Uspekhi Matematicheskikh Nauk
Peer-review bimonthly mathematical journal
Editor-in-chief
- Valery V. Kozlov, Member of the Russian Academy of Sciences, Doctor of physico-mathematical sciences, Professor
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
- Google Scholar
- Ulrich's Periodical Directory
- CrossRef
Scope
The journal publishes survey articles on the most topical research in mathematics, Brief Communications, and biographical materials.
Main webpage: https://www.mathnet.ru/rm
Access to the English version journal dating from the first translation volume is available at https://www.mathnet.ru/eng/umn.
Current Issue
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Vol 80, No 4 (2025)
- Year: 2025
- Articles: 9
- URL: https://bakhtiniada.ru/0042-1316/issue/view/20355
Introduction to the theory of choice and stable contracts
Abstract
The paper is devoted to the presentation of the basic concepts and results of the theory of stable contract systems. This theory originated in 1962 and has significantly been developed since then. The main results (existence, polarization, latticing) were obtained in a bipartite situation, when contracting agents are divided into two groups, and contracts are concluded between agents from opposite groups. Another important limitation is that the agents' preferences are described by so-called Plott choice functions. The first part of the paper is devoted to this concept, which generalizes the concept of partial order. The second part sets out the theory of stable contracts itself.
3-46
Multi-component Toda lattice hierarchy
Abstract
We give a detailed account of the $N$-component Toda lattice hierarchy, which can be regarded as a generalization of the well-known Toda chain model and its non-abelian version. This hierarchy is an extension of the one introduced earlier by Ueno and Takasaki. Our version contains $N$ discrete variables rather than one. We start from the Lax formalism, deduce the bilinear relation for wave functions from it, and then, based on the latter, prove the existence of the tau-function. We also show how the multi-component Toda lattice hierarchy is embedded into the universal hierarchy, which is basically the multi-component Kadomtsev–Petviashvili hierarchy. Finally, we show how the bilinear integral equation for the tau-function can be obtained using the free fermion technique. An example of exact solutions (a multi-component analogue of one-soliton solutions) is given.
47-120
Stein method and characteristic functions
Abstract
We present a survey of various application of the method of the description of approximating distribution by means of differential equations for characteristic functions and, in particular, of applications of this description to estimates for the closeness of distributions. This idea was originally put forward by the author in 1976. Subsequently, this approach, which is called the Stein–Tikhomirov method by some authors (for instance, see papers by Eichelsbacher, Rednoss, Sunklodas, and Formanov), was significantly developed.
121-172
Zeros of a family of multivalued cone functions on a metric space with TVS-valued cone metric
173-174
On the existence of a non-anticipative selection for a non-anticipative multivalued map
175-176
Remarks on regular and smooth DG algebras
177-178
Combinatorics of type $D$ singularities of a front
179-180
Tight lower bounds for Shannon entropy from ‘quantum pyramids’
181-182
Yuri Gennadievich Prokhorov (on his sixtieth birthday)
183-192