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The International Sirius Mathematics Center, located on the Black Sea coast, was founded in 2019 by the Talent and Success Foundation for organizing mathematical conferences and other events promoting the development of mathematics in Russia. In 2024, the Center has acquired its own Russian-language journal for publication of original research papers by participants of conferences held at the Center. The authors are invited to submit papers to the journal at https://ef.msp.org/submit/sirius [ABSTRACT FROM AUTHOR]

The Euler problem on the stability of a thin elastic rod under compressing forces is widely known. In a number of papers this problem is generalized to finding the shape of such a rod under the simultaneous action of a compressing force and a torsional moment. The shape is determined by solving a complex nonlinear boundary value problem by numerical methods. In this paper, an approach providing a full analytical solution of the problem for a broad range of external conditions is discussed. [ABSTRACT FROM AUTHOR]

UDC 515.164 (Journal of Mathematical Sciences, Vol. 159, No. 6, pp. 753-760 (2009)) There is a misprint in the formulation of Lemma 3. Instead of the dimension constraints n-k = [...]

In the problem of gliding flight, i.e., aircraft longitudinal movement with its engines switched off, the aircraft was traditionally assumed to be an absolutely rigid body, the Earth was not rotating and had a plane surface, and the atmosphere was quiet. Further, the attack angle and the air density were assumed constant. The aim of this paper is to discuss the applicability limits of these assumptions. [ABSTRACT FROM AUTHOR]

In the present paper, a finite-dimensional phenomenological model of unsteady interaction of a rigid plate with a flow is proposed. It is assumed that the plate performs translational motion across the flow. The internal dynamics of the flow is modeled by the attached second order dynamical system. It is shown that the model allows satisfactory agreement with experimental data. With the developed model an inverse problem of dynamics is examined for the situation where the plate performing uniform translational motion at some moment begins uniform deceleration and finally stops. It is shown that for sufficiently large values of the plate acceleration for some time range the flow does not resist the motion of the plate but “accelerates” it. It is shown also that the equations of motion in the context of the proposed model can be reduced to the integro-differential form, and comparison with the known model of S. M. Belotserkovsky is performed. The structural resemblance of the motion equations for a body in flow in both models is noted. The domain of applicability of the quasi-stationary model is examined. [ABSTRACT FROM AUTHOR]

The Steward platform is employed in dynamic simulation of a number of controlled mechanical systems, in control of the active surface of a telescope mirror, and other constructions. Position and orientation of this platform is regulated by changing the lengths of its supporting bars, and corresponding change of their angles relative to the base. Viable motions of the platform depend on how the bars are hinged to the base and to the platform. This paper studies dynamics and stabilization of a platform leaning on three bars of controlled length under wind loads. This problem is of interest for design of active mirror surfaces of radio telescopes. [ABSTRACT FROM AUTHOR]

In airborne gravimetry the data received from an airborne survey system is used to obtain the specific gravity along the aircraft path and to construct maps of the gravity anomaly. The quality of the maps depends largely on both the instrument noise and modeling errors. The paper discusses the errors in the estimated gravity caused by imperfect calibration of the gravimeter and how to calibrate the instrument using the survey flights data and the gravity maps. [ABSTRACT FROM AUTHOR]

This paper investigates algorithms of motion planning for a six-legged walking machine over complex terrain. Application of the Rodrigues-Hamilton parameters for describing the orientation of the body enables one to develop algorithms of motion planning for the body and legs in an absolute coordinate frame with automatic adaptation to the surface. Experiments with a laboratory scale walking machine have demonstrated the efficiency of proposed algorithms. [ABSTRACT FROM AUTHOR]

The present paper considers a discrete analog of the parking problem. Let n be an integer. If n > 1, then we randomly locate an interval (t, t + 1) with integer endpoints on a segment [0, n]. Thus, the original segment is divided into two: [0, t] and [t + 1, n], and each of them is further considered separately likewise the original one. The phrase "randomly" in this problem means that t is a uniformly distributed on a set {1,... , n − 1} random variable. The process of location of the intervals finishes when the lengths of all the remaining intervals are less than 2. Define as Xn the total amount of the located intervals. In the present paper, the expectations {Xn} are calculated. The process described above can be interpreted as a parking process of cars with handlebars on the left. Hence, the driver is able to leave his car only if the place on his left is free. This is exactly the case when the driver cannot take the left end place of any free segment. In this case, Xn stands for the amount of the parked cars. [ABSTRACT FROM AUTHOR]

This paper discusses different approaches to constructing approximate mathematical models. [ABSTRACT FROM AUTHOR]

The paper gives a survey of some recent results of the authors concerning the function ψ(G), which is the sum of orders of elements of a finite group; more precisely, the authors consider the question, how does the value of ψ(G) affect the structure of G. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of congruence for regions in lattice path models. This turns out to be useful for deriving a path counting formula for the auxiliary lattice path model in the presence of long steps, source and target points of which are situated near the filter restrictions. This problem was motivated by the fact, that weighted numbers of paths in such model mimic multiplicities in tensor power decomposition of Uq(sl2)-module T(1)⊗N at roots of unity. We expand on combinatorial properties of such model and introduce the punchline of a proof for explicit path counting formula. [ABSTRACT FROM AUTHOR]

In this paper, an analog of the conformable fractional derivative is defined in an arbitrary finite-dimensional commutative associative algebra. Functions taking values in the indicated algebras and having derivatives in the sense of a conformable fractional derivative are called φ-monogenic. A relation between the concepts of φ-monogenic and monogenic functions in such algebras has been established. Two new definitions have been proposed for the fractional derivative of the functions with values in finite-dimensional commutative associative algebras. [ABSTRACT FROM AUTHOR]

This article, published in the Journal of Mathematical Sciences, explores the computation of the component group of an arbitrary real algebraic group. The author demonstrates that the component group is always an elementary Abelian 2-group. The computation is based on structure results on algebraic groups and Galois cohomology methods. The paper provides necessary material on algebraic groups and Galois cohomology, and includes an example of the real locus of an elliptic curve. This document discusses the computation of the group of connected components of the real locus of a connected algebraic group defined over R. It introduces the concepts of cocycles, exact sequences of groups, and Galois cohomology. The main result of the document is a formula for computing the group of connected components, which involves lattices and coroot lattices. The proof of the formula is similar to a previous proof in another paper. The given text discusses the component groups of certain mathematical structures, specifically linear algebraic groups and Abelian varieties. It presents theorems and examples related to these component groups, providing mathematical proofs and explanations. The text explores different cases and scenarios, such as when the period lattice is preserved by complex multiplication or when it is multiplied by certain values. The examples given include elliptic curves and their connected components. The text is written in a technical and mathematical language, and it may be useful for researchers studying these specific topics. [Extracted from the article]

The given document is a research paper titled "Quasiregular Radicals of Nonassociative Algebras" written by A. Yu. Golubkov. The paper discusses various mathematical concepts related to Lie algebras, Jordan linear pairs, and linear triple systems. It explores the construction of quasiregular radicals and their applications in the Amitsur-Procesi theorem. The document also discusses the properties and relationships of different radicals in these algebraic structures. The author acknowledges funding support and provides their contact information for further inquiries. [Extracted from the article]

In this paper a retrial queuing system is considered with the help of two-way communication where the server is subject to random breakdowns. This is a M/M/1//N type of system so the population of the source is finite. The server becoming idle enables calls the customers in the orbit (outgoing call or secondary customers). The service time of the primary and secondary customers follows exponential distribution with different rates μ1 and μ2 respectively. All the random variables included in the model construction are assumed to be totally independent of each other. The novelty of this paper is to show the effect of the different distributions of failure time on the main performance measures such as the mean waiting time of an arbitrary customer or the utilization of the service unit. In order to achieve a valid comparison a fitting process is done; thus, in case of every distribution the mean value and dispersion is the same. Graphical illustrations are given with the help of the self-developed simulation program. [ABSTRACT FROM AUTHOR]

The drop of the smoothness of an analytic function compared to the smoothness of its modulus is discussed for the unit ball of ℂn. The paper is devoted to local aspects of the problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new candidate for a one-way ring homomorphism induced by a one-way (non-Abelian) group homomorphism. A multi-party digital signature scheme is also given as an application of the proposed one-way ring homomorphism. [ABSTRACT FROM AUTHOR]

The paper surveys results obtained mainly by the author with A. Marcone, P. Shafer, and G. Soldà centered around two theorems due to I. Rival and B. Sands. We analyze the strength of these theorems and their variations within the framework of reverse mathematics and Weihrauch reducibility. Some related combinatorial results are presented, as well as generalizations of these results to the uncountable. Open questions are formulated. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a new type of tasks for control theory for stochastic dynamical systems — programmed control with Probability 1 (PCP1). PCP1 is an application of an invariant theory. We use the PCP1 concept for dynamical processes described by a system of Itô differential equations with jump-diffusion (GSDES). The considered equations include the drift, the diffusion, and the jumps, together or not. Features of our approach are both a wide set of dynamical systems and investigation of such systems for their unique trajectories. Our method is based on the concept of a stochastic first integral (SFI) for GSDES and its equations which author studied before. The purpose of the present paper is to construct a differential equation system (both stochastic and deterministic) using a known set of FIs for the investigating process. Several examples are given. [ABSTRACT FROM AUTHOR]