共查询到20条相似文献,搜索用时 31 毫秒
1.
Din' Zung 《Journal of Mathematical Sciences》1986,35(6):2859-2875
The paper deals with imbedding theorems and harmonic approximation for classes of periodic functions of several variables. Necessary and sufficient conditions for imbedding are found for various classes of smooth functions. The paper contains asymptotic estimates for fractional order derivatives of multidimensional Dirichlet and Favard kernels, for Fourier best approximation and for the Kolmogorov diameter of smooth function classes.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 10, pp. 207–226, 1984. 相似文献
2.
Müfit Sezer 《Journal of Pure and Applied Algebra》2006,205(1):210-225
We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gröbner basis for the Hilbert ideal and the corresponding monomial basis for the coinvariants. We also describe the decomposition of the coinvariants as a module over the group ring. For one family of representations, we are able to describe the coinvariants despite the fact that an explicit generating set for the invariants is not known. In all cases our results confirm the conjecture of Harm Derksen and Gregor Kemper on degree bounds for generators of the Hilbert ideal. As an incidental result, we identify the coefficients of the monomials appearing in the orbit product of a terminal variable for the three-dimensional indecomposable representation. 相似文献
3.
V. S. Tikhonov 《Journal of Mathematical Sciences》1998,90(6):2474-2478
This paper presents a method for computing the complex eigenvalues for a boundary-value problem describing the rotation of
deep-water drill columns for drilling at depths of thousands of meters. A solution is sought for a singularly perturbed boundary-value
problem in the form of an asymptotic expansion in a small parameter ε for two parts of the of the drill column: a lower compressed
length, and the upper length. The method can be used to investigate the stability of drill columns used for deep-water drilling.
Translated fromDinamicheskie Sistemy. Vol. 12. pp. 29–36, 1993. 相似文献
4.
Bogdan Sasu 《Applicable analysis》2013,92(11):1165-1172
The aim of this article is to give a unified treatment for the theorems of Rolewicz and Neerven type for uniform exponential stability of evolution families. We obtain necessary and sufficient conditions for uniform exponential stability of evolution families, generalizing a stability theorem due to Rolewicz and we present a new proof for the Rolewicz theorem, based on the theory of Banach function spaces. Finally, we apply our results and we deduce a generalization for a classical stability theorem due to Przyluski and Rolewicz. 相似文献
5.
S. Ia. Makovenko 《Journal of Applied Mathematics and Mechanics》1983,47(6):775-782
New versions of the formulation of static non-linear elasticity theory problems are elucidated in terms of stresses for materials with locally reversible state laws (for instance, for a semilinear John material /1/), that reduce to the solution of nine equations in the Piola stress tensor component for six or three boundary conditions and three integral conditions. This paper is related to the investigations in /2–7/ devoted to analogous problems of the mechanics of a solid linearly deformable body. Examples are presented of the realization of one of the versions. 相似文献
6.
I. G. Filippov 《Mechanics of Composite Materials》1973,9(3):382-388
A new method is proposed for solving dynamic problems for viscoelastic media based on the introduction of potential functions and transformation of equations of motion. The equations obtained for potential functions are used for constructing the general solution in the case of the effect of moving loads on viscoelastic media with plane-parallel interfaces. The problem of the propagation of Rayleigh surface waves is solved independently of the form of the kernels of the linear operators; a formula is obtained for determining the velocity of the Rayleigh surface wave with an arbitrary form of the viscoelastic operators. A method of experimental determination of the kernels determining the linear viscoelastic operators is proposed.V. V. Kuibyshev Moscow Civil Engineering Institute. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 429–435, May–June, 1973. 相似文献
7.
A. M. Meirmanov 《Journal of Mathematical Sciences》2009,163(2):111-150
A linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space
is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main differential equations
involve nonsmooth oscillatory coefficients, both big and small, under the differentiation operators. The rigorous justification,
under various conditions imposed on physical parameters, is fulfilled for homogenization procedures as the dimensionless size
of the pores tends to zero, while the porous body is geometrically periodic. As the results for different ratios between physical
parameters, we derive Biot’s equations of poroelasticity, a system consisting of nonisotropic Lamé’s equations for the solid
component and acoustic equations for the liquid component, nonisotropic Lamé’s equations or equations of viscoelasticity for
one-velocity continuum, decoupled system consisting of Darcy’s system of filtration or acoustic equations for the liquid component
(first approximation) and nonisotropic Lamé’s equations for the solid component (second approximation), a system consisting
of nonisotropic Stokes equations for the liquid component and acoustic equations for the solid component, nonisotropic Stokes
equations for one-velocity continuum, or, finally a different type of acoustic equations for one- or two-velocity continuum.
The proofs are based on Nguetseng’s two-scale convergence method of homogenization in periodic structures. 相似文献
8.
9.
Solvability of Control Problems for Stationary Equations of Magnetohydrodynamics of a Viscous Fluid 总被引:1,自引:0,他引:1
We consider the boundary-value problem for the stationary equations of magnetohydrodynamics of a viscous incompressible fluid with nonhomogeneous boundary conditions for the velocity and electromagnetic field. We study global solvability of this problem and establish some sufficient conditions for uniqueness of its solution. We state control problems for the model of magnetohydrodynamics under consideration, study their solvability, give and examine optimality systems for both arbitrary and particular quality functionals. 相似文献
10.
A. S. Bratus'' 《Journal of Applied Mathematics and Mechanics》1994,58(6):1029-1038
A class of isoperimetric problems of stability optimization is considered. These arise, for example, when maximizing the Euler force in the destabilization of a column (rod) of varying cross-section and given volume (Lagrange's problem). It is well known that an extremum which depends on the form of the boundary conditions can be achieved for both simple and double eigenvalues. A class of problems is identified for which a global maximum is found at a simple eigenvalue. The possibility of achieving a local extremum for the first (simple) eigenvalue at stationary points is analysed qualitatively in terms of the parameter values and the form of the boundary conditions. 相似文献
11.
S. V. Yanchuk 《Ukrainian Mathematical Journal》1997,49(10):1615-1620
We obtain necessary and sufficient conditions for the existence of a sliding mode and also for the knotting of solutions of the equation for components of a normal system of first-order differential equations. 相似文献
12.
O. S. Rozanova 《Journal of Mathematical Sciences》2007,143(4):3355-3376
One considers a class of solutions with finite total energy and moment of inertia for the equations of motion of compressible
fluids. It is shown that for a wide class of right-hand sides, including the viscosity term, initially smooth solutions may
acquire singularities on a finite time interval. A sufficient condition for the appearance of singularities is found. This
condition may be called “the best possible sufficient condition” in the sense that one can explicitly construct a time-global
smooth solution for which this condition does not hold to within arbitrary infinitely small quantities. For a nontrivial constant
state, perturbations with compact support are considered. A generalization is proved for the known theorem on the initial
conditions for which the solution acquires singularities on a finite time interval. The effect of dry friction and rotation
on the formation of singularities of smooth solutions is examined.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 274–308, 2007. 相似文献
13.
We have shown that the solution of any boundary-value problem for two conjugated half-planes with different elastic constants,
in the case where the stresses are persistently continuable across the boundary between half-planes, can be expressed via
one common elastic constant if the stresses and external force factors are nondimensionalized by the reduced modulus of elasticity.
Owing to this, it is possible to obtain the solution of the problem for two conjugated half-planes directly from the solution
of the corresponding problem for one elastic half-plane. This property also holds true for axially symmetric problems formulated
for two conjugated half-spaces. 相似文献
14.
B.I. Konosevich 《Journal of Applied Mathematics and Mechanics》2008,72(6):673-681
An estimate is obtained, by small-parameter methods, of the error of the solution for the system of equations of motion of a projectile in the atmosphere, linearized for small angles of attack with respect to the variables describing the angular oscillations of the axis of symmetry, compared with the solution of the initial non-linear system for the same initial conditions. 相似文献
15.
A. N. Skrypnik 《Journal of Mathematical Sciences》1998,91(3):2990-3001
We consider two functionals of sums of independent random variables and demonstrate that the validity of the central limit
theorem for the sums of independent random variables that enter the arguments of those functionals is a sufficient condition
for one of the functionals and a necessary and sufficient condition for the other one to have a weak limit.
Proceedings of the Seminar on Stability Problems for Stochastic Models. Moscow. Russia. 1996. Part II. 相似文献
16.
Tests are given for uniform convergence of Fourier series for spaces of functions of generalized bounded variation; along with the well-known tests (of Salem–Oskolkov–Young, Chanturiya, and Waterman) we suggest new tests. We show that the Waterman test for uniform convergence of Fourier series is strongest and unimprovable. We present a theorem on exact estimates for the Fourier coefficients for spaces of functions of bounded variation which contains classical results, improves several well-known results, and gives some new results. 相似文献
17.
Gui-Qiang G. Chen Feimin Huang Tian-Yi Wang Wei Xiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(3):75
A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass conservation and the vorticity. Another observation is that the incompressibility of the limit for the homentropic Euler flow is directly from the continuity equation, while the incompressibility of the limit for the full Euler flow is from a combination of all the Euler equations. As direct applications of the compactness framework, we establish two incompressible limit theorems for multidimensional steady Euler flows through infinitely long nozzles, which lead to two new existence theorems for the corresponding problems for multidimensional steady incompressible Euler equations. 相似文献
18.
L 《Journal of Approximation Theory》2005,136(2):182-197
It is well known that for functions , 1p∞. For general functions fLp, it does not hold for 0<p<1, and its inverse is not true for any p in general. It has been shown in the literature, however, that for certain classes of functions the inverse is true, and the terms in the inequalities are all equivalent. Recently, Zhou and Zhou proved the equivalence for polynomials with p=∞. Using a technique by Ditzian, Hristov and Ivanov, we give a simpler proof to their result and extend it to the Lp space for 0<p∞. We then show its analogues for the Ditzian–Totik modulus of smoothness and the weighted Ditzian–Totik modulus of smoothness for polynomials with . 相似文献
19.
The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed. 相似文献
20.
A. S. Tarasenko 《Siberian Advances in Mathematics》2018,28(4):303-308
We obtain moment inequalities for the sum of the indicators of events and an upper estimate for a convex function of such a sum. Our results generalize inequalities that were obtained earlier for moment characteristics of the sojourn time of a random walk on a half-axis. 相似文献