Editorial backlog
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Кутлымуратов Б.Ж. О некоторых множествах, достаточных для голоморфного продолжения интегрируемых функций с граничным свойством Морера
Status: reviewing
Abstract. В данной статье рассматриваются интегрируемые функции, заданные на границе ограниченной области $D$ в ${{\mathbb{C}}^{n}}$, $n>1$, и обладающие обобщенным граничным свойством Морера. Исследуется вопрос о существовании голоморфного продолжения таких функций в область \(D\) для некоторых достаточных множеств \(\Gamma \) комплексных прямых.
Date of submission: 18 December 2023 г.
- Podkletnova S.V. A series of boundary value problems for the Euler-Darboux equation with two lines of degeneracy
Status: reviewing
Abstract. This paper introduces a new partial differential equation which is an extension of the well-known Euler-Poisson-Darboux equation. Based on the proven properties of the solution of the introduced equation, general solutions are found explicitly for various values of parameters, existence and uniqueness theorems are proved. Based on the general solutions of the introduced equation, Cauchy problems and modified Cauchy problems are set and solved in the area of the upper right-angled triangle. Explicit solutions are derived. The existence and uniqueness theorems of the solution of all the tasks are proved.
Date of submission: 23 December 2023 г.
- On the Level Sets of the Generalized Resolvent Norm
of Operators Pencils
Status: reviewing
Abstract. This paper presents a proof demonstrating that the generalized resolvent operator, defined within a Hilbert space, cannot remain constant within any open subset of the resolvent set. We also study the same result over a complex uniformly convex Banach space under certain conditions. These findings extend existing results in the literature.
Date of submission: 23 December 2023 г.
- Napalkov V.V., Nuyatov A.A. On the question of embedding Hilbert spaces with reproducing kernel
Status: reviewing
Abstract. In this paper, necessary and sufficient conditions for embedding one Hilbert space with a reproducing kernel (RKHS) into another RKHS are obtained.This article is a continuation of the authors' works, in which the problem of the coincidence or equivalence of two RKHS's was studied.
An important role is played by the condition of matching two two complete systems of functions with some linear continuous operator, introduced by the authors earlier.
The results obtained are illustrated with specific examples.
Date of submission: 27 December 2023 г.
- Nazarov S.A. Different types of localization for eigenfunctions of scalar mixed boundary value problems in thin polyhedra
Status: reviewing
Abstract. Построена асимптотика собственных пар смешанной краевой задачи для оператора Лапласа в тонком многограннике с параллельными сближенными основаниями и скошенными узкими боковыми гранями. На основаниях назначены условия Дирихле, а на боковых гранях --- условия Дирихле или Неймана, распределение которых по граням, а также углы наклона последних оказывают существенное влияние на поведение собственных функций при истончении области. Обнаружены ситуации, в которых собственные функции распределены вдоль всего многогранника и локализованы около его боковых граней или вершин. Результаты основаны на анализе спектра (точка отсечки, изолированные собственные числа, пороговые резонансы и пр.) вспомогательных задач в полуполосе и четверти слоя со скошенными торцом и боковыми сторонами соответственно. Сформулированы открытые вопросы, относящиеся как к спектральному, так и асимптотическому анализу.
Date of submission: 05 January 2024 г.
- Krivosheev A.S., Krivosheeva O.A. Interpolation and fundamental principle
Status: reviewing
Abstract. In this paper we study the spaces of analytic functions in convex domains of the complex plane.
We consider subspaces of such spaces. These subspaces are invariant with respect to the differentiation operator.
The problem of the fundamental principle for the invariant subspace is investigated, i.e. the problem of representation all
its elements using a series the eigenfunctions and associated functions of the differentiation operator in
this subspace --- exponents and exponential monomials. We give a complete description of the space of sequences of the coefficients
of series by which functions from the invariant subspace are represented. The problem of multiple interpolation in spaces of entire
functions of exponential type is also studied. The duality of problems of interpolation and fundamental principle is considered.
The problem of this duality is completely solved. The duality of the problems of fundamental principle and interpolation for an arbitrary
convex domain without any restrictions is established.
Date of submission: 07 January 2024 г.
- Existence of gradient Gibbs measures for the \emph{HC}-Blume-Capel model with a countable number of states on a Cayley tree
Status: reviewing
Abstract. In this paper, we study the \emph{HC}-Blume-Capel model with a countable set of $\mathbb Z$ spin values on a Cayley tree. This model is determined by a countable set of parameters (i.e., the activity function $\theta>0$, $i\in \mathbb Z$). We solve the model exactly on the Cayley trees of order one and two. We show the co-existence of Gibbs measure and gradient Gibbs measures under the some values of parameters.
Date of submission: 08 January 2024 г.
- Two shared sets problem in wider sense on $\mathbb{C}
Status: reviewing
Abstract. In this manuscript, in view of the introduced definition of weighted
sharing of sets in wider sense, we nurture the relation between two meromorphic
functions having multiple poles, sharing the zeros of two sets of polynomials, each
characterized by distinct zeros. In the applications part of our paper we have further
refined our results for a specific class of functions and supported by examples to
enhance the coherence of the paper.
Date of submission: 09 January 2024 г.
- On the Convergence of Random Fourier--Jacobi Series in $\mathrm{L}_{[-1,1]}^\mathrm{p}(d\mu_{\zeta,\eta})$ Space
Status: reviewing
Abstract. On the Convergence of Random Fourier--Jacobi Series in $\mathrm{L}_{[-1,1]}^\mathrm{p}(d\mu_{\zeta,\eta})$ Space
Date of submission: 11 January 2024 г.
- BIHARMONIC HYPERSURFACES IN TERMS OF THE
INDUCED METRIC OF TENSOR RICCI
Status: reviewing
Abstract. The manuscript presents an investigation into biharmonic hypersurfaces
specifically focusing on their study within the Sasakian space form using
the induced metric of tensor Ricci. We explore the existence of necessary
and sufficient condition for biharmonic hypersurface in the context. Furthermore,
we demonstrate biharmonic Hopf hypersurface is minimal when the gradient
of the mean curvature aligns with the structural vector fields.
Date of submission: 31 January 2024 г.
- $(N,\varepsilon)$-PSEUDOSPECTRA OF CLOSED LINEAR OPERATORS
ON ULTRAMETRIC BANACH SPACES
Status: reviewing
Abstract. In this paper, we establish that the essential pseudospectrum of
closed linear operator pencils is invariant under perturbation of completely
continuous linear operators on ultrametric Banach spaces over a spherically
complete field K and we obtain a characterization of the essential pseudospec-
trum of a closed linear operator pencils by means of the spectra of any per-
turbed completely continuous operators. Furthermore, we introduce and study
the concept of (n,ε)-pseudospectrum of closed linear operators and the notion
of (n,ε)-pseudospectrum of closed linear operator pencils on ultrametric Ba-
nach spaces. We prove some results about them. Finally, several illustrative
examples are provided.
Date of submission: 02 February 2024 г.
- A time-dependent inverse source problem for an integro-differential pseudoparabolic equation
Status: reviewing
Abstract. In this paper, we consider two inverse source problems for
a pseudo-parabolic equation with memory. PDEs with a memory, in par-
ticular, pseudo-parabolic equations have many applications in the various
field of science and technology, since many of mathematical models of them
express by such type equations. However, the appearance of such memory
term in equation, along with this important physical meaning, in mathe-
matical point of view, this causes some mathematical difficulties in both
of analytical and numerical studies. The studying here inverse problems
consist of finding a time dependent right-hand side coefficient by one of
two type integral overdetermination conditions. Under suitable conditions
on the data, we establish the existence and uniqueness of strong solutions.
Along these analytical results, we also investigate the numerical solutions
of these inverse problems. The created numerical algorithms tested by
examples.
Date of submission: 02 February 2024 г.
- Kabanko M.V., Malyutin K.G. Interpolation sets in spaces of functions of finite order in the half-plane
Status: reviewing
Abstract. Examples of interpolation sets in the space of functions of finite order that are analytic in the upper half-plane are given. These examples are similar to interpolation sets in the space of analytic bounded functions in the upper half-plane.
Date of submission: 03 February 2024 г.
- Reconstruction of the Potential Function of Discontinuous Sturm-Liouville Operator from Spectral Data
Status: reviewing
Abstract. This paper deals with the inverse spectral problem of the discontinuous Sturm-Liouville operator that
is indicated in the way: to determine the potential $q(x)$ and the boundary constant $h$ according
to spectral data. Finally, the reconstruction algorithm of the potential $q(x)$ from the spectral data is given.
Date of submission: 07 February 2024 г.
- BOUND FOR CERTAIN HANKEL DETERMINANTS AND THE
ZALCMAN CONJECTURE ASSOCIATED WITH MULTIVALENT
BOUNDED TURNING FUNCTIONS OF ORDER ALPHA
Status: reviewing
Abstract. In this paper, we investigate for a sharp upper bound to certain
generalized second Hankel determinant, the Zalcman conjecture and an upper
bound to the third, fourth Hankel determinants for the class of multivalent
analytic bounded turning functions of order α, for α ∈ [0,1). Further, we
estimate an upper bound for third and fourth Hankel determinants with respect
to two-fold and three-fold symmetric functions belongs to the same class. The
practical tools applied in the derivation of our main results are the coefficient
inequalities of the Carathéodory class P.
Date of submission: 09 February 2024 г.
- Kudasheva E.G., Menshikova E.B., Khabibullin B.N. Dual construction and the existence of (pluri)subharmonic minorant
Status: reviewing
Abstract. Рассматривается проблемы существования и построения субгармонической или плюрисубгармонической функции, огибающей снизу функцию на подмножестве в конечномерном вещественном или комплексном пространстве. Такие проблемы естественным образом возникали в теориях равномерных алгебр, потенциала и комплексного потенциала, что нашло отражение в работах Д.~А.~ Эдвардса, Т.~В.~Гамелина, Е.~А.~Полецкого, С.~Бу и В.~Шахермайера, Б. Коула и Т.~Рансфорда, Ф. Ларуссона и Р. Сигурдссона и многих других. В наших работах 1990-х гг. и последних лет было показано, что эти проблемы играют ключевую роль при исследовании нетривиальности весовых пространств голоморфных функций, при описании нулевых множеств и подмножеств функций из таких пространств, в вопросах представления мероморфных функций в виде отношения голоморфных функций с ограничениями на их рост, при изучении аппроксимации экспоненциальными системами в функциональных пространствах и пр. Основные результаты статьи о существовании субгармонической или плюрисубгармонической функции-миноранты выводятся из нашей общей теоретико-функциональной схемы, которая позволяет дать двойственное определение нижней огибающей относительно выпуклого конуса в проективном пределе векторных решёток. Эта схема разрабатывалась нами в последние годы и основана на развитии абстрактной формы выметания. Идеология абстрактного выметания восходит к А. Пуанкаре и М.~В.~Келдышу в рамках выметания мер и субгармонических функций в теории потенциала. Она широко используется в теории вероятности, например, в известной монографии П.~Мейера, а также отражена, зачастую неявно, в монографиях Г.~П.~Акилова, С.~С.~Кутателадзе, А.~М.~Рубинова и др., связанных с теорией упорядоченных векторных пространств и решёток. В нашей статье разработанная нами схема адаптируется для выпуклых подконусов конуса всех субгармонических или плюрисубгармонических функций. Это позволяет получить новые критерии существования субгармонической или плюрисубгармонической миноранты для функций на области.
Date of submission: 11 February 2024 г.
- Gladkov A.L. Global and blow-up solutions for a parabolic
equation with nonlinear memory under nonlinear nonlocal boundary condition
Status: reviewing
Abstract. In this paper we consider parabolic equation
with nonlinear memory and absorption
\begin{equation*}
u_t= \Delta u + a \int_0^t u^q (x,\tau) \, d\tau - b u^m, \;x \in \Omega,\;t>0,
\end{equation*}
under nonlinear nonlocal boundary condition
\begin{equation*}
u(x,t) = \int_{\Omega}{k(x,y,t)u^l(y,t)}\,dy, \; x\in\partial\Omega, \; t > 0,
\end{equation*}
and nonnegative continuous initial datum. Here $ a, b,\,q, \,m,\,l $ are positive numbers, $\Omega$ is a bounded domain in $\mathbb{R}^N$
for $N\geq1$ with smooth boundary $\partial\Omega,$ $k(x,y,t)$ is a nonnegative continuous function defined for $x
\in \partial \Omega$, $y \in \overline\Omega$ and $ t \ge 0.$ We prove that every solution of the problem is global if
$\max (q,l) \leq 1$ or $\max (q,l) > 1$ and $ l < (m + 1)/2, \, q \leq m.$
For $l>\max\{1, (p+1)/2\}$ and positive for small values of $ t$ function $k(x,y,t)$ solutions
blow up in finite time for large enough initial data. The obtained results improve previously established conditions for the existence and the absence of global solutions.
Date of submission: 20 February 2024 г.
- Petrosyan G.G. On systems of semilinear fractional differential inclusions with non-densely defined operators in Banach spaces.
Status: reviewing
Abstract. В настоящей работе изучаются системы полулинейных дифференциальных включений дробных порядков. Предполагается, что линейные части включений представлены операторами Хилле-Иосида в банаховых пространствах. Нелинейные части включений являются многозначными отображениями типа Каратеодори, зависящими от времени и конечного набора функций. Для исследования задачи существования решений такой системы используется теория дробного математического анализа, теория обобщенных метрических пространств, а также теория топологической степени для многозначных уплотняющих отображений. Идея решения поставленной задачи состоит в следующем. Мы представляем разрешающий многозначный оператор для данной системы и описываем его свойства. Показано, в частности, что этот мультиоператор является уплотняющим относительно специальной векторной меры некомпактности. Это дает возможность, применяя некоторые теоремы о неподвижной точке для указанных мультиоператоров, доказать локальную и глобальную теоремы существования интегральных решений данной системы. В последнем случае обосновывается также компактность множества таких решений и полунепрерывная сверху зависимость множества решений от начальных данных.
Date of submission: 28 February 2024 г.
- Akmanova S.V. Controllability and stabilization of nonlinear continuous-discrete dynamic systems
Status: reviewing
Abstract. Nonlinear dynamic systems described by a set of differential and difference equations are considered, the latter including a control vector. The states of these systems contain both continuous and discrete components, therefore such systems are called continuous-discrete (CDS), or hybrid.
The article outlines the necessary and sufficient controllability criteria for nonlinear hybrid systems with a constant sampling step $h>0$, taking into account the transition from these systems to equivalent, in a certain sense, nonlinear discrete dynamic systems (DDS). A transformation is presented that makes it possible to bring the system of the first approximation of a nonlinear DDS to the canonical Brunovsky form, and on its basis the construction of a stabilizing control for the corresponding CDS with scalar control. Sufficient signs of stabilization of nonlinear CDS have been established, both without taking into account and taking into account the feedback regulator.
Date of submission: 29 February 2024 г.
- New results on generalized quaternion algebra involving
generalized Pell-Pell Lucas quaternions
Status: reviewing
Abstract. This work presents a new sequence, generalized Pell-Pell Lucas quaternions,
we prove that the set of these elements forms an order of generalized quaternions with
3-parameters k λ 1 ,λ 2 ,λ 3 as defined by ring theory. In addition, we present some properties
of these elements. The properties of this article are related to k λ 1 ,λ 2 ,λ 3 algebras and
sometimes to the 2-parameter algebra H(α,β).
Date of submission: 29 February 2024 г.
- Smirnov A.O., Шиловский S.D. О векторном производном нелинейном уравнении Шредингера
Status: reviewing
Abstract. В работе предлагается последовательность пар Лакса, условиями совместности которых являются векторные интегрируемые нелинейные уравнения. Первыми уравнениями этой иерархии являются векторные уравнения Каупа-Ньюэлла, Чень-Ли-Лью и Герджикова-Иванова. Тип векторного уравнения зависит от дополнительного параметра $\alpha$. Предложенная нами форма векторного уравнения Каупа-Ньюэлла имеет небольшие отличия от классической. Показано, что эволюция простейших нетривиальных решений этих уравнений является композицией эволюции длины вектора решения и эволюции ориентации вектора решения. Исследованы свойства спектральных кривых простейших нетривильных решений векторных уравнений из построенной иерархии.
Date of submission: 01 Mart 2024 г.
- Determining of a space dependent coefficient of
fractional wave equation with the Generalized
RiemannLiouville time derivative
Status: reviewing
Abstract. This work investigates an initial-boundary value and an inverse coefficient prob-
lem of determining a space dependent coefficient in the fractional wave equation
with the generalized Riemann-Liouville (Hilfer) time derivative order 1 < α ≤ 2.
In the beginning, it is considered the initial boundary value problem (direct
problem). By the Fourier method, this problem is reduced to equivalent integral
equations, which contain Mittag-Leffler type functions in free terms and ker-
nels. Then, using the technique of estimating these functions and the generalized
Gronwall inequality, we get apriori estimate for solution via unknown coefficient
which will be used to study the inverse problem. The inverse problem is reduced
to the equivalent integral equation of Volterra type. To show existence unique
solution to this equation the Schauder principle is applied. The local existence
and uniqueness results are obtained.
Date of submission: 04 Mart 2024 г.
- Conformable functional evolution inclusions in Banach space
Status: reviewing
Abstract. In this paper we are considering the Cauchy problem for a
semilinear conformable fractional evolution inclusions in a general Banach
space. This result allows to apply a fixed point result for condensing
multivalued maps, we prove the existence of mild solutions to this problem.
An example concerning with a functional conformable feedback control
system is presented.
Date of submission: 06 Mart 2024 г.
- The solvability of $p$-kirchhoff type problems with critical exponent
Status: reviewing
Abstract. The article is aimed to study new current problems in the theory
of non-classical partial differential equations and their applications, proving
the existence and non-existence of solutions to p-Kirchhoff type problems with
critical exponent of Sobolev in R n , which are of great interest for the study of
this type of problems for equations of mathematical physics. We showed the
existence of local minimizer with negative/positive energy, by using variational
methods. More precisely, we considered a minimization of E λ constrained in
a neighborhood of zero by using the Ekeland variational principle, then we
found the first critical point of E λ which achieves the local minimum of E λ
whose level is negative, next around the zero point, using the mountain pass
theorem, we also obtained a critical point whose level is positive. Besides,
we studied the case of λ = 0, where found no non-trivial solution by using
the contradiction principle. We also established the infinitely solutions and
discussing the different cases.
Date of submission: 19 Mart 2024 г.
- The norming sets of $L_s(^6 \ell_1^2)$
Status: reviewing
Abstract. ...
Date of submission: 22 Mart 2024 г.