首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 643 毫秒
1.
In this paper, we explore the asymptotic distribution of the zeros of the partial sums of the family of entire functions of order 1 and type 1, defined by G(,,z)=0 1(t)t –1×(1–t)–1e zt dt, where Re,Re>0, is Riemann-integrable on [0,1], continuous at t=0, 1 and satisfies (0)(1)0.  相似文献   

2.
We prove a convergence theorem and obtain asymptotic (as 0) estimates for a solution of a parabolic initial boundary-value problem in a junction that consists of a domain 0 and a large number N 2 of -periodically located thin cylinders whose thickness is of order = O(N –1).  相似文献   

3.
Let t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M n , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d t and, for each x M, we define a smooth real function x (t) : (1 + i (t)), where the i(t) are the eigenvalues of AA T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t , restricted to v at the point x -t M n.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that x ' (t) 0 for all x M and real t; then, if x t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.  相似文献   

4.
LetS be a finite union of boxes inR d . Forx inS, defineA x ={yx is clearly visible fromy via staircase paths inS}, and let KerS denote the staircase kernel ofS. Then KerS={A x x is a point of local nonconvexity ofS}. A similar result holds with clearly visible replaced by visible and points of local nonconvexity ofS replaced by boundary points ofS.Supported in part by NSF grant DMS-9207019.  相似文献   

5.
, . . Q k [0,2],k=1,2, — . F(x, y)L(T), T=[0, 2]2, G(x, y)L(T) , G(x,y)=F(x,y) Q=Q 1 ×Q 2 - .  相似文献   

6.
A closed subset E of the unit circumference T is said to be a peak set for the analytic Hölder class A, 0 < < 1 there exists a functionf,fA such that f¦E1 and ¦f(z)¦<1 for. It is shown that the set E is a peak set of the algebra A if and only if there exists a nonnegative Borel measure on T such that the function coincides almost everywhere with a function of the Hölder class , equal to zero on E. A sufficient condition in order that a closed set E should belong to the family of peak sets is obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 129–136, 1987.  相似文献   

7.
Consider the stochastic partial differential equationdu (t,x) = (t)u (t, x)dt + dW Q(t,x), 0 t T where = 2/x 2, and is a class of positive valued functions. We obtain an estimator for the linear multiplier (t) and establish the consistency, rate of convergence and asymptotic normality of this estimator as 0.  相似文献   

8.
Let A be a self-adjoint operator, let (, ) be an inner gap in the spectrum of the operator A, and let B(t) = A + tW * W, where the operator W(AiI)-1 is not necessarily bounded. Conditions are obtained under which the spectrum of B(t) in (, ) is discrete. Let N(, A, W, ), (, ), > 0, be the number of eigenvalues of the operator B(t) passing the point (, ) as t increases from 0 to . The asymptotics of N(, A, W, ) as + is obtained in terms of the spectral asymptotics of a certain self-adjoint compact operator. Bibliography: 5 titles.  相似文献   

9.
Let n be n-dimensional Euclidean space, and let : [0, L] n and : [0, L] n be closed rectifiable arcs in n of the same total length L which are parametrized via their arc length. is said to be a chord-stretched version of if for each 0s tL, |(t)–(s)| |(t)–(s)|. is said to be convex if is simple and if ([0, L]) is the frontier of some plane convex set. Individual work by Professors G. Choquet and G. T. Sallee demonstrated that if were simple then there existed a convex chord-stretched version of . This result led Professor Yang Lu to conjecture that if were convex and were a chord-stretched version of then and would be congruent, i.e. any chord-stretching map of a convex arc is an isometry. Professor Yang Lu has proved this conjecture in the case where and are C 2 curves. In this paper we prove the conjecture in general.  相似文献   

10.
Jongen  H. Th.  Jonker  P.  Twilt  F. 《Mathematical Programming》1986,34(3):333-353
We deal with one-parameter families of optimization problems in finite dimensions. The constraints are both of equality and inequality type. The concept of a generalized critical point (g.c. point) is introduced. In particular, every local minimum, Kuhn-Tucker point, and point of Fritz John type is a g.c. point. Under fairly weak (even generic) conditions we study the set consisting of all g.c. points. Due to the parameter, the set is pieced together from one-dimensional manifolds. The points of can be divided into five (characteristic) types. The subset of nondegenerate critical points (first type) is open and dense in (nondegenerate means: strict complementarity, nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints). A nondegenerate critical point is completely characterized by means of four indices. The change of these indices along is presented. Finally, the Kuhn-Tucker subset of is studied in more detail, in particular in connection with the (failure of the) Mangasarian-Fromowitz constraint qualification.  相似文献   

11.
Summary We examine the problem:u+a(x)ub(x)u=f(x) for 0<x<1,a(x)>0,b(x)>, 2 = 4>0,a, b andf inC 2 [0, 1], in (0, 1],u(0) andu(1) given. Using finite elements and a discretized Green's function, we show that the El-Mistikawy and Werle difference scheme on an equidistant mesh of widthh is uniformly second order accurate for this problem (i.e., the nodal errors are bounded byCh 2, whereC is independent ofh and ). With a natural choice of trial functions, uniform first order accuracy is obtained in theL (0, 1) norm. On choosing piecewise linear trial functions (hat functions), uniform first order accuracy is obtained in theL 1 (0, 1) norm.  相似文献   

12.
13.
We prove the existence of continuously differentiable solutions with required asymptotic properties as t +0 and determine the number of solutions of the following Cauchy problem for a functional differential equation:
where : (0, ) (0, +), g: (0, ) (0, +), and h: (0, ) (0, +) are continuous functions, 0 < g(t) t, 0 < h(t) t, t (0, ), , and the function is continuous in a certain domain.  相似文献   

14.
In this paper we study particular sets of a Steiner systemS. More precisely, we study the setsA such that ¦A ¦ d modh for all lines ofS, withd andh integers satisfyingd 0,h 2.Dedicated to Professor M. Scafati Tallini on the occasion of her sixtyfifth birthday  相似文献   

15.
We consider the method for constrained convex optimization in a Hilbert space, consisting of a step in the direction opposite to an k -subgradient of the objective at a current iterate, followed by an orthogonal projection onto the feasible set. The normalized stepsizes k are exogenously given, satisfying k=0 k = , k=0 k 2 < , and k is chosen so that k k for some > 0. We prove that the sequence generated in this way is weakly convergent to a minimizer if the problem has solutions, and is unbounded otherwise. Among the features of our convergence analysis, we mention that it covers the nonsmooth case, in the sense that we make no assumption of differentiability off, and much less of Lipschitz continuity of its gradient. Also, we prove weak convergence of the whole sequence, rather than just boundedness of the sequence and optimality of its weak accumulation points, thus improving over all previously known convergence results. We present also convergence rate results. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Research of this author was partially supported by CNPq grant nos. 301280/86 and 300734/95-6.  相似文献   

16.
We prove a local limit theorem (LLT) on Cramer-type large deviations for sums S V = t V ( t ), where t , t Z , 1, is a Markov Gaussian random field, V Z , and is a bounded Borel function. We get an estimate from below for the variance of S V and construct two classes of functions , for which the LLT of large deviations holds.  相似文献   

17.
Weighted Composition Operators on Bergman and Dirichlet Spaces   总被引:3,自引:0,他引:3  
Let H() denote a functional Hilbert space of analytic functions on a domain . Let w : C and : be such that w f is in H() for every f in H(). The operator wC given by f w f is called a weighted composition operator on H(). In this paper we characterize such operators and those for which (wC )* is a composition operator. Compact weighted composition operators on some functional Hilbert spaces are also characterized. We give sufficient conditions for the compactness of such operators on weighted Dirichlet spaces.  相似文献   

18.
Summary Considerf+ ff+ (1–f2)+ f=0 together with the boundary conditionsf(0)=f(0)=0,f ()=1. If=–1,>0, arbitrary there is at least one solution which satisfies 0<f<1 on (0, ). By the additional conditionf>0 on (0, ) or, alternately 0<1, the uniqueness of the solution is demonstrated.If=1,<0, arbitrary the existence of solutions for which –1<f<0 in some initial interval (0,t) and satisfying generallyf>1 is established. In both problems, bounds forf (0) and qualitative behavior of the solutions are shown.
Sommario Si consideri il problema definito dall'equazionef+ f f+ (1–f2)+ f=0 e dalle condizioni al contornof(0)=f (0)=0,f()=1. Assumendo=–1,>0, arbitrario si dimostra che esiste almeno una soluzione che soddisfa 0<f<1 nell'intervallo (0, ). Se in aggiunta si ipotizzaf>0 in (0, ), oppure 0<=1, l'unicità délia soluzione è assicurata.Successivamente si considéra il problema di valori al contorno con=1,<0, arbitrario. In questo caso esiste un'intera classe di soluzioni che soddisfano –1<f<0 in un intorno dell'origine e tali chef>1, in generale.Di detti problemi viene studiato il comportamento délle soluzioni e vengono determinate dalle maggiorazioni e minorazioni del valoref(0).
  相似文献   

19.
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   

20.
We study the rate of convergence of the process(tT)/T to the processw(t)/ asT , where(t) is a solution of the stochastic differential equationd(t)=a((t))dt+((t))dw(t) Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1424–1427, October, 1994.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号