Editorial backlog
- Sazonov A.P. About the a priori and asymptotic estimates for Emden-Fowler problem on model Riemannian manifolds
Status: reviewing
Abstract. This work is devoted to study for Emden-Fowler problem on the model Riemannian manifolds. In particular, it will be obtained a priori and asymptotic estimates for radially symmetric solutions for this problem in the considered manifolds. The results of this work summarize similar statements obtained earlier in the work
S.I. Pohozaeva for the space $R^n$.
Date of submission: 07 July 2022 г.
- Ashurov R.R., M.D. Inverse problem for the subdiffusion equation with fractional Caputo derivative
Status: reviewing
Abstract. The inverse problem of determining the right-hand side of the subdiffusion equation with the fractional Caputo derivative is considered. The right-hand side of the equation has the form $f(x)g(t)$ and the unknown is function $f(x)$. The condition $ u (x,t_0)= \psi (x) $ is taken as the over-determination condition, where $t_0$ is some interior point of the considering domain and $\psi (x) $ is a given function. It is proved by the Fourier method that under certain conditions on the functions $g(t)$ and $\psi (x) $ the solution of the inverse problem exists and is unique. An example is given showing the violation of the uniqueness of the solution of the inverse problem for some sign-changing functions $g(t)$. For such functions $g(t)$, we find necessary and sufficient conditions on the initial function and on the function from the over-determination condition, which ensure the existence of a solution to the inverse problem.
Date of submission: 02 November 2022 г.
- Nazarov S.A. The influence of the Winkler--Steklov conditions
on natural oscillations of an elastic weighty body.
Status: reviewing
Abstract. We consider the spectral problem for the spacial system of equations of the elasticity theory.
%Small parts of the body surface are supplied with the Winkler--Steklov conditions which
%model spring mount while the remaining part of the boundary is traction-free.
%In several cases (the relative stiffness of springs and their disposition are varied)
%we consider asymptotics of eigenfrequencies of the body. Certain cases are analysed in detail,
%open questions are formulated and pathological situations leading to the loss of the customary
%properties by the spectrum, are discussed.
Date of submission: 24 December 2022 г.
- Makhmudov O.I., Niyozov I.E. The Cauchy problem for the system of elasticity theory
Status: reviewing
Abstract. In this paper, we considered the problem of analytical continuation of the solution of the system equations of the moment theory of elasticity in spacious bounded domain from its values and values of its strains on part of the boundary of this domain, i.e., the Cauchy's problem. The condition of solvability of this problem is considered.
Date of submission: 28 December 2022 г.
- Inequalities for Meromorphic functions with Prescribed Poles
Status: reviewing
Abstract. For a rational function $P\in \mathcal{P}_n,$ Dewan et al.[J. Math Anal. Appl.\textbf{363(1),}(2010), 38-41] proved:
$$\bigg|zP'(z)+\dfrac{n\beta}{2}P(z)\bigg|\geq n\bigg|1+\dfrac{\beta}{2}\bigg|\min \limits_{z\in T_k}{|P(z)|}.$$
In this paper we prove some refinements of Bernstein-type inequalities for meromorphic functions with prescribed poles and restricted zeros. These results not only generalize some inequalities for rational functions but also improve as well as generalize some polynomial inequalities too.
Date of submission: 10 January 2023 г.
- Balakhnev M.Yu. On the symmetry classification
of integrable evolution equations of the 3rd order
Status: reviewing
Abstract. New results within classification of nonlinear evolution vector equations of the 3rd order are obtained
Date of submission: 10 January 2023 г.
- EXISTENCE AND FINITE-TIME STABILITY OF SOLUTIONS
FOR A CLASS OF NONLINEAR HILFER FUZZY
FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS
WITH TIME-DELAYS
Status: reviewing
Abstract. In the current paper, we investigate a novel class of nonlinear Hil-
fer fuzzy fractional stochastic differential equations with time-delays. Firstly,
we convert the system under consideration into an analogous integral system.
Secondly, using Schauder and Banach fixed point theorem, the existence and
uniqueness results of solutions for nonlinear Hilfer fuzzy fractional stochastic
differential equations are then established. Additionally, we explore the finite-
time stability result of solution for the system under consideration. Lastly, an
example is provided to visualize the theoretical results.
Date of submission: 11 January 2023 г.
- Allahverdiev B.P., Tuna H. On a $\phi$-fractional Dirac equation
Status: reviewing
Abstract. In this paper, we construct a $\phi$-fractional Dirac system by using $\phi$-
Riemann-Liouville and $\phi$-Caputo derivatives: Some properties of this system investigated. Finally, a sufficient condition on eigenvalues for the
existence and uniqueness of the associated eigenfunctions is given.
Date of submission: 05 February 2023 г.
- Shamaev A.S., Shumilova V.V. Homogenization of the equations of motion for a medium consisting
of an elastic material and an incompessible Kelvin-Voigt fluid
Status: reviewing
Abstract. We consider an initial-boundary problem
describing the motion of a two-phase medium with a periodic structure.
The first phase of the medium is an isotropic elastic material
and the second phase is an incompressible viscoelastic Kelvin-Voigt fluid.
For the stated problem, we deduce the corresponding homogenized
problem describing the motion of a homogeneous viscoelastic medium
with memory. We find the explicit analytical expressions
for the coefficients and convolution kernels of the homogenized
equations corresponding to the case of a layered medium.
Date of submission: 14 February 2023 г.
- Timergaliev S.N. Solvability of Nonlinear Boundary Value Problems for Non-Sloping Timoshenko-Type Isotropic Shells of Zero Principal Curvature
Status: reviewing
Abstract. We study the solvability of a boundary value problem for a system of nonlinear
partial differential equations of the second order
under given boundary conditions, which describes the equilibrium state of elastic non-sloping isotropic inhomogeneous shells with loose edges in the framework of the Timoshenko shear model.
The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in the Sobolev space, the solvability of which is established from
using the contraction mapping principle.
Date of submission: 22 February 2023 г.
- Baranov D.A., Nozdrinova E.V., Pochinka O.V. Scenario of a stable transition from the torus isotopic identity diffeomorphism to the skew product of rough transformations of the circle
Status: reviewing
Abstract. In this paper, we consider isotopic gradient-like diffeomorphisms of a two-dimensional torus. The model (simplest) representative in the considered class are the skew products of rough transformations of the circle. We will show that any gradient-like diffeomorphism of a torus that is isotopic and identical to a torus is connected by a stable (which does not qualitatively change its properties under small perturbations) arc with some model diffeomorphism, which is a skew product of rough transformations of the circle.
Date of submission: 16 Mart 2023 г.
- Акрамова Д.И. ОБРАТНАЯ КОЭФФИЦИЕНТНАЯ ЗАДАЧА ДЛЯ
ДРОБНОГО-ДИФФУЗИОННОГО УРАВНЕНИЯ С
ОПЕРАТОРОМ БЕССЕЛЯ
Status: reviewing
Abstract. Исследуется вторая начально-краевая задача в огра-
ниченной области для дробного - диффузионного уравнения с опера-
тором Бесселя и производной Герасимова-Капуто. Получены теоре-
мы существования и единственности решения обратной задачи опре-
деления младшего коэффициента в одномерном дробно - диффузион-
ном уравнении при условии интегрального наблюдения. Для доказа-
тельство существования решения использовался принцип Шаудера.
Date of submission: 16 Mart 2023 г.
- Zvereva M.B., Kamenskii M.I. The problem of strings system vibrations on a star –shaped graph with a nonlinear condition at a node
Status: reviewing
Abstract. In this paper, we study an initial-boundary value problem that describes the oscillatory process for a strings system on a geometric star – shaped graph with a hysteresis type condition at a node. This kind of condition arises due to a limiter on the movement of strings installed in the node. It is assumed that the limiter itself can move in a direction perpendicular to the plane of the graph. As long as the limiter does not come into contact with the nodal point of the strings system, the transmission condition (Kirchhoff condition) is satisfied. As soon as the nodal point touches the limiter, their joint movement begins. A formula for representing the solution is obtained, and the boundary control problem of vibrations is considered.
Date of submission: 10 Aprel 2023 г.
- Мансимов K.B., МАСТАЛИЕВ R.O. Оптимальное управление в стохастическими нелинейными динамическими системами Ито с негладким критерием качества
Status: reviewing
Abstract. The proposed article considers a mathematical model of a stochastic nonsmooth optimal control problem described by a system of ordinary stochastic differential equations of Ito. In this case, the goal of control is to minimize the mathematical expectation of the Mayer type functional. Considering the stochastic properties of the problem and using a modified version of the increment method, we obtain the necessary optimality conditions in terms of the directional derivative. In addition, the minimax problem has been studied. By imposing various smoothness conditions on these problems, a number of necessary first order optimality conditions are established.
Date of submission: 13 Aprel 2023 г.
- Baidaulet A.T., Suleimenov K.M. On embedding in Lorentz spaces (a distant case)
Status: reviewing
Abstract. The paper studies the upper bound of a non-increasing non-negative function from the space $L^{p}(0,1)$ through the modulus of continuity of variable increment $\omega_{p,\alpha,\psi}(f,\delta)$. It is shown that for an increment of a function of the form $f(x)-f(x+hx^{\alpha}\psi(x))$ in the evaluation of the continuity module will take the form $\omega_{p,\alpha,\psi}\left(f,\frac{\delta}{\delta^{\alpha}\psi\left(\frac{1}{\delta}\right)}\right)$. The embedding of $\tilde H_{p,\alpha,\psi}^\omega\subset L(\mu,\nu)(\mu\not=p)$(distant case) is also studied.
Date of submission: 29 Aprel 2023 г.
- ABSOLUTE SUMMABILITY OF FACTORED FOURIER
INTEGRALS
Status: reviewing
Abstract. In this paper we study the absolute Norlund summability of
factored Fourier Integrals. In some sense, our main result is a generalization
of a special case of result of S. N. Lal and and A. k. Singh. Also, in
particular case our result generalize the result of L. Boitsun. Also, as a
corollary, we obtain a result concerning absolute Cesaro summability of
factored Fourier integrals.
Date of submission: 19 May 2023 г.
- Tukhliev D.K., Shabozov M.Sh. On the mean-square approximation of functions in the Bergman space
and the
value of the widths of some classes of functions
Status: reviewing
Abstract. In this paper studies extremal problems
related to the best approximation of functions analytic in the unit
circle and belonging to the Bergman space $B_2$. A number of exact
theorems are obtained and the values of various n-widths of some
classes of functions in $B_2$ are calculated.
Date of submission: 16 June 2023 г.
- On density of polynomials in the algebra of
holomorphic functions of exponential type on a linear lie group
Status: reviewing
Abstract. It is shown by the author in [J. Lie Theory 29:4, 1045–1070, 2019] that for
every connected linear complex Lie group the algebra of polynomials (regular functions)
is dense in the algebra of holomorphic functions of exponential type. However, the
argument is quite involved. Here we present a short proof.
Date of submission: 20 June 2023 г.
- Generalized composition operators on weighted Fock spaces
Status: reviewing
Abstract. Given analytic functions $g$ and $\Phi$ on the complex plane $\mathbb C$, we
characterize bounded and compact properties of generalized composition operators $J_g^\Phi$
and $C^\Phi_g$, induced by $g$ and $\Phi$, on weighted Fock spaces $F^\Psi_g$
with weight function $\Psi$ satisfying some smoothness condition. Moreover, we investigate the
Schatten $S_p(F^\Psi_2)$ class membership property of these operators.
Date of submission: 27 June 2023 г.
- Bukusheva A.V., Galaev S.V. Geometry of sub-Riemannian manifolds equipped with a semimetric quarter-symmetric connection
Status: reviewing
Abstract. The semimetric quarter-symmetric connection on a sub-Riemannian manifold of contact type is introduced. This connection is given by an intrinsic metric connection and two structural endomorphisms, which save the distribution of a sub-Riemannian manifold. Conditions for the metricity of the introduced connection are found. We study structural endomorphisms of a semimetric connection consistent with a sub-Riemannian quasi-statistical structure. We study the properties of a semimetric quarter-symmetric connection defined on a nonholonomic Kenmotsu manifold and on an almost quasi-Sasakian manifold. Conditions are found when these manifolds are Einstein manifolds relative to a quarter-symmetric connection.
Date of submission: 07 July 2023 г.
- Kytmanov A.M., Khodos O.V. On real roots of systems of transcendental equations
Status: reviewing
Abstract. The article is devoted to investigation of real roots of systems of transcendental equations. It is shown that the number is related to the number of real roots of the resultant of the system. An example for a system of equations arising in chemical kinetics is given.
Date of submission: 12 July 2023 г.
- Some further results on weighted bi unique range sets over non-archimedean field meromorphic functions
Status: reviewing
Abstract. In this paper, we consider $f$ and $g$ be a two non-constant functions and we have studied on
weighted bi-URSM corresponding to a most generalized form of a polynomial over a non-Archimedean
field. The exhibition of our results are devoid of any extra suppositions.The paper significantly improved
the results of A. Banerjee et al.
Date of submission: 13 July 2023 г.
- Parfenov A.I. Inductive methods for the Hardy inequality on trees
Status: reviewing
Abstract. We study the two weight Hardy inequality on a rooted tree as well as
its versions for trees with boundary and for the family of all dyadic cubes. In the general and diagonal
cases, several new inductive criteria for the validity of the Hardy inequality are established. In the lower
triangular case, we simplify two known proofs of the criterion due to Arcozzi, Rochberg and Sawyer
(2002) which are based on the Marcinkiewicz interpolation theorem and the capacitary criterion,
and also give new proofs based on induction, the inductive formula for capacity and the integration
by parts formula. For the diagonal case, the last proof yields the optimal constant $p$ which coincides
with Bennett's constant in the Hardy inequality for sequences.
Date of submission: 17 July 2023 г.
- Grishin S.V. Random Walks on a Line and Algebraic Curves
Status: reviewing
Abstract. This paper is devoted to the research on generating function of the positive half-line first passage time for discrete homogenous random walk on a line. Equations on the generating function have been derived in several cases of random walk with independent increases and fixed correlation between each increase and previous one. Genus has been calculated for corresponding algebraic curves, and the problem of their rationality has been solved. Recurrent equations on probabilities imply certain systems of equations, and using the resultant from the theory of polynomials has helped to exclude all values besides two of them we are interested in. For computing the genus, the widely used topological $\delta$-invariant of curves' singularities has been applied: given degree of a curve and the mentioned invariants of all its singularities, the well-known formula gives its genus. Some curves has turned out to be rational, other ones have genus 1 or 2.
Date of submission: 17 July 2023 г.
- On the $\phi$- order of growth of solutions of complex linear differential equations near an essential singular point
Status: reviewing
Abstract. For this article, we will take care about an interesting topic
which is the study of the $\phi$- order of growth of solutions of some given
linear differential equations with analytic coefficients in $\mathbb{C} − \{z_0 \}$, where
$z_0\in\mathbb{C}$ represents an essential singularity. What we’ll do on this paper is a
generalization for the work of Long and Zeng by introducing the concept of
the $\phi$–order of growth near an essential singularity.
Date of submission: 20 July 2023 г.
- Rakhimova A.I. Hypercyclic and chaotic operators in the space of analytic functions in the band
Status: reviewing
Abstract. This article discusses the space $H(\Omega_r)$ of analytic functions in the band $\Omega_r$, endowed with the standard topology of uniform convergence on compacts of $\Omega_r$. It examines the issues of hypercyclicity, chaoticity and frequently hypercyclicity of differentiation and shift operators by definitions and using classical theorems.
The main results of the article are given in Theorems 5, 10 and 11. In Theorem 5 it is proved that the linear continuous operator $T$ in $H(\Omega_r)$ commuting with the differential operator is hypercyclic. Theorem 10 shows that it is chaotic, and Theorem 11 is frequently hypercyclic in $H(\Omega_r)$.
Date of submission: 10 Avgust 2023 г.
- Higher-order topological asymptotic formula for the
elasticity operator and application
Status: reviewing
Abstract. This paper is concerned with a geometric inverse problem related to the elas-
ticity equation. We aim to identify an unknown hole from boundary measurements of the
displacement field. The Kohn-Vogelius concept is employed for formulating the inverse
problem as a topology optimization one. We develop a topological sensitivity analysis
based method for detecting the location, size and shape of the unknown hole. We derive
a higher-order asymptotic formula describing the variation of a Kohn-Vogelius type func-
tional with respect to the creation of an arbitrary shaped hole inside the computational
domain.
Date of submission: 11 Avgust 2023 г.
- Оценки жесткости кручения выпуклой области
через новые геометрические характеристики
области
Status: reviewing
Abstract. В статье введены новые геометрические характеристики выпуклой области с конечной длиной границы и приведен алгоритм их вычисления. Доказан ряд изопериметрических неравенств между новыми функционалами и известными интегральными характеристиками области.
Отметим, что некоторые неравенства имеют широкий класс экстремальных областей. Рассмотрены приложения новых характеристик к задаче об оценке жесткости кручения выпуклой области.
Date of submission: 15 Avgust 2023 г.
- Braichev G.G. О нулях и тейлоровских коэффициентах целой функции логарифмического роста
Status: reviewing
Abstract. В статье для важного класса целых функций нулевого порядка выявляются непосредственные,
прямые связи между скоростью стремления к бесконечности последовательности нулей
и скоростью стремления к нулю последовательности тейлоровских коэффициентов.
Применяя коэффициентную характеризацию роста целых функций и некоторые тауберовы теоремы из выпуклого анализа,
мы получаем точные асимптотические оценки, связывающие нули~$\lambda_n$
и спрямленные по Адамару тейлоровские коэффициенты~$\hat{f_n}$
для целых функций логарифмического роста. В ситуациях, когда функция обладает той или иной регулярностью поведения,
упомянутые оценки переходят в точные асимптотические формулы.
Например, если целая функция имеет регулярный по Борелю рост и точка $a=0$ не является ее борелевским исключительным значением,
то при $n\to\infty$ справедливо асимптотическое равенство
$\ln |\lambda_n|\sim \ln(\hat{f}_{n-1}/\hat{f_n})$.
Результат верен и для функций совершенно регулярного логарифмического роста,
причем в~последнем случае дополнительно можно утверждать, что
$\ln|\lambda_1\lambda_2\,\ldots\,\lambda_n|\sim\ln\hat{f_n}^{-1}$ при $n\to\infty$.
Date of submission: 15 Avgust 2023 г.
- Durdiev D.K. An undetermined coefficient problem for a mixed
equation of parabolic-hyperbolic type with non-local
boundary conditions on the characteristics
Status: reviewing
Abstract. For an equation of a mixed parabolic-hyperbolic type with a characteristic
line of type change, we study the inverse problem associated with the search for an unknown
coefficient at the lowest term of the parabolic equation. In the direct problem, we consider an
analog of the Tricomi problem for this equation with a nonlocal condition on the characteristics
in the hyperbolic part and Dirichlet’s conditions in the parabolic part of the domain. To
determine undetermined coefficient, with respect to the solution, defined in the parabolic part of
the domain, the integral overdetermination condition is specified. Global results on the unique
solvability of the inverse problem in the sense of the classical solution are proved.
Date of submission: 12 September 2023 г.
- $p$-Laplacian, generalized Morrey spaces, Strong unique continuation.
Status: reviewing
Abstract. We study some basic properties of generalized Morrey spaces $\mathcal{M}^{p,\phi}(\R^{d})$. Also, the problem $-\mbox{div}(|\nabla u|^{p-2}\nabla u)+V|u|^{p-2}u=0$ in $\Omega$, where $\Omega$ is a bounded open set in $\R^d$, and potential $V$ is assumed to be not equivalent to zero and lies in $\mathcal{M}^{p,\phi}(\Omega)$, is studied. Finally, we establish the strong unique continuation for the $p$-Laplace operator in the case $V\in\mathcal{M}^{p,\phi}(\R^d)$.
Date of submission: 14 October 2023 г.
- Krause Mean Processes Generated by Cubic
Stochastic Matrices with Positive Influences
Status: reviewing
Abstract. The Krause mean process serves as a comprehensive model for the
dynamics of opinion exchange within multi-agent system wherein opinions are
represented as vectors. In this paper, we propose a framework for opinion ex-
change dynamics by means of the Krause mean process that is generated by a
cubic doubly stochastic matrix with positive influences. The primary objective is
to establish a consensus within the multi-agent system.
Date of submission: 20 October 2023 г.
- Well-posedness and Stability result for a Timoshenko system with
thermodiffusion effects and time-varying delay term
Status: reviewing
Abstract. n the actual article, we investigate a Timoshenko beam model with thermodiffusion effects and a time-dependent
delay. We show that the problem is well-posed in the sense of C0-semigroup theory. We illustrate the general
decay result of the problem’s solution using a suitable Liapunov function.
Date of submission: 21 October 2023 г.
- On $\mathscr{I}$-convergence of sequences in Neutrosophic $2$-normed spaces
Status: reviewing
Abstract. In this paper, we have studied the concept of $\mathscr{I}$-convergence of sequences in neutrosophic $2$-normed spaces, which is a generalized version of statistical convergence of sequences. Also the idea of $\mathscr{I}$-Cauchy sequences has been defined and discussed some of its basic properties.
Date of submission: 29 October 2023 г.
- Haliullin S.G. Extreme points for a total convex structure of generalized states
Status: reviewing
Abstract. It is well known that the set of states of a certain quantum mechanical system is closed from the point of view of the operational approach if we want to form mixtures or convex combinations. That is, if $s_1$ and $s_2$ are states, then so are $\lambda s_1+(1-\lambda) s_2$, where $0 < \lambda < 1$, must be states. We can define a convex combination of elements in a linear space, but unfortunately, in the general case, linear space is artificial for a set of states and has no physical meaning, but the operation of forming mixtures of states has a natural meaning. For this reason, an abstract definition of mixtures will be given, which does not depend on the concept of linearity. We will call this space a convex structure.
The paper will consider state spaces, spaces of generalized states in which pure states, operations, effects associated with operations are distinguished.
We will also consider ultraproducts of sequences of these structures, operations and effects.
Date of submission: 01 November 2023 г.
- Shishkin K.A., Gumerov R.N., Lipacheva E.V. A categorical criterion for the existence of universal $C^*$-algebras
Status: reviewing
Abstract. The article deals with categories which determine universal $C^*$-algebras. These categories are called the compact $C^*$-relations. They were introduced by T.A.~Loring. For a given set $X$, the compact $C^*$-relation on $X$ is the category whose objects are functions from $X$ to $C^*$-algebras and morphisms are $\ast$-homomorphisms of $C^*$-algebras making the appropriate triangle diagrams commute. Moreover, these functions and $\ast$-homo\-mor\-phisms satisfy certain axioms. In this article, we prove that every compact $C^*$-relation is both complete and cocomplete. As an appli\-cation of the completeness of compact $C^*$-relations, we obtain the criterion for the existence of universal $C^*$-algebras.
Date of submission: 03 November 2023 г.
- IDENTIFYING THE TIME-DEPENDENT TERMS IN THE FOURTH-ORDER
BOUSSINESQ-LOVE EQUATION FROM INTEGRAL MEASUREMENTS
Status: reviewing
Abstract. Sobolev-type (pseudohyperbolic) equations arise in many mathematical models con-
nected with physics, mechanics and biology. In this paper, simultaneous time-dependent po-
tential and source control terms identification of a Sobolev-type equation, called fourth-order
Boussinesq-Love equation, from knowledge of additional integral measurements is studied by
means of contraction mapping.
Date of submission: 14 November 2023 г.
- Generalization of the Concepts of Norm and Seminorm on a Vector Space to Groups
Status: reviewing
Abstract. The article contains the results of generalization of the concepts of norm and seminorm on a linear space to the algebraic structure of a group. The definition of the generalized concept of a (semi)norm is based on the classical axioms of a (semi)normed vector space: the triangle inequality, homogeneity, and non-degeneracy (of a norm). Since, in general, multiplication by scalars is not defined for groups, the homogeneity of the generalized norm extends only to integers, which can be put in correspondence with the powers of the group elements. Non-degeneracy on groups consists of the requirement that the norm must be equal to zero only on the identity element of the group. The presence of a norm on a group imposes some restrictions on its elements and defines new properties that can be used to analyze the group. An important consequence of this generalization is the possibility of applying algebraic methods to the study of normed spaces used in functional analysis since normed spaces are a special case of normed groups.
Date of submission: 15 November 2023 г.