Transients in a shock-excited hydroelastic system of cylindrical shells of finite length

Forced oscillations of a system of cylindrical shells filled with a liquid are considered. The initial—boundary-value problem is solved by Godunov's method. Plots of kinematic parameters of the hydroelastic system reflecting the behavior of the wave fields are given.Institute of Geophysics of the Ukrainian Academy of Sciences. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 67, pp. 62–66, 1989.     

On the composition length of finite primitive linear groups

LetG be a finite primitive linear group over a fieldK, whereK is a finite field or a number field. We bound the composition length ofG in terms of the dimension of the underlying vector space and of the degree ofK over its prime subfield. As a byproduct, we prove a result of number theory which bounds the number of prime factors (counting multiplicities) ofq ⁿ−1, whereq, n>1 are integers, improving a result of Turull and Zame [6].     

Mappings with finite length distortion

General properties of mappings of finite metric distortion and of finite length distortion are studied. Uniqueness, equicontinuity, boundary behavior and removability of singularities are obtained under minimal additional assumptions.     

On a class of finite linear spaces with few lines

A famous result of de Bruijn and Erdős (Indag. Math. 10 (1948) 421–423) states that a finite linear space has at least as many lines as points, with equality only if it is a projective plane or a near-pencil. This result led to the problem of characterizing finite linear spaces for which the difference between the number b of lines and the number v of points is assigned.

In this paper finite linear spaces with b−vm, m being the minimum number of lines on a point, are characterized.     

Contact interaction of cylindrical shells of different lengths

We solve a problem of determination of the contact rigidity of a structural joint of a steel thin-walled pipe under the action of internal pressure with a shroud made of a composite material using a special technology. A mathematical model of the contact interaction of the pipe and shroud modeled by cylindrical shells of different length was constructed using the classical Kirchhoff–Love theory of shells. We obtain an analytic solution of the contact problem under conditions of ideal contact of the elements of the structural joint by the conjugation method. A numerical analysis of the influence of geometric and physicomechanical characteristics of the shroud on the contact pressure and rigidity of the shrouded pipe is presented.     

The sharp Hausdorff measure condition for length of projections

In a recent paper, Pertti Mattila asked which gauge functions have the property that for any Borel set with Hausdorff measure 0$">, the projection of to almost every line has positive length. We show that finiteness of , which is known to be sufficient for this property, is also necessary for regularly varying . Our proof is based on a random construction adapted to the gauge function.

     

An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings

The construction of shortest feedback shift registers for a finite sequence \(S_1,\ldots ,S_N\) is considered over finite chain rings, such as \({\mathbb Z}_{p^r}\). A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for the sequence of numbers \(S_1,\ldots ,S_N\), thus solving an open problem in the literature. The algorithm iteratively processes each number, starting with \(S_1\), and constructs at each step a particular type of minimal basis. The construction involves a simple update rule at each step which leads to computational efficiency. It is shown that the algorithm simultaneously computes a similar parametrization for the reverse sequence \(S_N,\ldots ,S_1\). The complexity order of the algorithm is shown to be \(O(r N^2)\).     

Free oscillations of shells of complex geometry with finite shear stiffness

By applying isoparametric approximations we develop a finite-element method for studying the oscillations of shells whose middle surfaces are Monge surfaces. As the starting point we take the model of shells of Timoshenko type. To solve the eigenvalue problem we apply the method of iterations in a subspace. Two figures. Five tables. Bibliography: 14 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 13–17.     

Gorenstein modules of finite length

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Symmetrically Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers. We show that their graded minimal free resolution is selfdual in a strong sense. Applications include a proof of the dependence of the monoid of Betti tables of Cohen‐Macaulay modules on the characteristic of the base field. Moreover, we give a new proof of the failure of the generalization of Green's Conjecture to characteristic 2 in the case of general curves of genus 2ⁿ ?1. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Compactness theory and mappings with finite length distortion

The present paper is devoted to the study of mappings with finite length distortion introduced in 2004 by O. Martio, V. Ryazanov, U. Srebro, and E. Yakubov. It is proved that the locally uniform limit of homeomorphisms with finite length distortion is a homeomorphism or a constant provided that the so-called inner dilatations of the sequence of homeomorphisms are almost everywhere (a.e.) majorized by a locally integrable function. In particular, it is studied the pointwise behavior of the so-called outer dilatations. For these dilatations, the pointwise semicontinuity and semicontinuty in the mean are proved. It is also proved some theorems on the convergence of matrix dilatations.     

Contact interaction of composite shells,subjected to follower loads,with a rigid convex foundation

Based on a 7-parameter shell model, a numerical algorithm is developed for solving the contact problem for a multilayered composite shell lying on a rigid convex foundation, which is subjected to a follower pressure and undergoes arbitrarily large rotations. A new geometrically exact solid shell element is formulated, which permits one to solve the nonlinear deformation problem for thin-walled composite structures under unilateral contact constraints by using a small number of load steps. The calculation of a homogeneous ring and an angle-ply toroidal shell interacting with plane and cylindrical foundations is considered.     

On an effective two-phase model of a medium with cracks of finite length

An effective two-phase model of media with cracks filled with liquid is generalized to the case of finite cracks. Wave propagation in a half-space and in a free layer, described by the new model, is investigated. The results are compared with experimental data and with corresponding results in the case of media with infinite cracks. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 137–155. Translated by L. A. Molotkov.