共查询到20条相似文献,搜索用时 46 毫秒
1.
V. M. Petrichkovich 《Journal of Mathematical Sciences》1999,96(2):3022-3025
We describe all the factorizations A=BC (up to associates) of a matrix A over a commutative principal ideal domain parallel to the factorization DA= of its canonical diagonal form DA ( and are diagonal matrices), that is, the factorizations such that the matrices B and C are equivalent to the matrices and respectively.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 96–100. 相似文献
2.
H. Kita 《Acta Mathematica Hungarica》1998,81(3):175-193
Let and be positive increasing convex functions defined on [0, ). Suppose satisfies the 2-condition, that is, (t)2 (C1t) for sufficiently large t, and has some nice properties. If -1(u)log(u+1) C2-1(u) for sufficiently large uthen we have S*(f) L CfL for all f L ([-, ])where S*(f) is the majorant function of partial sums of trigonometric Fourier series and fL is the Orlicz norm of f. This result is sharp. 相似文献
3.
Bolesław Gaweł 《Aequationes Mathematicae》1996,52(1):55-71
Summary In the paper we consider, from a topological point of view, the set of all continuous functionsf:I I for which the unique continuous solution:I – [0, ) of(f(x)) (x, (x)) and(x, (x)) (f(x)) (x, (x)), respectively, is the zero function. We obtain also some corollaries on the qualitative theory of the functional equation(f(x)) = g(x, (x)).
No assumption on the iterative behaviour off is imposed. 相似文献
4.
Tassilo Küpper 《Numerische Mathematik》1976,25(2):201-214
Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea
2 and for given functions = we require =C
0[0, 1] C
2([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and . 相似文献
5.
A sharp almost sure bound is derived for limit points of average sum of weakly dependent random variables, which ensures strong laws of large numbers for and -mixing random variables, without assumptions on rate of tending to zero of and -mixing parameters n and n. 相似文献
6.
This work deals with the guidance and control of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its center of mass, about the disk center. There are given N points P
i, i=1, ..., N, in the horizontal plane, a set of angles 2i
, i=1, ..., N, a finite-time interval [0, t
f], and a sequence of times 1=0<2<...<
N
=t
f. Using the concept of path controllability, a closed-loop control law is derived to steer the system in such a manner that the disk center and the rod angle of rotation 2 will pass through (P
i, 2i
) at the times
i
, i=1,...,N, respectively. This system serves as a model for the motion of a simple mobile robot. 相似文献
7.
Anders Lundberg 《Aequationes Mathematicae》1992,43(2-3):127-144
Summary A real solution of the functional equation(x + (y – x)) = f(x) + g(y) + h(x)k(y) on a set 2 is a 6-tuple (f, g, h, k, , ) of real valued functions such that the equation is identically fulfilled on. Except for cases known before—e.g. when is linear—we present all real solutions in an arbitrary region where the functions have derivatives of second order. 相似文献
8.
Maciej Sablik 《Aequationes Mathematicae》1990,39(1):19-39
Summary The functional equation(x) + (y) = (xf(y) + yf(x)) (1) for the unknown functionsf, and mapping reals into reals appears in the title of N. H. Abel's paper [1] from 1827 and its differentiable solutions are given there. In 1900 D. Hilbert pointed to (1), and to other functional equations considered by Abel, in the second part of his fifth problem. He asked if these equations could be solved without, for instance, assumption of differentiability of given and unknown functions. Hilbert's question was recalled by J. Aczél in 1987, during the 25th International Symposium on Functional Equations in Hamburg-Rissen. In particular Aczél asked for all continuous solutions of (1). An answer to his question is contained in our paper. We determine all continuous functionsf: I ,: A
f
(I × I) and: I that satisfy (1). HereI denotes a real interval containing 0 andA
f
(x,y) := xf(y) + yf(x), x, y I. The list contains not only the differentiable solutions, implicitly described by Abel, but also some nondifferentiable ones.Applying some results of C. T. Ng and A. Járai we are able to obtain even a more general result. For instance, the assertion (i.e. the list of solutions) remains unchanged if we replace continuity of and by local boundedness of orf(0)I from above or below. Strengthening a bit the assumptions onf we can preserve a large part of the assertion requiring only the measurability of either orf(0)I. 相似文献
9.
Every translation invariant positive definite Hermitian bilinear functional on the Gel'fand-Shilov space sMpMp(n×nK) of general type S is of the form B(,) = (x)(x)d(x), , sMpMp (n), where is a positive {M}-tempered measure, i.e., for every > 0 exp[-M(|x|)] d(x) < . To prove this we prove Schwartz kernel theorem for {M}-tempered ultradistributions and need Bochner-Schwartz theorem for {M}-tempered ultradistributions. Our result includes most of the quasianalytic cases. Also, we obtain parallel results for the case of Beurling type (Mp. 相似文献
10.
Summary We consider the Cauchy problem for the generalized porous medium equation ut=(u) where u=u(x, t), xRn and t>0, and the initial datum u(x, 0) is assumed to be nonnegative, integrable mid to nave compact support. The nonlinearity (u) is a C1 function defined for uO which grows like a power of u. Our assumptions generalize the porous medium case, (u)=um, m>1, and also include the equation of the Marshak waves. This problem has finite speed of propagation. We estimate the rate of growth of the support of the solution with precise estimates for t 0 and t. Our main result deals with the regularity of the solutions. We show that after a certain time t0 the pressure, defined by v=(u), with (u)=(u)/u and (0)=0, is a Lipschitz-continuous function of x and t and the interface is a Lipschitz-continuous surface in RN+1; the solution u is Hölder continuous for all times t> 0.Both authors partially supported by CAICYT, Project 2805-83. The second author also supported by USA-Spain Joint Research Grant CCB-8402023. 相似文献
11.
12.
Norbert Kuhlmann 《manuscripta mathematica》1969,1(2):147-189
In this paper we study spaces of level sets of holomorphic mappings. We give an elementary (i.e. we are using elementary means) proof of a theorem a special case of which is the following statement: Let : XY be a holomorphic mapping of the irreducible normal complex space into the reduced complex space Y, which degenerates nowhere; the last condition means in the present case all -level sets having the same dimension; a -level set is a connected component of a fibre –1(Q), Q (X). Then the space Z of -level sets is a quasicomplex space and the natural mapping : XZ which maps each P X onto the -level set to which P belongs is open. If we substitute the assumption degenerating nowhere by the assumption having compact level sets, we get a space Z of level sets, which is a complex space. - The first part of this statement is a generalisation of a theorem of K. Stein, the second part is a special case of a theorem of H. Cartan and a well known theorem of H. Grauert on proper mappings. We will use our theorem in order to give a new proof of Grauert's theorem in a subsequent paper. 相似文献
13.
Norbert Polat 《Czechoslovak Mathematical Journal》2001,51(3):477-492
For an end and a tree T of a graph G we denote respectively by m() and m
T
() the maximum numbers of pairwise disjoint rays of G and T belonging to , and we define tm() := min{m
T(): T is a spanning tree of G}. In this paper we give partial answers — affirmative and negative ones — to the general problem of determining if, for a function f mapping every end of G to a cardinal f() such that tm() f() m(), there exists a spanning tree T of G such that m
T
() = f() for every end of G. 相似文献
14.
A. S. Zinov'ev 《Mathematical Notes》1972,12(5):743-746
We obtain sufficient conditions for the absolute convergence of Fourier series for functions of L
d
2
depending on the properties of the function being expanded and the rate of growth of the sums
of the system of functions {k(t)} orthonormalized in [a, b] with respect to d(t). We show that if at some point x [a, b] the function (t) has a discontinuity, at that point the Fourier series of any functionf(t) L
d
2
, converges absolutely.Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 511–516, November, 1972. 相似文献
15.
N. B. Lebedinskaya 《Journal of Mathematical Sciences》1985,29(6):1649-1659
The article is devoted to the problem of finding an optimal schedule for a class of functionals ƒ which allows for the existence of a structural set of activities. The functionalƒ(R), where, is defined in the following way: where {i(t)} is a structural set of functions, and the function F is defined on any finite set of arguments and satisfies the following conditions: 1)F(x)=(x); 2) F(x1,x2)=(x1,x2), F(x1,x2,...x3)= (x1, F(x2,...,xs)), S2; 3) and do not decrease in each of their arguments, and moreover, 3a) strictly increases with the increase of both arguments, 3b) if (x1,x2)>(x1, x2 (x2, x3)> (x2,x3), then F(x1,x2,x3)>F(x1,x2,x3).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 124, pp. 5–20, 1983. 相似文献
16.
Nikolaos S. Papageorgiou 《Analysis Mathematica》1991,17(2):141-152
17.
F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if ·
E(M,)
is not proportional to ·
L
2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council 相似文献
18.
Clasine van Winter 《Integral Equations and Operator Theory》1986,9(3):387-451
Let H(0) be a dilation-analytic three-particle Schrödinger operator with analytic continuation H() (>0). Let a be zero or the energy of a two-particle bound state. Let- (a) be the Laplace operator representing the kinetic energy of the relative motion of fragments scattered in channel a. By recent results, wave operators W (±, a, ) with conjugates W (±, a, ) exist such that W (±, a, ) W (±, a, ) is a projection P (a, ) commuting with H () while [H ()-a]W (±, a, ) equals-W(±, a, ) (a) e2i. This paper shows that the wave operators transform dilation-analytic functions of particle coordinates into dilation-analytic functions. Specifically, if the left shoulder of the spectrum of P (a,) H () does not sweep across eigenvalues of H() when , then W(-, a, ) and W (+, a, ) are dilation analytic in [, ]. If the right shoulder does not sweep across eigenvalues, W(+, a, ) and W(-, a, ) are dilation analytic in [,]. A semisimple eigenvalue of H () embedded in the spectrum of P (a, ) H () does not prevent the wave operators from being dilation analytic in an interval [, ] with as an interior point.This work was supported in part by the National Science Foundation under grant DMS-8301096. 相似文献
19.
V. A. Slousch 《Journal of Mathematical Sciences》2003,115(2):2272-2278
Let A be a self-adjoint elliptic second-order differential operator, let (, ) be an inner gap in the spectrum of A, and let B(t) = A + tW
*
W, where W is a differential operator of higher order. Conditions are obtained under which the spectrum of the operator B(t) in the gap (, ) is either discrete, or does not accumulate to the right-hand boundary of the spectral gap, or is finite. The quantity N(, A, W, ), (, ), > 0 (the number of eigenvalues of the operator B(t) passing the point (, ) as t increases from 0 to ) is considered. Estimates of N(, A, W, ) are obtained. For the perturbation W
*
W of a special form, the asymptotics of N(, A, W, ) as + is given. Bibliography: 5 titles. 相似文献
20.
Dr. Alexander Kovačec 《Monatshefte für Mathematik》1981,92(1):19-35
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional :
n
, such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map
n
n
, which is functional increasing (i.e. for each x
n
(which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)(
u))(
2(u))...
n
(u)). Under quite general conditions one finds that the sequence {
n
(u)}
n converges tov=v(u). As a consequence one obtains the inequality (u)(v). 相似文献