Editorial backlog

  1. Rakhmelevich I.V. On the multi-dimensional partial differential equations with power-law non-linearities of the first derivatives
    Status: reviewing
    Abstract.
    We consider a class of multidimensional partial differential equations, containing a linear differential operator of arbitrary order and power-law nonlinearity by the first derivatives. Under some additional assumptions for this operator, we study the solutions of multidimensional travelling waves that depend on some linear combinations of the original variables. The original equation is transformed to reduced one, which can be solved by separation of variables. Solutions of the reduced equation have been found for the cases of additive, multiplicative and combined separation of variables.
    Date of submission: 30 October 2015 г.


  2. Khrystiyanyn A.Y., Vyshyns'kyi O.S. Growth regularity of the arguments of meromorphic in $\mathbb{C}\setminus \{0\}$ functions of completely regular growth
    Status: accepted в т.0 №0
    Abstract.
    The asymptotic behaviour of the arguments of meromorphic function in $\mathbb{C}\setminus \{0\}$ of completely regular growth with respect to a growth function $\lambda$ is studied. It appears that the key role in the description of this behaviour belongs to the function $\lambda_1 (r) = \int_1^r \lambda (t) / t \, dt.$
    Date of submission: 23 November 2015 г.


  3. Zaharov S.V., Elbert A.E. Compression waves modelling with a large initial gradient in the Korteweg -- de Vries hydrodynamics
    Status: accepted в т.9 №1
    Abstract.
    The Cauchy problem for the Korteweg -- de Vries equation with a small parameter at the higher derivative and large gradient of the initial function is considered. By numerical and analytical methods it is shown that the formal asymptotics obtained with the help of renormalization, corresponding compression waves, is an asymptotic solution of the KdV equation. Plots of the asymptotic solution are obtained, including cases of nonmonotone initial data.
    Date of submission: 04 December 2015 г.


  4. Nasibullin R.G. Sharp Hardy type inequalities with weights dependent on the Bessel function
    Status: accepted в т.0 №0
    Abstract.
    We obtain a new sharp Hardy type inequality with weights. Using the Bessel functions we prove Lp one dimensional inequality and their multidimensional analogs in convex domains. The weight functions depend on the Bessel functions and Lamb's constants.
    Date of submission: 08 December 2015 г.


  5. Dyshaev M.M., Fedorov V.E. Symmetries and exact solutions of a pricing options nonlinear equation
    Status: accepted в т.0 №0
    Abstract.
    The group structure is researched for Sch\"onbucher--Wilmott equation with a free parameter. It is modeling the pricing options. A five-dimensional group of equivalence transformations for the equation is found. With its help four-dimensional Lie algebras are calculated in the cases of two free element specifications. A three-dimensional Lie algebra corresponds to other nonequivalent specifications. Optimal subalgebras systems and cor\-res\-ponding invariant solutions or invariant submodels are found for every Lie algebra.
    Date of submission: 28 December 2015 г.


  6. Андронова О.А., Войтицкий В. И. О спектральных свойствах одной краевой задачи с поверхностной диссипацией энергии
    Status: accepted в т.9 №1
    Abstract.
    В работе изучается спектральная задача в ограниченной области $\Omega \subset R^{m} $, зависящая от ограниченного операторного коэффициента S$>$0 и параметра диссипации $\alpha >0$. В общем случае установлены достаточные условия, при которых задача имеет дискретный спектр, состоящий из счётного числа изолированных конечнократных собственных значений с предельной точкой на бесконечности, а также условия при которых из системы корневых элементов можно выделить полную подсистему в $L_{2}^{} (\Omega )$. В модельной одномерной и двумерной задаче установлена локализация собственных значений и найдены критические значения $\alpha $.
    Date of submission: 01 February 2016 г.


  7. Каримов О.Х. О коэрцитивных свойствах и разделимости бигармонического оператора с матричным потенциалом
    Status: accepted в т.9 №1
    Abstract.
    In this paper we investigate the coercive properties of the nonlinear biharmonic operator with matrix potential in the space $L_2(R^n)^l$ and prove its separability in this space. The considered nonlinear operators are not weak perturbation of the linear ones. The case of linear biharmonic operator is considered separately.
    Date of submission: 10 February 2016 г.


  8. Bilal B.T., Gasymov T.B. On basicity of a system of eigenfunctions of second order discontinuous differential operator
    Status: accepted в т.0 №0
    Abstract.
    The spectral problem of second order discontinuous differential operator with spectral parameter in the boundary condition is considered. A method for establishing the basicity of systems of eigenfunctions of such problems is presented. A direct expansion for a Banach space with respect to subspaces is also considered. A method for constructing a basis for a space, proceeding from bases for subspaces, is proposed. Cases when the bases for subspaces are isomorphic and the corresponding isomorphisms are not required are also considered. Completeness, minimality and uniform minimality of corresponding systems are studied. This approach has an extensive applications in the spectral theory of discontinuous differential operators.
    Date of submission: 12 February 2016 г.


  9. Muhamadiev E.M., Naimov A.N., Sattorov A.H. Аналог теоремы Боля для одного класса линейных дифференциальных уравнений в частных производных
    Status: accepted в т.9 №1
    Abstract.
    Для одного класса линейных дифференциальных уравнений в частных производных высоких порядков с постоянными коэффициентами исследован вопрос о существовании и единственности ограниченного во всем пространстве решения. Сформулирована и доказана теорема о необходимых и достаточных условиях существования и единственности ограниченного решения для исследуемого класса уравнений. Данная теорема является аналогом теоремы Боля, известной в теории обыкновенных дифференциальных уравнений. В одном частном случае условия однозначной разрешимости выражены через свойства коэффициентов уравнения и приведено интегральное представление ограниченного решения.
    Date of submission: 15 February 2016 г.


  10. Parfenov A.I. Dicrete Holder estimates for a certain kind of parametrix. II
    Status: accepted в т.9 №1
    Abstract.
    In the first part of the paper we have introduced a certain parametrix and its respective potential. The parametrix corresponds to a uniformly elliptic second order differential operator having locally H\"older continuous coefficients in the half-space. Here we show the potential to be an approximate left inverse of the differential operator modulo hyperplane integrals, with the error estimated by the local H\"older norms. As a corollary, we evaluate approximately the potential whose density and differential operator originate from the straightening of the special Lipschitz domain. This corollary is meant for the future derivation of approximate formulas for harmonic functions.
    Date of submission: 14 Mart 2016 г.


  11. Kozhanov A.I., Safiullova R.R. On a determination of the parameters in the telegraph equation
    Status: accepted в т.9 №1
    Abstract.
    We consider the inverse problems with an unknown coefficient $c$ for a telegraph equation $$u_{tt}-\Delta u +cu=f(x,t)$$ and investigate the solvability of the problem. We prove the theorems of the existence of the problem's regular solutions. The distinctiveness of the problems is a presence the new overdetermination conditions for the considered class equations.
    Date of submission: 25 Mart 2016 г.


  12. Babaghanov B.A., Интегрирования уравнение типа периодической цепочки Тоды
    Status: reviewing
    Abstract.
    In this paper, the inverse spectral problem is applied to the integration of the periodic Toda-type Lattice.
    Date of submission: 31 Mart 2016 г.


  13. Arabov M.K., Muhamadiev 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 №1
    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.


  14. Аvkhadiev F.G., Shabalin P.L. Конформные отображения круговых областей на конечно-связные области несмирновского типа
    Status: accepted в т.0 №0
    Abstract.
    Рассматриваются каноническая факторизация и интегральные представления для производных конформных отображений круговых областей на конечно-связные области несмирновского типа. С использованием функций класса Зигмунда получены условия глобальной однолистности. Аналогичные результаты ранее были доказаны рядом авторов лишь для случая односвязных областей.
    Date of submission: 11 May 2016 г.


  15. 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.


  16. 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.


  17. Braeutigam I.N., Mirzoev K.A., Safonova T.A. Analogue of the Orlov's theorem about deficiency numbers for matrix differential operators of the second order
    Status: accepted в т.9 №1
    Abstract.
    In this paper we consider operators generated by the matrix linear symmetric quasi-differential expression of second order $$l[y]=-(P(y^{\prime}-Ry))^{\prime}-R^*P(y^{\prime}-Ry)+Qy$$ on the set $[1,+\infty)$ where $P^{-1}(x)$, $Q(x)$ are Hermitian matrix functions and $R(x)$ is a complex matrix function of order $n$ with entries $p_{ij}(x), q_{ij}(x)$, $r_{ij}(x) \in L^1_{loc}[1,+\infty)$ ($i,j=1,2,\ldots,n$). We describe the minimal closed symmetric operator $ L_0 $ generated by this expression in the Hilbert space $\mathcal{L}^2_n[1,+\infty)$ and prove an analogue of the Orlov's theorem on the deficiency index of linear scalar differential operators.
    Date of submission: 24 May 2016 г.


  18. Шафигуллин И.К. Нижняя оценка константы Харди для произвольной области в $\mathbb{R}^n$.
    Status: accepted в т.0 №0
    Abstract.
    В работе получены отличные от нуля нижние оценки константы Харди для произвольных областей, не совпадающих со всем пространством. Данные оценки являются точными по порядку, при $n \rightarrow \infty$, где $n$ --- размерность пространства.
    Date of submission: 25 May 2016 г.


  19. Klishchuk B.A., Salimov R.R. LOWER BOUNDS FOR AREAS OF IMAGES OF DISCS
    Status: reviewing
    Abstract.
    In this article we consider Q-homeomorphisms with respect to the p-modulus on the complex plane with p > 2. It is obtained a lower area estimate for image of discs under such mappings. We solved the extremal problem about minimization of the area functional of images of discs.
    Date of submission: 16 June 2016 г.


  20. MAHDAVIAN RAD H., NIKNAM A. Multi-Tuple Derivations and Automatic Continuity
    Status: reviewing
    Abstract.
    Let A be an algebra and m a natural number. A linear operator d : A → A is called a multi-tuple derivation of degree m if there exist families {δ u },{ε u } of linear operators on A, where u ∈ Z,1 ≤ u ≤ m − 1, such that d(ab) = d(a)b + ad(b) + m−1 ∑ u=0 (δ u (a)ε u (b) + ε u (a)δ u (b)) for all a,b ∈ A. We study some algebraic properties of these mappings and give a formula for calculat- ing d n (ab). After that, we state a few theorems and corollaries regarding the concept automatic continuity. Also we define a new terminology named higher multi-tuple derivation and prove that under certain conditions, it is continuous on semi-simple Banach algebras.
    Date of submission: 17 June 2016 г.


  21. Rani N., Vamshee Krishna D., Venkateswarlu B. Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha
    Status: accepted в т.0 №0
    Abstract.
    In this paper we obtain the best possible upper bound to the third Hankel determinants for the functions belonging to the class of reciprocal of bounded turning functions using Toeplitz determinants
    Date of submission: 29 June 2016 г.


  22. Balkizov Zh.A. The first boundary problem for parabolic-hyperbolic equation of third order with degeneration of the type and order in the domain of hyperbolicity
    Status: accepted в т.9 №1
    Abstract.
    We investigated an analog of the Tricomi problem for a parabolic-hyperbolic equation of third order with multiple characteristics, containing terms with lower derivatives. Under certain conditions specified functions and parameters that are included in this equation, a theorem on the existence and uniqueness of solutions of the problem. The uniqueness of the solution of the problem is proved by using the generalized method of Tricomi existence - the method of integral equations.
    Date of submission: 07 July 2016 г.


  23. Khubiev K.U. Analog of Tricomi problems for characteristicly loaded hyperbolic-parabolic equations with variable coefficients
    Status: accepted в т.9 №1
    Abstract.
    In this paper the analog of Tricomi problem for loaded equation of hyperbolic-parabolic type with variable coefficients is considered. The existence and uniqueness theorem of solution the problems is proved. The uniqueness of solution is proved by maximum principle and the solution existence is proved by integral equation methods.
    Date of submission: 07 July 2016 г.


  24. Горбацевич V.V. О геометрии решения приближенных уравнений и их симметриях
    Status: reviewing
    Abstract.
    The article is devoted to the development of the geometric approach to the theory of approximate equations (including ODE and PDE) and their symmetries. We introduce dual Lie algebras, manifolds over dual numbers and dual Lie group. We describe some constructions for these objects. On the basis of these constructions it is shown how it is possible to formulate basic concepts and methods in the theory of approximate equations and their symmetry. The proofs of many general results here can be obtained almost automatically from classical one's, unlike used now in studying of the approximate equations methods.
    Date of submission: 14 July 2016 г.


  25. 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.


  26. 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.


  27. Berdellima A. KHABIBULLIN’S CONJECTURE: Khabibullin’s Theorem, a Counterexample and Further Observations
    Status: accepted в т.9 №1
    Abstract.
    We prove a restricted variant of Khabibullin’s Theorem, construct a counterex- ample to the conjecture when $n = 2$ and $\alpha > 1/2$ and explore some relations of the integral inequalities with the beta and Cauchy distribution
    Date of submission: 26 July 2016 г.


  28. Ахмадуллин R.Z. О НЕРАВЕНСТВЕ РОБИНА ДЛЯ ГИПОТЕЗЫ РИМАНА
    Status: reviewing
    Abstract.
    Рассмотрена гипотеза Римана о распределении нулей дзета-функции в формулировке, не использующем понятия комплексного переменного. Получены необходимые и достаточные условия, при которых неравенство выполнено для всех натуральных чисел N, за исключением их некоторого конечного количества.
    Date of submission: 28 July 2016 г.


  29. 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.


  30. 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.


  31. 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.


  32. 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.


  33. 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.


  34. 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.


  35. 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.


  36. 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.


  37. Kalyakin L.A. Adiabatic approximation for a model of resonance capture
    Status: accepted в т.9 №1
    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.


  38. 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.


  39. Tunc C. A note on the qualitative properties of solutions of nonlinear retarded Volterra integro-differential equations
    Status: reviewing
    Abstract.
    In this article, we construct new sufficient conditions for the asymptotically stability and boundedness of solutions to nonlinear Volterra integro-differential equations of first order with constant delay. Our analysis is based on the successful construction of suitable Lyapunov –Krasovskii functionals. The results of this paper are new and correct, and they improve that obtained in literature.
    Date of submission: 30 December 2016 г.


  40. 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.


  41. 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.


  42. 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.


  43. Malyutin K.G., Shevtsova T.V. The delta-subharmonic functions of finite $(\gamma,\varepsilon)$-growth
    Status: reviewing
    Abstract.
    Let $\gamma(r)$ be growth function and $\varepsilon(r)>0$ be non-increasing function satisfying the condition $\varepsilon(r(1+\varepsilon(r)))\geqslant(\varepsilon(r))^\eta$ for some $\eta>1$ for all large $r$. We consider the class $\delta\mathcal{S}(\gamma,\varepsilon)$ delta-subharmonic functions $v$ in $\mathbb{C}$ such that the Nevanlinna characteristic $T(r,v)$ is estimated by the inequality $T(r,v)\leqslant\frac{a}{(\varepsilon(r))^{\alpha}}\gamma(r+\beta\varepsilon(r)r)$ for some positive constants $a,\ \alpha,\ \beta$. The necessary and sufficient conditions for a function $v$ in class $\delta\mathcal{S}(\gamma,\varepsilon)$ is obtained. These criteria are formulated in terms of $c_k (r, v)=\frac1{2\pi}\int_0 ^{2\pi}v(re^{i\theta})e^{-ik\theta}\,d\theta$, $k\in\mathbb Z$, the Fourier coefficients of the function $v$.
    Date of submission: 28 January 2017 г.


  44. 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.


  45. 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.


  46. Gaitsgory V.G., Muhamadiev E.M., Naimov A.N. The research of some properties of recurrent and almost periodic functions.
    Status: reviewing
    Abstract.
    В работе исследованы известные и новые свойства рекуррентных и почти периодических функций. Эти свойства актуальны как с точки зрения анализа и теории функций, так и с точки зрения теории дифференциальных уравнений и динамических систем. Приводятся новые доказательства теорем о рекуррентности и почти периодичности неопределенных интегралов от рекуррентных и почти периодических функций. А также по новой схеме доказывется теорема о совместной рекуррентности любой пары рекуррентной и почти периодической функции. На основе схемы доказательства этой теоремы предложен и обоснован алгоритм построения новых рекуррентных функций по уже заданным рекуррентным функциям.
    Date of submission: 26 February 2017 г.


  47. 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.


  48. 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.


  49. Yazovtseva O.S. The local component-wise asymptotic equivalence and its application to investigate for stability with respect to a part of variables
    Status: reviewing
    Abstract.
    The article introduces the notion of a local component-wise asymptotic equivalence of systems of ordinary differential equations in relation to some standart functions. The sufficient conditions preserving of component-wise stability, asymptotic stability and asymptotic equilibrium are received. There was considered the mathematical model of the ethane pyrolysis brutto-reaction as a nonlinear system of ordinary differential equations. There was built the one-to-one mapping, which had established the local component-wise asymptotic equivalence of solutions of the researched system and its linear approximation. A nontrivial equilibrium of the system was investigated for stability with respect to a part of variables based on the constructed one-to-one mapping. The asymptotic of the solutions was found.
    Date of submission: 10 Mart 2017 г.