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In the present paper, necessary and sufficient conditions are given for the equality of the power rezidue symbols $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ and $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ in the cyclotomic field ℚ(ζ n), 2 ∤ n, for a ∈ ℤ, ( a, n) = 1. This result is a generalization of the classical Eisenstein reciprocity law and its continuation in a Hasse’s paper. Bibliography: 3 titles. [ABSTRACT FROM AUTHOR]

It is shown that an approach earlier used by the author for classification of closed simply connected 6-manifolds (reduction to the problem of calculating certain bordism groups) can also be applied for easily obtaining the results by Barden (1965) on classification of closed simply connected 5-manifolds. Bibliography: 11 titles. [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]

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]

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]

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]

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]

This is an attachment to a letter of the author to Alexander Zvonkin (dated November 1, 1995). It is reproduced here with the kind permission of the author. [ABSTRACT FROM AUTHOR]

Some gaps in two of my publications dated 1958 and 1959 years are indicated, and the way of closing them is given. Bibliography: 10 titles. [ABSTRACT FROM AUTHOR]

Congruences mod p for a prime p and partial products of the numbers 1,..., p − 1 are obtained. Bibliography: 2 titles. [ABSTRACT FROM AUTHOR]

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]

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

In this paper, we present a technique for constructing generalized solutions of the Cauchy problem for abstract integro-differential equations with degeneration in Banach spaces. A generalized solution is constructed as the convolution of the fundamental operator function (fundamental solution, influence function) of the integro-differential operator of the equation with a generalized function of a special form, which involves all input data of the original problem. Based on the analysis of the representation for the generalized solution, we obtain sufficient solvability conditions for the original Cauchy problem in the class of functions of finite smoothness. Under these sufficient conditions, the generalized solution constructed turns out to be a classical solution with the required smoothness. The abstract results obtained in the paper are applied to the study of applied initial-boundary-value problems from the theory of oscillations in viscoelastic media. [ABSTRACT FROM AUTHOR]

In this paper, we consider problems for partial differential equations that contain a small parameter in the principal part. We construct exact solutions of the original singularly perturbed problems and, passing to the limit, we state a correspondence between these solutions and solutions of the limit problems obtained from the original problems if the small parameter is set equal to zero. Examples given in this paper show that among singularly perturbed problems for partial differential equations, there are problems that possess characteristic properties of regularly perturbed problems and allow constructing asymptotic solutions by methods of the theory of regular perturbations. [ABSTRACT FROM AUTHOR]

In this paper, we examine the optimal control problem for a hyperbolic system with differential constraints on the boundary, taking into account the delay. Controls are selected from the class of smooth functions that satisfy pointwise constraints. Problems of this type arise, in particular, in modeling the processes of population dynamics. The approach proposed in this paper is based on the use of "internal variations" of the control, which preserves the smoothness of the control function and ensures the fulfillment of pointwise constraints. We obtain an estimate of the state increment, prove a necessary optimality condition, and develop a scheme of an iterative method. [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 study a two-state Hard-Core (HC) model with activity λ > 0 on a Cayley tree of order k ≥ 2. It is known that there are λcr, λ cr 0 , and λ cr ′ such that • for λ ≤ λcr this model has a unique Gibbs measure μ*, which is translation invariant. The measure μ* is extreme for λ < λ cr 0 and not extreme for λ > λ cr ′ ; • for λ > λcr there exist exactly three 2-periodic Gibbs measures, one of which is μ*, the other two are not translation invariant and are always extreme. The extremity of these periodic measures was proved using the maximality and minimality of the corresponding solutions of some equation, which ensures the consistency of these measures. In this paper, we give a brief overview of the known Gibbs measures for the HC-model and an alternative proof of the extremity of 2-periodic measures for k = 2, 3. Our proof is based on the tree reconstruction method. [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]