Vol 238 (2025)
Articles
3-23
Algorithms for enumeration of lattice paths with constraints and root trees by various parameters
Abstract
Approaches to enumerating various types of objects are demonstrated: with restrictions, marked, and unmarked. An algorithmic scheme for constructing geometric interpretations of families of combinatorial numbers has been developed. The issues of enumerating flat and non-flat trees according to various parameters are considered.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;238:24-35
24-35
Optimization methods for bilinear control systems based on fixed point problems
Abstract
In the class of bilinear optimal control problems, conditions of optimality and control improvement in the form of special fixed-point problems on a set of admissible controls are considered. The obtained conditions of optimality and control improvement in the form of fixed-point problems make it possible to apply and modify the technique of the fixed-point theory and methods known in computational mathematics to search for extremal and improving controls. Iterative methods for the search for extremal and improving controls are constructed and analyzed. The efficiency of the proposed optimization methods are compared with the known methods.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;238:36-48
36-48
Secularity condition for the Broadwell kinetic system
Abstract
In this paper, we study the Broadwell kinetic system for four groups of particles with periodic initial data in a weight space. The solution is sought in a neighborhood of the equilibrium state. The perturbation is expanded in a Fourier series. Conditions for local equilibria for solutions of the Cauchy problem are found.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;238:49-58
49-58
An efficient algorithm for finding final vertices in a generalized functional graph
Abstract
In the paper, 2-outgoing graphs are introduced into consideration, generalizing functional graphs and modeling discrete dynamic systems of a special type. The vertices and arcs of a 2-outgoing graph are classified, paths on these graphs are defined, and some properties of these paths are proved. As a result, an efficient algorithm is constructed that, with linear complexity, constructs final vertices for paths starting at each of the vertices of a 2-outgoing graph, and its correctness is proven.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;238:59-68
59-68
Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. III. Seventh-order systems
Abstract
In this paper, we present new examples of integrable dynamical systems of the seventh order that are homogeneous in part of the variables. In these systems, subsystems on the tangent bundles of lower-dimensional manifolds can be distinguished. In the cases considered, the force field is partitioned into an internal (conservative) part and an external part. The external force introduced by a certain unimodular transformation has alternate dissipation; it is a generalization of fields examined earlier. Complete sets of first integrals and invariant differential forms are presented.The first part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 236 (2024), pp. 72–88.The second part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 237 (2024), pp. 49–75.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;238:69-100
69-100
Letter to the editor
Abstract
Corrections to the author's paper “Inequalities for the best ‘`angular” approximation and the smoothness modulus of a function in the Lorentz space’'// Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory. — 2023. — 230. — P. 8–24.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;238:101-102
101-102