This paper is concerned with abnormal geodesics on the Carnot group with growth vector (2,3,5,8,14) . Because of a large number of symmetries, this problem reduces to an analysis of the five-dimensional flow. Using the Kovalevskaya method, integrable cases of the resulting system are identified. For these cases, first integrals and explicit solutions are found. It is shown that in the general case the system admits no additional meromorphic first integrals. The paper concludes by discussing some problems regarding the abnormal geodesics on Lie groups.
The work investigates the possibility of obtaining the electrode material of supercondensers by mechanactivation and short-income laser processing of the Al – C system. After mechanical grinding, the obtained powder materials were subjected to short-pulse laser treatment on the surface of the substrate — aluminum foil. An increase in the concentration of graphite in the Al – C composite does not lead to an increase in specific capacity, which is associated with the content of graphite-like carbon located on the surface of the electrode. The obtained electrodes based on nanocomposite have a homogeneous porous structure with an average particle size of 20 microns and a specific surface of 31 m2/g. The analysis of the complex of modern research methods to determine the structural-phase composition showed that the mechanactivation and short-impulse laser processing of the Al – C system leads to the formation of aluminum and aluminum oxide, and the main part of the carbon on the electrodes is in a reduced state. X-ray diffraction analysis of the sintered layers reveals the appearance of crystalline aluminum carbide Al4C3. The maximum capacity of the electrodes of supercondensers from the material obtained corresponds to the composition of Al – 47 wt. % C – 12 wt. % Si and amounted to 23 F/g.
In this paper we address the problem of a body of revolution moving on a plane within the framework of the rubber rolling model. By “rubber” rolling we mean the rolling of the body without slipping at the point of contact and without twisting relative to the vertical. We write the equations of motion in local coordinates and reduce them to Hamiltonian form. We prove the isomorphism of the reduced systems for bodies of revolution whose surfaces are equidistant to each other. As an example, we consider the problem of a torus of revolution rolling on a plane, for which we carry out a complete bifurcation analysis of partial solutions. Also, we analyze the dynamics of the torus in absolute space and perform a classification of trajectories of motion. In addition, we touch upon the question of whether a retrograde turn is possible as the torus rolls on the plane.
This paper addresses the problem of simple pursuit of one evader by a group of pursuers in a differential game described by equations with Caputo fractional derivatives from the interval (0, 1). Integral constraints are imposed on the players' controls, and the pursuers use quasi-strategies. The goal of the group of pursuers is to bring at least one of them within any predetermined distance of the evader. It is proven that if the total energy of the pursuers is greater than the energy of the evader, then the capture occurs in the game.
This article presents an approach to deductive program synthesis using Gentzen's sequent calculus within the framework of logic programming. By leveraging sequent calculus as a formal system for structured logical inference, our method automates the derivation of provably correct programs from specifications expressed in negation-free first-order predicate logic. We formalize the syntax and semantics of sequent calculus, implementing its core inference rules (introduction and elimination rules) as predicates in logic programming to enable scalable synthesis. Practical examples demonstrate the transformation of logical specifications into executable programs. The approach ensures formal correctness through a constructive semantics inspired by Kleene's realizability, with synthesized programs operating in a subrecursive language to guarantee termination. We evaluate the method's strengths, including its reliability for safety-critical systems, and its limitations, such as computational complexity for unbounded constructions. Compared to AI-driven synthesis, our approach prioritizes formal guarantees, complementing modern trends like relational programming. Future research directions include optimizing computational efficiency and extending applicability to complex real-world problems.
