Editorial backlog

  1. Rathod A. Uniqueness and Value Sharing of Meromomorphic Functions on Annuli
    Status: reviewing
    Abstract.
    In this paper, we study meromorphic functions that share only one value on annuli and prove the following results. Let f(z) and g(z) two non constant meromorphic functions on annli and For n ≥ 11, if f n f 0 and g n g 0 share the same nonzero and finite value a with the same multiplicities on an- nuli, then f ≡ dg or g = c 1 e cz and f = c 2 e −cz , where d is an (n + 1) th root of unity, c, c 1 and c 2 being constants.
    Date of submission: 04 June 2019 г.


  2. Shaikhullina P.A. Sectorial normalization of simplest germs of semihyperbolic maps in half-neighborhood
    Status: reviewing
    Abstract.
    There are considered the problem of analytical classification of the semi-hyperbolic maps by example of the simplest class of such germs on the plane (namely, the class of germs that are formally equivalent of 1-time shift of vector field $x^2\frac{\partial}{\partial x}+e^{\lambda}y\frac{\partial}{\partial y},~\lambda\in\mathbb{R}_+$). The theorem of sectorial normalization of such germs in semi-neighborhood in which is not exist a central manifold is proved. Also it's proved that the semi-formal normalizing map is asymptotic for the sectorial analytic normalizing map.
    Date of submission: 25 June 2019 г.


  3. МАСТАЛИЕВ R.O. ОСОБЫЕ УПРАВЛЕНИЯ В СТОХАСТИЧЕСКИХ СИСТЕМАХ С ЗАПАЗДЫВАНИЕМ
    Status: reviewing
    Abstract.
    Рассматривается задача оптимального управления, в который состояние процессы определяется систем стохастических дифференциальных уравнений Ито с запаздывающим аргументом. На основе вариаций управления установлены новые необходимые условия оптимальности особых управлений в процессах, описываемых системой стохастических дифференциальных уравнений с запаздывающим аргументом.
    Date of submission: 17 July 2019 г.


  4. Falaleev M.V. Fundamental Operator-functions of Integro-Differential Operators Under Spectral or Polynomial Constraints
    Status: reviewing
    Abstract.
    This paper investigates the Cauchy problem for a degenerate high order integro-differential equation in Banach spaces. For the equations under study, the corresponding fundamental operator functions are constructed, with the help of which the only generalized solution of the original Cauchy problem in the class of distributions with a left-bounded carrier is restored. The analysis of the resulting generalized solution allows us to investigate the solvability problem in the classical sense. The fundamental operator-function is constructed in terms of the theory of semigroups of operators with kernels. Abstract results are illustrated by examples of initial-boundary value problems of viscoelasticity theory.
    Date of submission: 25 September 2019 г.


  5. Nazarov M., Mukhamadiev E.M. Regularity of almost periodic solutions of Poisson's equation
    Status: reviewing
    Abstract.
    The paper discusses almost periodic solutions of the Poisson's equation $-\Delta u = f$ in $\mR^n$, where $f$ is an almost periodic function. It is proven that if $u$ is {\em a bounded generalized solution} of the Poisson's equation, then $u$ and its partial derivatives $\p u/ \p x_i$ are continuous, bounded and almost periodic functions.
    Date of submission: 28 September 2019 г.


  6. Halim B., Senouci A., Sofrani M. Some Chebyshev type Inequalities for a certain integral operator
    Status: reviewing
    Abstract.
    In this work, some weighted Chebyshev type inequalities are obtained by using a more general fractional integral operator, than the Riemann-Liouvile one.
    Date of submission: 30 September 2019 г.


  7. Garif'yanov F.N., Strezhneva E.V. On the moment problem for entire functions generated by a doubly periodic group
    Status: reviewing
    Abstract.
    The lacunar problem of Stieltjes moments with exponential weight is considered. The solution is sought in the class of entire functions of exponential type, the indicator diagram of which is a certain square. Nontrivial solutions of the corresponding homogeneous problem are constructed. This problem boils down to the study of a linear total equation in the class of functions holomorphic outside four squares. At infinity, they have zero multiplicities of at least three. Their boundary values ??satisfy the Holder condition on any compactum that does not contain square vertices. At the vertices, at most, logarithmic features are allowed. The solution is sought in the form of an integral of Cauchy type with an unknown density along the boundary of these squares. A method for regularizing the total equation is proposed. The condition of equivalence of this regularization is clarified. Particular cases are highlighted when the obtained Fredholm equation of the second kind is solvable. For this, the principle of compressive mappings in a Banach space is used.
    Date of submission: 09 October 2019 г.


  8. HEIDARI TAVANI M.R., NAZARI A. TRIPLE WEAK SOLUTIONS FOR THREE-POINT BOUNDARY VALUE PROBLEMS OF KIRCHHOFF-TYPE
    Status: reviewing
    Abstract.
    In this paper , we establish the existence of at least three positive weak solutions for a perturbed three-point boundary value problem of Kirchhoff-type. The approach is based on variational methods and critical point theory. As applications of these methods, we get several multiplicity results for the problems under consideration. Are presented the results were extention of some existing results.
    Date of submission: 18 October 2019 г.


  9. ZUBELEVICH O. ON EXISTENCE OF COINCIDENCE POINTS FOR MAPPINGS IN BANACH SPACES
    Status: reviewing
    Abstract.
    In this article we prove an existence theorem for co- incidence points of mappings in Banach spaces. This theorem gen- eralizes the Kantorovich fixed point theorem.
    Date of submission: 23 October 2019 г.


  10. Mirzaev O.E., Khasanov A.B. О семейства изоспектральных краевых задачи Штурма-Лиувилля
    Status: reviewing
    Abstract.
    In this paper is presented an algorithm for constructing a family of different Sturm-Liouville boundary-value problems whith a same spectrum.
    Date of submission: 24 October 2019 г.


  11. Volchkov V.V., Volchkov V.V. An overdetermined boundary Neumann problem on unbounded domains
    Status: reviewing
    Abstract.
    The study of overdetermined boundary value problems for elliptic partial differential equations was initiated by D.~Serrin in 1971. In his work, he established the property of radial symmetry for solutions of some overdetermined Poisson problem. In addition to significant independent interest, problems of this type have important applications in potential theory, integral geometry, hydrodynamics, electrostatics, and the theory of capillarity. Usually their the solution is based on the maximum principle, the Hopf lemma on an angular boundary point and the method of moving hyperplanes introduced by A.D.~Alexandrov to study some geometric problems associated with the characterization of spheres. Among other, more modern methods that do not use the maximum principle in the problems under consideration, we note the duality method, the volume derivative method, and also the integral method. This article discusses the overdetermined Neumann problem for the Laplace equation $\Delta f = 0$ on flat unbounded domains. It is shown that under certain conditions (see Theorem~\ref{th 1} in Section~1) such a problem is solvable only for the exterior of the circle. A distinctive feature of Theorem~\ref{th 1} is that for the first time in such problems an exact condition is obtained for the growth of $f$ at infinity. In addition, as can be seen from Theorem~\ref{th 2} in Section~2, other conditions in Theorem~\ref{th 1} are also necessary. In contrast to the works of predecessors, the proof of Theorem~\ref{th 1} uses some boundary properties of conformal mappings, the V.I.~Smirnov theorem on functions of the class $H_p$, and the Fejer-Riesz theorem on non-negative trigonometric polynomials.
    Date of submission: 31 October 2019 г.


  12. Dagli M.C. Some relations on certain Hardy sums and two-term exponential sums
    Status: reviewing
    Abstract.
    In this paper, we deal with a computational problem of one kind mean value involving certain Hardy sums and the two-term exponential sum with the help of the properties of Gauss sums, and derive some interesting precise computational formulae.
    Date of submission: 04 November 2019 г.


  13. Sacvhin V.M., Trinh P.T. Nonpotentiality of the Sobolev system and the construction of a semibounded functional
    Status: reviewing
    Abstract.
    The nonpotentiality of the operator of a boundary value problem for the Sobolev system of partial differential equations with respect to the classical bilinear form is proved. It is shown that this system does not admit a matrix variational multiplier of the given form. A semibounded functional for the given problem is constructed.
    Date of submission: 10 November 2019 г.


  14. Zarifzoda S.Q. A Construction of exact solutions for some classes of singular partial integro-differential equations
    Status: reviewing
    Abstract.
    In this work for one class of second order model and nonmodel partial integro-differential equation with singularity in the kernel, obtained integral representation manifold solution by arbitrary functions. First of all in the given paper it is entered a new class of such functions that at point (a,b) is converted to zero with some asymptotic behavior and the solution of given equation is found in this class. Also, singular integro-differential operators are entered and main property of entered operators are learned. For these operators the inverse operators are found. It is shown that the solution of studied equation is equivalent to the solution of system of two ordinary integro-differential equations by variable x and y. In the cases when the solution of given integro-differential equation depends of any arbitrary constant a Cauchy type problems are investigated. For the investigation of Cauchy type problems first of all the property of obtained solution studied. It is shown that, when some conditions are fulfilled the Cauchy type problems have only unique solution.
    Date of submission: 20 November 2019 г.


  15. Абдушукуров Ф.А. Пуассоновские предельные теоремы в схемах размещения различимых частиц
    Status: reviewing
    Abstract.
    Рассматривается случайная величина $\mu_r(n, K, N)$ - 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. Эти условия имеют наиболее простой вид, когда количество частиц $r$ принадлежит ограниченному множеству (\ref{th2}) или $K$ эквивалентно $\sqrt{N}$ (теорема 3). Тогда случайные величины $\mu_r(n, K, N)$ ведут себя как суммы независимых одинаково распределенных индикаторов (биномиальные случайные величины) и наши условия совпадают с условиями классической пуассоновской предельной теоремы. Получены аналоги этих теорем для равновероятной схемы размещения $n$ различимых частиц по $N$ различным ячейкам. Доказательства теорем основаны на пуассоновской предельной теореме для сумм перестановочных индикаторов и аналоге локальной предельной теореме Гнеденко.
    Date of submission: 24 November 2019 г.


  16. Singh G., Singh G., Singh G. Certain Subclasses of Analytic Functions Defined with Generalized Sãlãgean Operator Subordinate to Bilinear Transformation
    Status: reviewing
    Abstract.
    The present investigation deals with certain subclasses of analytic-univalent functions in the open unit disc   : 1 E z z   . The coefficient estimates, distortion theorem, argument theorem and relation of these classes with some other class have been studied and the results so obtained generalize the results of several earlier works.
    Date of submission: 26 November 2019 г.


  17. Egorova A.E., Khabibullin B.N. Growth of subharmonic functions along the line and distribution of their Riesz measures
    Status: reviewing
    Abstract.
    Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$ are two subharmonic functions in the complex plane $\mathbb C$ with the Riesz measures $\nu_u$ and $\mu_M$ such that $u(z)\leq O(|z|)$ and $M(z)\leq O(|z|)$ as $z\to \infty$. If the growth of this function $M$ in some sense exceeds the growth of the function $u$ on some straight line, then we can expect the measure $\mu_M$ to dominate the measure $\nu_u$ in some sense. We give quantitative forms of such dominance. The main results are illustrated by a new uniqueness theorem for entire functions of exponential type.
    Date of submission: 26 November 2019 г.


  18. Lakaev S.N., Hamidov Sh.I. Пороговые эффекты в спектре одно-частичного оператора Шредингера на целочисленной решетке
    Status: reviewing
    Abstract.
    We consider a wide class of the Schrӧdinger operators describing a particle in an external field , on a - dimensional integer cubic lattice . We study the threshold effects in the spectrum of the one-particle Schrӧdinger operator , as well as the existence or absence of its bound states depending on the potential and dimension of the lattice . We found that the appearance of bound states of the operator depends on whether the threshold of its essential spectrum is a regular or singular point: namely, if the lower threshold of the essential spectrum of the operator is a regular point of its essential spectrum, then for small perturbations, the number of eigenvalues below the essential spectrum does not change, but if the lower threshold of the essential spectrum of the operator is a singular point, then for certain small perturbations the operator has eigenvalues below the essential spectrum. In addition, we obtained easily verifiable conditions for the existence of the eigenvalues of the operator lying below the essential spectrum.
    Date of submission: 04 December 2019 г.


  19. Saba N. Al-khafaji , Ahmed Hadi Hussain , Ali A. Shukur , Ali Al-Fayadh Third Hankel and Toeplitz Determinant for Certain Class of non-Bazilevic Functions and Pseudospectrum of Associated Toeplitz Matrix
    Status: reviewing
    Abstract.
    The main object in this paper is give an upper bound for the third determinant of the Hankel and the Toeplitz matrices for which the entries are belong to a new introduced certain class of non-Bazilevi? c functions N µ , analytic in the open unit disk D and associated with exponential function. Also, we studied so-called pseudospectrum of the Toeplitz matrix with entries belong to the introduced class of function N µ to give a particular view about the behavior of such matrix.
    Date of submission: 04 December 2019 г.


  20. Abdollah Borhanifar , Alaeddin Malek , Sohrab Valizadeh Compact ADI method for two-dimensional Riesz space fractional diffusion equation
    Status: reviewing
    Abstract.
    In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space frac- tional diffusion equation. The precision of the discretization method used in spatial directions is twice the order of the corresponding frac- tional derivatives. It is proved that the proposed method is uncondi- tionally stable via the matrix analysis method and the maximum error in achieving convergence is discussed. Numerical example is considered aiming to demonstrate the validity and applicability of the proposed technique.
    Date of submission: 06 December 2019 г.


  21. Myrzakul T.R., Tayshieva A.G., Nugmanova G.N. On the equivalence of one spin system and the two-component Kamass-Holm equation
    Status: reviewing
    Abstract.
    The work is devoted to the study of the equivalence of the two-component Camassa-Holm equation (CHE) and the spin system, which is a generalization of the Heisenberg ferromagnet equation. It is known that equivalence between nonlinear integrable equations enables an advanced search for their various exact solutions. For the CHE we apply the method of the inverse scattering problem through the system of linear partial differential equations with scalar coefficients. Compared to the CHE, the coefficients of linear systems corresponding to spin equations are related to the symmetric matrix Lax representations. There-fore when establishing equivalence between the above equations, additional difficulties arise. Based on this, the matrix Lax representation for the CHE in symmetric space is proposed. Using the result, a gauge equivalence between the two-component CHE and the spin system is established. The relationship between their solutions is shown.
    Date of submission: 10 December 2019 г.


  22. Mukhamadiev E.M., Nazimov A.B., Naimov A.N. On the solvability a class of nonlinear equations
    Status: reviewing
    Abstract.
    В статье исследована разрешимость одного класса нелинейных уравнений с малым параметром в банаховом пространстве. Исследование данного класса уравнений затруднено тем, что главная линейная часть уравнения не обратима. Для исследования разрешимости рассматриваемого класса уравнений применен новый метод, в котором сочетаются метод Понтрягина из теории автономных систем на плоскости и методы вычисления вращения векторных полей. Сформулирована и доказана теорема об условиях разрешимости исследуемого класса нелинейных уравнений. В качестве приложения доказаны новые теоремы о разрешимости периодических задач для нелинейных дифференциальных уравнений.
    Date of submission: 11 December 2019 г.


  23. K. R. PRASAD, M. RASHMITA, N. SOLVABILITY OF HIGHER ORDER THREE-POINT ITERATIVE SYSTEMS
    Status: reviewing
    Abstract.
    This paper is concerned to determine intervals of the eigenvalues λ 1 ,λ 2 ,· · ·,λ m for which the iterative system of n th order three-point non-homogeneous boundary value problem possesses a positive solution by an application of Guo–Krasnosel’skii fixed point theorem on a cone in a Banach space.
    Date of submission: 12 December 2019 г.


  24. Kwok-Pun Ho Exponential Rosenthal's and Marcinkiewicz-Zygmund inequalities
    Status: reviewing
    Abstract.
    We extend Rosenthal’s inequalities and Marcinkiewicz-Zygmund inequalities to exponential Orlicz spaces.
    Date of submission: 08 January 2020 г.


  25. Murugusundaramoorthy G. PARABOLIC STARLIKE AND UNIFORMLY CONVEX FUNCTIONS ASSOCIATED WITH PASCAL DISTRIBUTION SERIES
    Status: reviewing
    Abstract.
    The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. To be more precise,we investigate such connec- tions with the classes of parabolic starlike and uniformly convex functions associated with Pascal distribution series .
    Date of submission: 09 January 2020 г.


  26. Khamdamov I.M. PROPERTIES OF A CONVEX HULL GENERATED BY THE NONHOMOGENEOUS POISSON POINT PROCESS
    Status: reviewing
    Abstract.
    The paper is devoted to the limit distribution study of the external part of the area of a convex hull generated by independent observations of two-dimensional random points having Poisson distribu- tions above the parabola. Following P. Groeneboom (1988), we note that near the boundary of support, the Binomial point process is almost indistinguishable from the Poisson point process. Therefore, here we study the functionals of a convex hull generated by the Poisson point process. Using the properties of strong mixing and martingality of a Markovian jump vertex process, we prove the central limit theorem for the external part of the area of a convex hull.
    Date of submission: 14 January 2020 г.


  27. Karichery D., Pulickakunnel S. FG-coupled fixed point theorems for contractive and generalized quasi-contractive mappings
    Status: reviewing
    Abstract.
    In this paper, we prove FG-coupled fixed point theorems for different contractive mappings and generalized quasi- contractive mappings in partially ordered complete metric spaces. We prove the existence of FG-coupled fixed points of continuous as well as discontinuous mappings. Our first three results generalize the theorems of Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham; Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393]. We give some examples to illustrate the results.
    Date of submission: 15 January 2020 г.


  28. Kanguzhin B.E. Reestablishing two-point boundary conditions from a finite set of eigenvalues of boundary value problems for higher order differential equations
    Status: reviewing
    Abstract.
    An algorithm is proposed for reconstructing the two-point boundary conditions of a boundary value problem for higher-order differential equations. Finite sets are values of specially constructed boundary value problems. According to the terminology of V.A. Sadovnichiy such problems are called etalon problems. In this work, special attention is paid to the special choice of etalon problems.
    Date of submission: 15 January 2020 г.


  29. Petrosyan G.G. On antiperiodic boundary value problem for a semilinear differential inclusion of fractional order with a deviating argument in a Banach space
    Status: reviewing
    Abstract.
    In this paper we consider an antiperiodic boundary value problem for a semilinear differential inclusion with the fractional Caputo derivative with a deviating argument in a Banach space. It is assumed that the linear part of the inclusion generates a bounded $ C_0 $ -semigroup. We will be used the theory of topological degree for multivalued condensing mappings to solve the stated problem . The idea of to solve is as follows: the original problem is reduced to the problem of the existence of fixed points of the corresponding resolving multivalued integral operator. We will to prove the existence of fixed points of the resolving multioperator with use generalized fixed point theorem of the type by B.N. Sadovskii.
    Date of submission: 16 January 2020 г.


  30. Петросян A.S., Khachatryan K.A. О разрешимости одного класса многомерных интегральных уравнений в математической теории географического распространения эпидемии
    Status: reviewing
    Abstract.
    Исследуется многомерное интегральное уравнение типа свертки с вогнутой нелинейностью. Указанное уравнение возникает в математической теории географического распространения эпидемии. Сочетание известных методов многомерных операторов и методов построения инвариантных конусных отрезков для таких операторов с методами теории интегральных операторов типа свертки и предельных теорем теории функций позволяют доказать существование положительных ограниченных решений для таких уравнений. Также изучается асимптотическое поведение построенных решений. В конкретно выбранном конусном отрезке доказывается также единственность решения. Приводятся конкретные прикладные примеры указанных уравнений.
    Date of submission: 21 January 2020 г.


  31. Ahmedzade N.R., Kasumov Z.A. On the solvability Dirichlet problem for the Laplace equation with the boundary value in grand-Lebesgue space
    Status: reviewing
    Abstract.
    In this paper the weighted grand space of harmonic within the unit circle of functions $h_{w}^{p),\theta } $ is defined and the solvability of the Dirichlet problem for the Laplace equation in this space is considered. Using the boundedness of the maximum operator in the weighted grand-Lebesgue space, the solvability of the Dirichlet problem for the Laplace equation with a boundary value from the grand-Lebesgue weight space is proved.
    Date of submission: 24 January 2020 г.


  32. Sidikova A.I., Tanana V.P. Research and solution of a conditionally correct problem for the differential equation of thermal conductivity
    Status: reviewing
    Abstract.
    The article is devoted to the study and solution of the inverse boundary value problem of thermal conductivity for a hollow sphere consisting of composite materials. In the inverse problem, using information about the temperature of the heat flow in the media section at the point $r=r_1$, it is necessary to determine the temperature on the inner wall of the hollow ball and obtain an error estimate, which, as is known, significantly increases the reliability of the numerical results. In this paper, we study the completeness of the system of eigenfunctions in a direct problem, which allowed us to give a strict statement of the inverse problem and apply the Fourier transform in time to the inverse problem. An approximate solution of the inverse boundary value problem and an error estimate are obtained using the projection regularization method.
    Date of submission: 24 January 2020 г.


  33. Евстафьева V.V. СУЩЕСТВОВАНИЕ $T/k$-ПЕРИОДИЧЕСКИХ РЕШЕНИЙ РЕЛЕЙНОЙ НЕАВТОНОМНОЙ СИСТЕМЫ С ОТРИЦАТЕЛЬНЫМ СОБСТВЕННЫМ ЧИСЛОМ МАТРИЦЫ
    Status: reviewing
    Abstract.
    Рассматривается $n$-мерная система обыкновенных дифференциальных уравнений первого порядка с двухпозиционной релейной нелинейностью и непрерывной периодической функцией возмущения в правой части. Матрица системы имеет различные вещественные ненулевые собственные числа и по крайней мере одно отрицательное. Изучаются непрерывные периодические решения с периодами в целое число раз меньше периода функции возмущения. Устанавливаются условия существования периодических решений с двумя точками переключения в фазовом пространстве системы. Приведен пример, иллюстрирующий полученные результаты.
    Date of submission: 27 January 2020 г.


  34. Serikbaev D. INVERSE PROBLEM FOR FRACTIONAL ORDER PSEUDO-PARABOLIC EQUATION WITH INVOLUTION
    Status: reviewing
    Abstract.
    In this paper we consider an inverse problem of recovering the right- hand side of a fractional pseudo-parabolic equation with involution. The results on existence and uniqueness of solutions of this problem are presented by using Fourier analysis. The classical and generalized solutions of the inverse problem are studied. Moreover, the direct problem is also investigated.
    Date of submission: 04 February 2020 г.


  35. Аллахвердян A.A., Shabat A.B. Произведения собственных функций и вронскианы
    Status: reviewing
    Abstract.
    This paper considers new Wronskian identities recently discovered in Maykop. The relations of these identities with the theory of integrable systems and with the general theory of reversible Darboux transformations are discussed. Generalizations of equations for squares (for the case of cubes, etc.) of the eigenfunctions of the one-dimensional Schr?dinger operator are given. The special case of identities for exponential functions is investigated. The fundamental difference between Wronskian identities for operators of the second and third orders is established.
    Date of submission: 07 February 2020 г.


  36. Kytmanov A.M., Myslivets S.G. On some families sufficient for holomorphic continuation of functions with the Morera boundary property
    Status: reviewing
    Abstract.
    This article considers continuous functions defined on the boundary of a bounded domain $ D $ in $ \mathbb C ^ n $, $ n> 1 $, and having the Morera boundary property. We study the question of the existence of a holomorphic extension of such functions to the domain $ D $ for some sufficient sets $ \Gamma $ of complex lines.
    Date of submission: 08 February 2020 г.


  37. QASEMI S., PEDRAM L., ROSTAMY D. A NEW APPROACH FOR COMPUTING A POSTERIORI ERROR ESTIMATION FOR VLASOV-MAXWELL-FOKKER PLANCK SYSTEM
    Status: reviewing
    Abstract.
    In this paper, we propose a new splitting for reformulation of the Vlasov Maxwell Fokker Planck (VMFP). Therefore we produce a new successive algorithm for solving VMFP. We show that the algorithm converges to a unique solution. Also, we obtain an a posteriori error estimation in practical finite element analysis for sub-problems of successive algorithm. We also briefly comment upon the state of error estimations in VMFP and when mixed methods are used.
    Date of submission: 14 February 2020 г.


  38. Ahmadova A.N., Aliev R.A. Boundedness of the discrete Hilbert transform on discrete Morrey spaces
    Status: reviewing
    Abstract.
    The Hilbert transform has been well studied on classical Lebesgue and Morrey spaces. But its discrete version, which also has numerous applications, has not been fully studied. In this paper, we prove that the discrete Hilbert transform is a bounded operator in discrete Morrey spaces.
    Date of submission: 14 February 2020 г.


  39. Khabirov S.V. Invariant motions of particles for general three-dimensional subgroup of all translation group
    Status: reviewing
    Abstract.
    The equations of continuum mechanics are invariant under Galilei group extended by a dilatation. The group contains Abelian subgroup of the space translations including the uniform motion of the origin (galilei transformations). The Lie algebra of the group was studed and the optimal system of the subalgebras was constructed to within the inner automorphisms. The abelian subgroup of all space translations corresponds 6-dimensional abelian subalgebra that structure contains 13 dissimilar subalgebras. From them there is the general 3-dimensional subalgebra containing all operators of the galilei transformations. This subalgebra includes 5 arbitrary parameters which are the invariants of the inner automorphism group of the Lie algebra. For the general subalgebra we consider all invariant solutions with linear field of velocity for the ideal gas dynamics. The motions of particles are studed as a whole. The each particle moves on the straight line. The particles assemble on the linear manifold of blow up at the specific times. There are some manifolds of blow up depending on valuation of arbitrary parameters. The motions of isolated volumes from particles in the form of parallelepipeds projecting in the parallelogram on the manifold of blow up are considered. The movement of the sonic surfaces are studied for obtained solutions of gas dynamics equations depending on the state equation. The equations of the sound characteristics are introduced for the obtained invariant solutions. The example of the movement of a sonic conoid for simplest solution is reduced.
    Date of submission: 18 February 2020 г.


  40. Kasimova E.F., Khasanov Yu.Kh. About the relationship of a convolution type transform and the best approximation of periodic functions
    Status: reviewing
    Abstract.
    We consider a $2\pi$--periodic function $f(x)$ belonging to the space $L_p\,\,\, (1\leq p\leq\infty)$ on the period and a convolution type transformation containing some real function of bounded variation on the entire real axis. This transformation is a generalization of some specific transformations related to various characteristics of the function under consideration. As generalization of some results concerning features of the integral $L_p$--metric $(1Date of submission: 19 February 2020 г.