomov. Moreover, the regularized solu\-tions of singularly perturbed equations can converge in the usual sense. In this connection, it became necessary to study a special class of functions, pseudoholomorphic functions. This is a very important part of the analy\-sis, it is intended to substantiate the main points of the so-called analytic theory of singular perturbations. On the other hand, the relevance of the theory in question is also dictated by the fact that pseudoholomorphic functions, unlike holomorphic functions, are determined when the condi\-tions of the implicit function theorem are violated.
    Date of submission: 16 May 2017 г.


  33. Trynin A.Yu. Uniform convergence of sync-approximations on the functional class
    Status: reviewing
    Abstract.
    We obtain a uniform convergence inside the interval (0, \ pi) of the values of the Lagrange-Sturm-Liouville operators for functions from the class. The class is defined by means of one-way moduli of continuity and change
    Date of submission: 18 May 2017 г.


  34. Bobodzhanov A.A., Safonov V.F. Regularized asymptotics of solutions of integro-differential partial differential equations with rapidly varying kernels
    Status: reviewing
    Abstract.
    The method of Lomov regularization is generalized to partial differential equations with integral operators, the kernel of which contains a rapidly varying exponential factor. The case when the upper limit of the integral operator coincides with the differentiation variable is investigated. For such problems, an algorithm for constructing regularized asymptotics develops. In contrast to the work of Imanaliev M.I., where for analogous problems with slowly varying nuclei only the limit transition is investigated when the small parameter tends to zero, an asymptotic solution of any order (with respect to the parameter) is constructed here.
    Date of submission: 19 May 2017 г.


  35. Kulaev R.Ch., Shabat A.B. Some properties for Jost functions of a Schr\"odinger equation with potential, which is a distribution
    Status: reviewing
    Abstract.
    Работа посвящена задаче кардинального расширения пространства потенциалов в обратной задаче рассеяния для линейного уравнения Шр\"едингера на числовой прямой. Рассматривается оператор Шр\"едингера с потенциалом из пространства обобщенных функций. Это расширение включает в себя не только потенциалы типа $\delta$-функции, но и экзотику типа функции Кантора. На этом пути устанавливаются условия существования и единственности решений Йоста, изучаются их свойства.
    Date of submission: 23 May 2017 г.


  36. Fedotov A.I. Hermite-Fejer polynomials as an approximate solution of the singular integro-differential equations
    Status: reviewing
    Abstract.
    An approximate method for solving singular integro-differen-tial equations in periodic case is justified. An approximate solution is sought in a form of Hermite-Fejer polynomials. The convergence of the method is proved and the errors are estimated.
    Date of submission: 24 May 2017 г.


  37. Konechnaya N.N., Mirzoev K.A. Asymptotics of solutions of a class of linear differential equations
    Status: reviewing
    Abstract.
    In this paper the main term of asymptotics of some fundamen- tal system of solutions of a class of linear differential equations of arbitrary order $\tau y=\lambda y$ at infinity is found, where $\lambda$ is a fixed complex number. In this case, the conditions imposed on the coefficients of the differential equation are not related to their smoothness, but only provide a certain power-law growth of the coefficients at infinity. The results obtained are applied to the spectral analysis of the corresponding singular differential operators, including in the case when the expression $ \tau $ is a product of two differential expressions.
    Date of submission: 26 May 2017 г.


  38. Kachalov V.I. On the holomorphic regularization of strongly nonlinear singularly perturbed problems
    Status: reviewing
    Abstract.
    The method of holomorphic regularization, which is a logical extension of the Lomov method, allows one to construct solutions of nonlinear singularly perturbed initial problems in the form of series converging in the usual sense in powers of a small parameter. The method itself is based on a generalization of the Poincare decomposition theorem: in the regular case, solutions depend holomorphically on a small parameter, in the singular case the first integrals inherit this dependence.
    Date of submission: 29 May 2017 г.


  39. Zikkos E. A Taylor-Dirichlet series with no singularities on its abscissa of convergence
    Status: reviewing
    Abstract.
    In this paper it is proved that given any non-negative real number $d$, there exists a Taylor-Dirichlet series of the form \[ \sum_{n=1}^{\infty} \left(\sum_{k=0}^{\mu_n-1}c_{n,k} z^k\right) e^{\lambda_n z},\quad c_{n,k}\in \mathbb{C} \] with no singularities on its abscissa of convergence, such that its associated multiplicity-sequence $\Lambda=\{\lambda_n,\mu_n\}_{n=1}^{\infty}$ has the following properties: \noindent (1) the terms of $\Lambda$ are positive real numbers and uniformly separated, \noindent $(\inf_{n\in\mathbb{N}}(\lambda_{n+1}-\lambda_n)>0)$, \noindent (2) $\Lambda$ has density equal to $d$, $\left(\lim_{t\to\infty}\frac{\sum_{\lambda_n\le t}\mu_n}{t}=d<\infty\right)$, \noindent (3) the multiplicities of the terms of $\Lambda$ are unbounded, $(\mu_n\not=O(1))$. The proof is based on the fact that for this sequence $\Lambda$ its Krivosheev characteristic $S_{\Lambda}$ is negative. We remark that when $\mu_n=1$ for all $n\in\mathbb{N}$ the result is false by a well known theorem of P\'{o}lya.
    Date of submission: 30 May 2017 г.


  40. Kondrashov A.N. About admissible rate of convergence to zero of the solutions of some elliptic equations on non-compact Riemannian manifolds
    Status: reviewing
    Abstract.
    The asymptotic behavior of solutions of some linear second-order elliptic equations defined on a non-compact Riemannian manifolds is investigated. It is established two theorems on the admissible rate of convergence to zero of the solutions of these equations at the end of the manifold, depending on the type of the end. Also, we obtain an existence theorem for solutions with prescribed asymptotic behaviour at the end of the hyperbolic type.
    Date of submission: 01 June 2017 г.


  41. Vinnitskii B.V., Sharan V.L., Sheparovych I.B. About some interpolation problem in the class of functions of exponential type in a half-plane
    Status: reviewing
    Abstract.
    The conditions of solvability of the interpolation problem $f(\lambda_{k} )=d_{k} $ are found in the class of functions of exponential type. This results are applied to research of some problem of the function's splitting.
    Date of submission: 01 June 2017 г.


  42. Klimentov S.B. About Isomorphism of Some Integro-differential Operators
    Status: reviewing
    Abstract.
    In this work representations of <> for solutions of the linear general elliptic system of the first order in the unit circle are considered. The isomorphism of corresponding operators is established in Banach spaces $C^k_\alpha (\overline D) $ and $W^k_p (\overline D) $, $k\geq $1, $0 <\to alpha <$1, $p> $2. These results develop and supplement B.V. Boyarsky's works where representa\-tions of <> where obtained. Also this work supplements author’s results on representations of <> with more difficult operators.
    Date of submission: 02 June 2017 г.


  43. Braichev G.G. Two-sided estimates of the relative growth of functions and their derivatives
    Status: reviewing
    Abstract.
    В работе дано расширенное изложение доклада автора, подготовленного для международной математической конференции по теории функций, посвященной 100-летию чл.-корр. АН СССР А.\,Ф.~Леонтьева. Установлены равномерные двусторонние оценки относительного роста производных двух функций на основе информации об относительном росте самих функций. Рассмотрены примеры применения полученных результатов к исследованию поведения целых функций.
    Date of submission: 03 June 2017 г.


  44. Golichev I.I., Luchnikova N.I. Gradient methods of solving the problem of optimization of resource allocation with account of effectiveness and risk
    Status: reviewing
    Abstract.
    On the basis of gradient methods for minimizing functions, numerical methods for solving the problem of optimization of resource allocation are developed taking into account the effectiveness and risk according to various criteria. Among them, the focus is on the VaR criterion.
    Date of submission: 06 June 2017 г.


  45. Eliseev A.G., Ratnikova T.A., Shaposhnikova D.A. Singularly perturbed systems of Volterra integral equations of the second kind
    Status: reviewing
    Abstract.
    In this paper we study the initialization problem for singularly perturbed systems of Volterra integral equations of the second kind. A general approach to the construction of the regularized asymptotics of singularly perturbed integro-differential equations is described in the papers of S.A. Lomov and his progeny. In this paper, we study the problem of the passage to the limit and the estimate of the remainder in the initialization problem for the original singularly perturbed system of Volterra integral equations. Calculations are given, the class of right-hand sides is determined by the example of one singularly perturbed Volterra integral equation of the second kind.
    Date of submission: 07 June 2017 г.