Editorial backlog
- 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.
- 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.
- 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.
- $(N,\varepsilon)$-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.
- 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.
- 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.
- 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.
- The norming sets of $L_s(^6 \ell_1^2)$
Status: reviewing
Abstract. ...
Date of submission: 22 Mart 2024 г.