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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 = [...]

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 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]

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 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]

A new concept of surface waves of an interference nature is described in details for the case of a whispering gallery waves propagating along a smooth strictly concave surface embedded in 3D Euclidean space. Numerous papers consider whispering gallery and creeping waves in 2D case. However, in general, surface waves propagate along geodesic lines on the surface, and typically form caustics. The geodesic lines themselves are not plane curves in 3D and, therefore, their torsion must be taken into account. Our approach enables one to adequately describe surface waves propagation along smooth surfaces embedded in 3D Euclidean space. It is based on the consideration of the geodesic on a surface, which is associated with the surface wave generated by a source. For each geodesic line, we present an asymptotic solution of the Helmholtz equation, localized in its tubular and having no singularities on caustics. The surface wave under consideration is then presented as a superposition (integral) of the localized solutions. [ABSTRACT FROM AUTHOR]

In the present paper, we calculate the Mandel parameter QM for an oscillator-like system generated by generalized Chebyshev polynomials. The sign of the Mandel parameter QM characterizes the deviation of the excitation statistics from the Poisson one. This paper is a continuation of our works (2005). [ABSTRACT FROM AUTHOR]

The present paper is a continuation of the three-body one-dimensional scattering problem in the presence of bound states. Full description and justification of the generalized eigenfunction asymptotics in the case of repulsive potentials have a simple geometric description. In the case of the presence of the bound states, additional terms appear in the eigenfunction asymptotics. In previous papers, during the analysis of Faddeev's equations in coordinate representation an operator of special form appeared which was connected to scattering amplitude and which did not have a simple description. In the current paper, some properties of that operator are described. In particular, we derive the solvability of Faddeev's equations. [ABSTRACT FROM AUTHOR]

In this paper, we examine topological partitions of topological spaces that arise in connection with continuous mappings of topological spaces. The content of the paper is closely related to such classical fundamental concepts of general topology as compactness, homogeneity, and Čech completeness. New facts related to these concepts are obtained. [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]