共查询到20条相似文献,搜索用时 46 毫秒
1.
T. G. Hessami Pilehrood 《Mathematical Notes》2000,67(3):372-381
By using Padé approximations of the first kind, a lower bound for the modulus of a linear form with integer coefficients in
the values of certain hypergeometric functions at a rational point are obtained. This estimate depends on all the coefficients
of the linear form.
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 441–451, March, 2000. 相似文献
2.
According to the well-known Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We study analogues of this theorem for some locally compact Abelian groups X containing an element of order 2. We prove that if X contains an element of order 2, this leads to the fact that a wide class of non-Gaussian distributions on X is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. While coefficients of linear forms are topological automorphisms of a group.
相似文献3.
S. K. Persidskii 《Journal of Mathematical Sciences》1993,65(3):1661-1663
We give a method of construction of Lyapunov functions in the form of a linear form with respect to moduli of variables, for which there exist Krasovskii constants in the case of asymptotic stability, for linear systems with constant coefficients and some types of nonlinear systems of finite-difference equations. An application of the above functions as components of a vector Lyapunov function allowed us to obtain conditions on asymptotic stability for interrelated finite-difference systems.Translated from Dinamicheskie Sistemy, No. 8, pp. 68–71, 1989. 相似文献
4.
《复变函数与椭圆型方程》2012,57(9):797-801
The article deals with initial value problems of type δw/δt = Fw, w(0, ·) = φ where t is the time and F is a linear first order operator acting in the z = x ? iy-plane. In view of the classical Cauchy-Kovalevkaya Theorem, the initial value problem is solvable provided F has holomorphic coefficients and the initial function is holomorphic. On the other hand, the Lewy example [H. Lewy (1957). An example of a smooth linear partial differential equation without solution. Ann. of Math., 66, 155–158.] shows that there are equations of the above form with infinitely differentiable coefficients not having any solutions. The article in hand constructs, conversely, all linear operators F for which the initial value problem with an arbitrary holomorphic initial function is always solvable. In particular, we shall see that there are equations of that type whose coefficients are only continuous. 相似文献
5.
A. I. Vagabov 《Differential Equations》2010,46(1):17-23
We consider a system of first-order ordinary linear differential equations with coefficients depending on an arbitrary parameter
λ. For large λ, if the coefficients are smooth with respect to x, then there are known classical exponentially asymptotic (with respect to λ) formulas for the solution of the system. We generalize such formulas to the case in which the coefficients belong to the
class L
q
, q > 1. We use a new method for the reduction of problems to an integral system of special form. 相似文献
6.
M. M. Chyp 《Ukrainian Mathematical Journal》1992,44(7):900-902
Algebraic polynomials that occur in the generalized moment representation of a specified number sequence are found in the form of linear combinations of orthogonal polynomials. The coefficients of these linear combinations are computed from a system of algebraic equations and the polynomials that are found satisfy integral and differential equations.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 995–997, July, 1992. 相似文献
7.
This paper investigates general fuzzy linear systems of the form Ax = y and general dual fuzzy linear systems of the form Ax + y = Bx + z with A, B matrices of crisp coefficients and x, y fuzzy number vectors. The aim of this paper is twofold. First, by the unique least Euclidean norm solution we solve the systems
with non-full rank matrices A, B. Second, we give the new necessary and sufficient condition for a strong fuzzy solution existence. Moreover, some numerical
examples are designed. 相似文献
8.
We consider the scalar linear second-order differential-difference equation with delay {fx159-01}. This equation is investigated
by the method of polynomial quasisolutions based on the representation of an unknown function in the form of a polynomial
{ie159-01}. Upon the substitution of this polynomial in the original equation, the residual Δ(t) = O(t
N−1) appears. An exact analytic representation of this residual is obtained. We show the close connection between a linear differential-difference
equation with variable coefficients and a model equation with constant coefficients, the structure of whose solution is determined
by the roots of the characteristic quasipolynomial.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 140–152, January, 2008. 相似文献
9.
M. M. Chip 《Journal of Mathematical Sciences》1998,90(5):2416-2420
We propose studying generalized moment representations of a form in which it suffices to apply a system of orthogonal polynomials
in order to procure the biorthogonality conditions in the construction of superdiagonal Padé polynomials using generalized
moment representations. The algebraic polynomials in the moment representation are to be sought as the linear forms of biorthogonal
polynomials. We obtain the relations between the coefficients of these linear forms and the generalized moments, and we also
establish conditions for the existence and uniqueness of generalized moment representations of polynomial form.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 110–115. 相似文献
10.
We give sufficient conditions for the existence of positive solutions to some semilinear elliptic equations in bounded domains
with Dirichlet boundary conditions. We impose mild conditions on the domains and lower order (nonlinear) coefficients of
the equations in that the bounded domains are only required to satisfy an exterior cone condition and we allow the coefficients
to have singularities controlled by Kato class functions. Our approach uses an implicit probabilistic representation, Schauder's
fixed point theorem, and new a priori estimates for solutions of the corresponding linear elliptic equations. In the course
of deriving these a priori estimates we show that the Green functions for operators of the form on D are comparable when one modifies the drift term b on a compact subset of D. This generalizes a previous result of Ancona [2], obtained under an condition on b, to a Kato condition on .
Received: 21 April 1998 / in final form 26 March 1999 相似文献
11.
We consider a linear homogeneous difference equation of ordern with positive coefficients, which is presented in the normal form. We obtain necessary and sufficient conditions for the
stability and asymptotic stability.
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1276–1280, September, 1990. 相似文献
12.
I. N. Yakushina 《Journal of Mathematical Sciences》1995,73(3):408-413
Asymptotic expansions for solutions of n-th order linear differential equation with two turning points are constructed in
Olver's form. Analytic properties of the coefficients of the series obtained are investigated. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 172–179, 1990. 相似文献
13.
The purpose of this paper is to derive L
p
− L
q
decay estimates for linear thermoelastic systems with time-dependent coefficient in one space variable. When all coefficients
in the system have the same growth speed with small oscillations, we obtain a parabolic type decay estimate. For the system
with time-dependent coefficients, we need to investigate the delicate asymptotic behaviour of characteristic roots and the
remainder of diagonalization, which will be treated by dividing the phase space into three regions.
Received September 15, 2001; in revised form April 20, 2002 相似文献
14.
A. V. Pokrovskii 《Journal of Mathematical Sciences》2009,160(1):61-83
This paper is an overview of results devoted to metric conditions for removability of closed sets for solutions of homogeneous
partial differential equations in various function classes. The author considers equations with a quasi-homogeneous semi-elliptic
operator and with constant coefficients, linear second-order uniformly elliptic equations in the divergent form with real
bounded measurable coefficients, quasilinear equations with the p-Laplacian, and the minimal surface equation. A number of results is published for the first time.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal
Conference–2006, Part 3, 2008. 相似文献
15.
The well-known Skitovich-Darmois theorem asserts that a Gaussian distribution is characterized by the independence of two
linear forms of independent random variables. The similar result was proved by Heyde, where instead of the independence, the
symmetry of the conditional distribution of one linear form given another was considered. In this article we prove that the
Heyde theorem on a locally compact Abelian group X remains true if and only if X contains no elements of order two. We describe also all distributions on the two-dimensional torus which are characterized by the symmetry of the conditional distribution of one linear form given another. In so doing we
assume that the coefficients of the forms are topological automorphisms of X and the characteristic functions of the considering random variables do not vanish. 相似文献
16.
H. Guggenheimer 《Israel Journal of Mathematics》1971,9(1):49-52
We determine all third order homogeneous linear differential equations with periodic coefficients and only periodic solutions.
The method extends tonth order equations. As an application, we show that the Laguerre-Forsyth canonical form cannot be used for global investigations
i projective differential geometry.
Research supported by NSF Grant GP-8176.
To the Memory of Eri Jabotinsky 相似文献
17.
In this paper we study the relation between coefficients of a polynomial over finite field Fq and the moved elements by the mapping that induces the polynomial. The relation is established by a special system of linear equations. Using this relation we give the lower bound on the number of nonzero coefficients of polynomial that depends on the number m of moved elements. Moreover we show that there exist permutation polynomials of special form that achieve this bound when m|q−1. In the other direction, we show that if the number of moved elements is small then there is an recurrence relation among these coefficients. Using these recurrence relations, we improve the lower bound of nonzero coefficients when m?q−1 and . As a byproduct, we show that the moved elements must satisfy certain polynomial equations if the mapping induces a polynomial such that there are only two nonzero coefficients out of 2m consecutive coefficients. Finally we provide an algorithm to compute the coefficients of the polynomial induced by a given mapping with O(q3/2) operations. 相似文献
18.
Let be a Siegel modular form of weight ?, and let be an Eichler embedding, where denotes the Siegel upper half space of degree n. We use the notion of mixed Siegel modular forms to construct the linear map of the spaces of Siegel cusp forms for the congruence subgroup and express the Fourier coefficients of the image of an element under in terms of special values of a certain Dirichlet series. We also discuss connections between mixed Siegel cusp forms and
holomorphic forms on a family of abelian varieties.
(Received 28 February 2000; in revised form 11 July 2000) 相似文献
19.
M. H. Poursaeed 《International Journal of Mathematical Education in Science & Technology》2013,44(4):634-638
Formulas presented for the calculation of ∑ j=1 n jk (n, k ∈ N do not have a closed form; they are in the form of recursive or complex formulas. Here an attempt is made to present a simple formula in which it is only necessary to compute the numerical coefficients in a recursive form, and the coefficients in turn follow a simple pattern (almost similar to Pascal's Triangle). Although the pattern for calculating numerical coefficients based on forming a table is easy, non-recursive formulas are presented to determine the numerical coefficients. 相似文献
20.
Clestin Wafo Soh 《Communications in Nonlinear Science & Numerical Simulation》2010,15(2):139-143
We show that the structure of the Lie symmetry algebra of a system of n linear second-order ordinary differential equations with constant coefficients depends on at most n-1 parameters. The tools used are Jordan canonical forms and appropriate scaling transformations. We put our approach to test by presenting a simple proof of the fact that the dimension of the symmetry Lie algebra of a system of two linear second-order ordinary differential with constant coefficients is either 7, 8 or 15. Also, we establish for the first time that the dimension of the symmetry Lie algebra of a system of three linear second-order ordinary differential equations with constant coefficients is 10, 12, 13 or 24. 相似文献