Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
Peer-review bimonthly mathematical journal
Editor-in-chief
- Dmitri O. Orlov, Member of the Russian Academy of Sciences, Doctor of Physico-Mathematical Sciences
Publisher
- Steklov Mathematical Institute of RAS
Founders
- Russian Academy of Sciences
- Steklov Mathematical Institute of RAS
About
Frequency
The journal is published bimonthly.
Indexation
- Scopus
- Web of Science
- Russian Science Citation Index
- Math-Net.Ru
- MathSciNet
- zbMATH
- Google Scholar
- Ulrich's Periodical Directory
- CrossRef
Scope
The journal publishes only original research papers containing full results in the author's field of study. Particular attention is paid to algebra, mathematical logic, number theory, mathematical analysis, geometry, topology, and differential equations.
Main webpage: https://www.mathnet.ru/eng/im
Access to the English version journal dating from the first translation volume is available at https://www.mathnet.ru/eng/im.
Current Issue
Open Access
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Vol 89, No 4 (2025)
- Year: 2025
- Articles: 5
- URL: https://bakhtiniada.ru/1607-0046/issue/view/20357
Articles
Development of the new approach for existence of bounded solutions for point-type functional differential equations
Abstract
This paper is a continuations of the studies of [1] and [2] on existence of periodic bounded solutions for point-type functional differential equations, where deviations of the argument are defined in terms of a cyclic group of shifts on the real line. We prove an existence theorem for a bounded solution for equations in which the deviations of the argument are given by elements of a finitely generated group of orientation preserving diffeomorphisms of the real line.
3-31
On lattices in Lie groups of general type and some applications
Abstract
The article considers discrete uniform subgroups in Lie groups and their intersections with some types of Lie subgroups. The results obtained are applied to the study of fundamental groups of compact homogeneous spaces and the topological structure of such spaces.
32-53
On long-time asymptotics of solution to the non-local Lakshmanan–Porsezian–Daniel equation with step-like initial data
Abstract
The non-linear steepest descent method is employed to study the long-time asymptotics of solution to the non-local Lakshmanan–Porsezian–Daniel equation with step-like initial data$$q(x,0)=q_0(x)\to\begin{cases}0, &x\to-\infty,A, &x\to+\infty,\end{cases}$$where $A$ is an arbitrary positive constant. We first construct the basic Riemann–Hilbert (RH) problem. After that, to eliminate the influence of singularities, we use the Blaschke–Potapov factor to deform the original RH problem into a regular RH problem which can be clearly solved. Then different asymptotic behaviors on the whole $(x,t)$-plane are analyzed in detail. In the region $(x/t)^2<1/(27\gamma)$ with $\gamma>0$, there are three real saddle points due to which the asymptotic behaviors have a more complicated error term. We prove that the asymptotic solution constructed by the leading and error terms depends on the values of $\operatorname{Im}v(-\lambda_j)$, $j=1,2,3$, where $v(\lambda_j) =-(1/(2\pi))\ln|1+r_1(\lambda_j)r_2(\lambda_j)|-(i/(2\pi))\Delta(\lambda_j)$, $\Delta(\lambda_j)=\int_{-\infty}^{\lambda_j}d \arg(1+r_1(\zeta)r_2(\zeta))$, $r_i(\xi)$, $i=1,2$, are the reflection coefficients and $\lambda_j$ are the saddle points of thephase function $\theta(\xi,\mu)$. Besides, the leading term is characterized by parabolic cylinder functions and satisfies boundary conditions. In the region $(x/t)^2>1/(27\gamma)$ with $\gamma>0$, there are one real and two conjugate complex saddle points. Based on the positions of these points, we improve the extension forms of the jump contours and successfully obtain the large-time asymptotic results of the solution in this case.
54-110
A sample iterated small cancellation theory for groups of Burnside type
Abstract
We develop yet another technique to present the free Burnside group $B(m,n)$ of odd exponent $n$ with $m\ge2$ generators as a group satisfying a certain iterated small cancellation condition. Using the approach, we provide a reasonably accessible proof that $B(m,n)$ is infinite with a moderate bound $n > 2000$ on the odd exponent $n$.
111-218
A further sufficient condition for the determinantal conjecture
Abstract
Let $A$, $B$ be $n\times n$ normal matrices with eigenvalues $(a_1,…,a_n)$, $(b_1,…,b_n)$, respectively. We show that $\det(A+B)$ lies in the convex hull ofif all eigenvalues of $A$, $B$ are real, except for three eigenvalues of $B$.
219-226