Editorial backlog
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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: accepted в т.0 №0
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.
- 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: accepted в т.0 №0
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.
- Kononova A.A. On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio near infinity
Status: accepted в т.0 №0
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.
- 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.
- Rathod A. Nevanlinna’s Five-values Theorems for Algebroid Functions
Status: accepted в т.0 №0
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.
- 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.
- 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.
- 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.
- Trynin A.Yu. Uniform convergence of sync-approximations on the functional
class
Status: accepted в т.0 №0
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Klimentov S.B. About Isomorphism of Some Integro-differential Operators
Status: accepted в т.0 №0
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.
- Poluboyarova N.M. On the instability of extremals of the potential energy functional
Status: reviewing
Abstract. In this paper study has been done on problem of stability and instability of the potential energy functional. By stability we mean the sign-definiteness of the second variation. The expression for the second variation of the functional is calculated. With the capacitive method it is obtain to make the feature of instability extremals. Proved that stability parabolic extremals are planes. We have written the equation of extremals and the second variation of the functional for n-dimensional surfaces of revolution.
Date of submission: 18 June 2017 г.
- Berdellima A. ON A CONJECTURE OF KHABIBULLIN ABOUT A PAIR OF INTEGRAL INEQUALITIES
Status: accepted в т.9 №2
Abstract. It is known that in general Khabibullin’s conjecture is not true. Sharipov [8]
constructed a counterexample when $n = 2$ and $\alpha = 2$. In this paper we develop a method
of how to construct a counterexample for the more general case $n > 2$ and $\alpha > 1/2$.
Date of submission: 24 June 2017 г.
- Kopachevsky N.D., Tsvetkov D.O. Малые движения идеальной стратифицированной жидкости со свободной поверхностью, полностью покрытой крошеным льдом
Status: reviewing
Abstract. Let a rigid immovable vessel be partially filled with an ideal incompressible stratified fluid. We assume that in an
equilibrium state the density of a fluid is a function of the vertical variable $x_3,$ i.e., $\rho_0=\rho_0(x_3).$ In this case the
gravitational field with constant acceleration $\vec g=-g\vec e_3$ acts on the fluid, here $g>0$ and $\vec e_3$ is unit vector of the vertical
axis $Ox_3,$ which is directed opposite to $\vec g.$ Let $\Omega$ be the domain filled with a fluid in equilibrium state, $S$ be rigid wall of
the vessel adherent to the fluid, $\Gamma$ be a free surface completely covered with a crumbled ice.
The initial boundary value problem is reduced to the Cauchy problem
\begin{equation*}
\begin{split}
&\mathcal A \frac{d^2x}{dt^2} + \mathcal C x = f(t),
\quad x(0)=x^0, \quad x^{'}(0)=x^1, \\
&0<< \mathcal A= \mathcal A^{*} \in \mathcal L(\mathcal H),
\quad
0 \leq \mathcal C = \mathcal C^{*} \in \mathcal L(\mathcal H).
\end{split}
\end{equation*}
in some Hilbert space $\mathcal H$. The theorem on strong solvability of initial boundary value problem is proved.
Date of submission: 29 June 2017 г.
- Baskakov A.G., Uskova N.B. Linear differential operator with an involution as generator of group of operators
Status: accepted в т.0 №0
Abstract. We consider mixed problem for first order differential equation with involution.
By the method of similar operators, he differential operator, which defined by this differential
equation, is transformed in orthogonal direct sum of operators. By the main theorem we construct group of operators and
we describe the weak solutions of this problem. We use this theorem for Fourier method.
Date of submission: 29 June 2017 г.
- Garayev M., Guediri H., Sadrawi H. New Characterizations of Bloch spaces, Bers-type and Zygmund-type spaces and
Related Questions
Status: reviewing
Abstract. We give in terms of Berezin symbols new characterizations of\ the Bloch spaces
$\mathcal{B}$ and $\mathcal{B}_{0},$ Bers-type and the Zygmund-type spaces of
analytic functions on the unit disc $\mathbb{D}$ of the complex plane
$\mathbb{C}.$ Moreover, we discuss some properties of Toeplitz operators on
the Bergman space $L_{a}^{2}(\mathbb{D}).$ A new characterization of\ some
function space with variable exponents is also given.
Date of submission: 29 June 2017 г.
- Andriyan S.M., Kroyan A.K., Khachatryan K.A. On Solvability of a Class of Nonlinear Integral Equations in $p$ -adic String Theory
Status: accepted в т.0 №0
Abstract. In this paper a class of nonlinear integral equations, which has direct application in the $ p $ -adic string theory, is studied. The existence of a nontrivial continuous odd and bounded solution on the whole axis is proved. With some additional conditions, the uniqueness of the constructed solution in the certain class of continuous functions is established as well.
Date of submission: 15 July 2017 г.
- RamReddy T., Shalini D., Vamshee Krishna D. THIRD ORDER HANKEL DETERMINANT FOR STAR LIKE
FUNCTIONS OF ORDER $\alpha$
Status: reviewing
Abstract. The objective of this paper is to obtain best possible upper
bound to the third Hankel determinant for the class of starlike functions of
order $\alpha$ ($0 \leq \alpha < 1$), using Toeplitz determinants.
Date of submission: 17 July 2017 г.
- Muravnik A.B. On Qualitative Properties of Solutions of Quasilinear Parabolic
Equations Admitting Degenerations at Infinity
Status: reviewing
Abstract. We consider the Cauchy problem для for
quasilinear parabolic equations of the kind
$\rho(x)u_t=\Delta u + g(u)|\nabla u|^2,$ where the positive coefficient $\rho$
admits a degeneration at infinity, while the coefficient $g$ either is a continuous function
or admits power singularities such that the power does not exceed one.
The long-time
behavior of (classical) solutions of the specified problem is
investigated.
Date of submission: 21 July 2017 г.
- Ehrgashev T.G. Third Double-Layer Potential for a Generalized Bi-Axially
Symmetric
Helmholtz Equation
Status: accepted в т.0 №0
Abstract. The double-layer potential plays an
important role in solving boundary value problems for elliptic
equations, and in the study of which for a certain
equation, the properties of the fundamental solutions of the given
equation are used. All the fundamental solutions of the
generalized bi-axially symmetric Helmholtz equation were known,
and only for the first one was constructed the theory of
potential. Here, in this paper, we aim at constructing theory of
double-layer potentials corresponding to the third fundamental
solution. By using some properties of one of Appell's
hypergeometric functions in two variables, we prove limiting
theorems and derive integral equations concerning a denseness of
double-layer potentials.
Date of submission: 31 July 2017 г.
- Bandura A.I., Skaskiv O.B. Exhaustion by balls and entire functions of bounded $\mathbf{L}$-index in joint variables
Status: reviewing
Abstract. We prove criteria of boundedness of $\mathbf{L}$-index in joint variables which describe local behavior of partial derivatives
on sphere in $\mathbb{C}^n.$
Some obtained results are new even for entire functions
of bounded index in joint variables, i. e. $\mathbf{L}(z)\equiv 1,$
because we used an exhaustion of $\mathbb{C}^n$ by balls
instead an exhaustion of $\mathbb{C}^n$ by polydiscs.
Date of submission: 08 Avgust 2017 г.
- Baskakov A.G., Dikarev E.E. Spectral Theory of Functions in Research of Partial Differential Operators
Status: accepted в т.0 №0
Abstract. Spectral properties of differential operators with
constant coefficients defined on subspaces of space of bounded continuous functions are studied. Necessary and sufficient conditions of invertibility are
obtained under condition of regularity at the infinity (ellipticity type conditions) of polynomial which describes such operators. Spectrum, images and kernels are described. Conditions of compactness of resolvent of differential operators are obtained. Main results are obtained by methods of harmonic analysis and spectral theory of Banach modules.
Date of submission: 10 Avgust 2017 г.
- Rubinshtein A.I. On the Bary-Stechkin Theorem
Status: reviewing
Abstract. We concider the problem on the modulus of continuity for the analogue
conjugate functions in the case of functions in the case of functions defined
on the diadic group. It is shown that for this case no analogue a
Bary--Stechkin theorem.
Date of submission: 18 Avgust 2017 г.
- Das S. ON THE ZEROS OF A POLYNOMIALS
Status: reviewing
Abstract. In this paper we extend a classical result due to Cauchy [6] for
moduli of all zeros of a polynomial of degree $n$. our result is best possible and sharpen some well-known results. In many cases the new bounds are much better than some other known bounds.
Date of submission: 30 Avgust 2017 г.
- Gadylshin T.R., Mukminov F.Kh. Perturbation of second order nonlinear equations by
the delta-like potential
Status: reviewing
Abstract. Boundary value problems for
one-dimensional quasyilinear second order equation are
considered, perturbed by the Delta-shaped potential
$\varepsilon^{-1}Q\left(\varepsilon^{-1}x\right)$, where $Q(\xi)$
--- finite function, $0<\varepsilon\ll1$. By the method of integral inequalities
solutions to these boundary value problems are built with accuracy
$O(\varepsilon)$. To prove the existence of a solution the source
and limit problems the fixed point theorem is used. For linear
boundary value problem all types of boundary conditions are
considered.
Date of submission: 16 September 2017 г.
- Salakhudinov R.G. Some properties of domain functionals on level sets
Status: reviewing
Abstract. For a plane domain $G$ we consider special functionals that are constructed with the help of domain functions, such as the distance function from a point to the boundary $\partial G$, and the warping function of $G$.
Functionals that depend on the distance function are considered in the case of simply-connected domains. Functionals that depend on the distance function are considered in the case of simply-connected domains. Functionals depending on the warping function of a finitely connected domain are also studied.
We prove that isoperimetric monotonicity properties with respect to a free parameter of the functionals generate another monotonicity of the functionals. Namely, we consider the functionals as functions defined on subdomains of $G$. Some special cases of inequalities were obtained earlier by Payne. We note that the inequalities have been successfully applied to justify new estimates of the torsional rigidity of simply connected and multiply connected domains. In particular, new functionals of the domain with monotonic property in both their arguments are constructed.In addition, exact estimates of the rate of change of the functionals are found, that is, exact estimates of the derivatives are obtained.
Date of submission: 26 September 2017 г.
- Merzlyakov S. G. Systems of convolution equations in complex domains
Status: reviewing
Abstract. In this paper we study systems of convolution equations in spaces of vector-valued functions of one variable. For such systems an analogue of the interpolating function of Leot'ev is defined and a number of properties of this function are given.
A theorem on the representation of arbitrary vector functions in a series of elementary solutions of a homogeneous system of convolution equations is proved.
Date of submission: 24 October 2017 г.
- Rathod A. CHARACTERISTIC FUNCTION AND DEFICIENCY OF ALGEBROID FUNCTIONS ON ANNULI
Status: reviewing
Abstract. In this paper, the value distribution theory for meromorphic
functions with maximal deficiency sum will be considered for algebroid
functions on annuli and also the relationship between the deficiency of
algebroid function on annuli and that of their derivatives is studied.
Date of submission: 26 October 2017 г.
- Asylgareev A.S. On the application of comparison theorems to the study of stability with probability 1 of stochastic differential equations
Status: reviewing
Abstract. Comparison theorems for solutions of stochastic differential equations were proven. Based on the results obtained conditions of the stability with probability 1 of the perturbed solution of a stochastic differential equation were shown. The approach stated in the article is based on the fact that the solution of a stochastic differential equation can be represented as a deterministic function of a random argument. Due to the fact that this technique is based on properties of the individual trajectory, the results obtained in this work can be reformulated for deterministic analogs of stochastic differential equations.
Date of submission: 03 November 2017 г.
- Petrosova M.A., Tikhonov I.V., Sherstyukov V.B. A rate of growth of the coefficients in the Bernstein polynomials
of the standard module function on a symmetric interval
Status: reviewing
Abstract. We study the Bernstein polynomials for the standard module function
on a symmetric interval.
The question is a~rate of growth of the coefficients in these polynomials
with an explicit algebraic representation.
Particular attention is paid to the behaviour of the maximum coefficient
for which exact exponential asymptotics
and corresponding two-sided estimates are established.
It is shown that the coefficients ``neighboring'' with the maximum
have the same rate of growth.
The asymptotics for the sum of absolute values of all coefficients is obtained.
Date of submission: 17 December 2017 г.
- Krivosheyeva O.A. A basis in a invariant subspace of analytical functions
Status: reviewing
Abstract. A representation of functions from an invariant subspace in convex domain in complex plane are studied. A sufficient condition for the existence of a basis in the invariant subspace consisting of linear combinations of eigenfunctions and associated functions of differential operator in this subspace are received. Linear combinations are built on the system of exponential monomials, which are divided into relatively small groups. It is applies a method that uses interpolating function of A. F. Leontiev. Herewith is given a complete description of the space of coefficients of the series which provide a representation of functions from invariant subspace. Also is found the necessary conditions for the representation functions from an arbitrary invariant subspaces admitting spectral synthesis in an arbitrary convex domain. It is used the method of constructing of special series of exponential polynomials developed by the author earlier.
Date of submission: 27 December 2017 г.
- Gorbatkov S.A., Polupanov D.V. ИССЛЕДОВАНИЕ УСТОЙЧИВОСТИ РЕШЕНИЯ НЕЛИНЕЙНОЙ КРАЕВОЙ ЗАДАЧИ ДЛЯ ПАРАБОЛИЧЕСКОГО УРАВНЕНИЯ
Status: reviewing
Abstract. Получено аналитическое решение задачи анализа устойчивости решений нелинейной начально-краевой задачи теплопроводности в твердых телах, описываемой параболическим уравнением. Использован разработанный ранее авторами итеро-аппроксимативный метод (ИАМ) и метод функций Ляпунова. ИАМ позволяет выразить решение на каждом шаге итерации в виде рядов по собственным функциям линейной части параболического оператора задачи и создает все предпосылки для применения математического аппарата функций Ляпунова. Приведены результаты расчетов устойчивости теплофизического процесса в трехмерном металлическом теле с переменными по объему теплофизическими свойствами при возмущении начального состояния.
Date of submission: 28 December 2017 г.
- Singh G., Singh G., A New Subclass of Univalent Functions
Status: reviewing
Abstract. In this paper, a new subclass $\chi_t(A,B)$
of close-to-convex functions, defined by
means of subordination is investigated. Some results such as coefficient estimates, inclusion
relations, distortion theorems, radius of convexity and Fekete-Szego problem for this class
are derived. The results obtained here is extension of earlier known work.
Date of submission: 02 January 2018 г.
- Litvinov V.A. Variational interpolation of solutions of fractional differential equations
Status: reviewing
Abstract. Object of research are differential equations of fractional order. The subject of this study is to use the method of variational interpolation to obtain approximate solutions of differential equations of fractional order. The paper presents the method of variational inter\-pola\-tion, and demonstrated its application to the simplest differential equations of fractional order. It is shown that approximate solutions, built on two basic solutions to the equations of integer order, have error less than 10\% in the wide range of variables, and in some cases equivalent with the exact solutions. The described method can be used to obtain approximations of integro-differential equations of fractional order with a relatively small computational cost.
Date of submission: 05 January 2018 г.
- Khakimova A.R. К задаче описания обобщенных инвариантных многообразий нелинейных уравнений
Status: reviewing
Abstract. В статье обсуждается задача построения обобщенных инвариантных многообразий для нелинейных уравнений в частных производных. Обобщенное инвариантное многообразие является аналогом понятия симметрии и имеет приложения в теории интегрируемости. Обобщенные инвариантные многообразия позволяют эффективно строить пары Лакса и операторы рекурсии для интегрируемых уравнений. В работе дано полное описание обобщенных инвариантных многообразий порядка $(2,2)$ для уравнения Кортевега-де Фриза. Показано как связано это многообразие с парой Лакса и с оператором рекурсии.
Date of submission: 15 January 2018 г.
- Alhouzani M., Chuprunov A.N. ПУАССОНОВСКИЕ ПРЕДЕЛЬНЫЕ ТЕОРЕМЫ В СХЕМАХ РАЗМЕЩЕНИЯ РАЗЛИЧИМЫХ ЧАСТИЦ
Status: reviewing
Abstract. Рассматривается случайная величина - число ячеек, содержащих $r$ частиц, среди первых $K$ ячеек
в равновероятной схеме размещения не более $n$ различимых частиц по $N$ различным ячейкам. Найдены условия, обеспечивающие сходимость этих случайных величин
к пуассоновской случайной величине. Получено описание предельного распределения. Показано, что эти результаты переносятся на схему размещения различимых частиц по различным ячейкам.
Date of submission: 18 January 2018 г.
- Borisov D.I. On spectral gaps of a Laplacian in a strip with a bounded periodic
perturbation
Status: reviewing
Abstract. В работе рассматривается Лапласиан с краевым условием Дирихле в
бесконечной плоской полосе, возмущённый ограниченным периодическим оператором.
Основной полученный результат – отсутствие спектральных лакун в нижней части
спектра при достаточно малом периоде потенциала. Верхняя оценка на период, гаран-
тирующая данный результат, выписана явно в числовом виде. Также явно выписана
длина части спектра, в которой гарантировано отсутствие лакун.
Date of submission: 25 January 2018 г.
- Galkina V.S., Polyntseva S.V. Two problems of identification of two lower coefficients in the many-dimensional parabolic equation of a special type
Status: reviewing
Abstract. We consider two problems of identification of two lower coefficients of the many-dimensional parabolic equa\-tions of a special type. In the first problem the overdetermination conditions are given on the same hyperplane, and in the second problem this conditions are given on two various hyperplanes. The inverse problems are reduced to Cauchy's direct auxiliary problems by means of the overdetermination conditions. The resolvability of direct auxiliary problems are proved. The theorems of existence and uniqueness of classical solutions of the inverse problems are proved in the classes of smooth bounded functions.
The solutions of the inverse problems are represented explicitly in terms of the solutions of the direct problems.
Date of submission: 29 January 2018 г.