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1.
Summary The following Artin type characterization of : + + is proved: Assume thatf: + + satisfies the Gauss multiplication formula for some fixedp 2,f is absolutely continuous on [l/p, 1 + ] for some > 0 and lim x 0 xf(x) = 1. Thenf(x) = (x) forx > 0.The optimality of this result is checked by means of counterexamples. For instance, it is shown that the result is no longer true, if f is absolutely continuous is replaced by f is continuous and of finite variation.  相似文献   

2.
Summary Let X={X(t), t N} be a centred Gaussian random field with covariance X(t)X(s)=r(t–s) continuous on N×N and r(0)=1. Let (t,s)=((X(t)–X(s)) 2)1/2; (t,s) is a pseudometric on N. Assume X is -separable. Let D 1 be the unit cube in N and for 0<k, D k= {xN: k –1 xD1}, Z(k)=sup{X(t),tD k}. If X is sample continuous and ¦r(t)¦ =o(1/log¦t¦) as ¦t¦8 then Z(k)-(2Nlogk) 1/20 as k a.s.  相似文献   

3.
A class of nonseparable dynamic programming problems   总被引:3,自引:0,他引:3  
A solution procedure is proposed for a class of deterministic sequential decision problems whose objective functions are of the form f n(x n)+(g n(x n)) where is differentiable and either concave or convex. The procedure calls for the collaboration between dynamic programming and c-programming, and is demonstrated in our treatment of a minimum variance type problem.  相似文献   

4.
The following result is proved: Let D be a quasi-symmetric 3-design with intersection numbers x, y(0x<y<k). D has no three distinct blocks such that any two of them intersect in x points if and only if D is a Hadamard 3-design, or D has a parameter set (v, k, ) where v=(+2)(2+4+2)+1, k=2+3+2 and =1,2,..., or D is a complement of one of these designs.  相似文献   

5.
We study the limiting behavior of the weighted central paths{(x(), s())} > 0 in linear programming at both = 0 and = . We establish the existence of a partition (B ,N ) of the index set { 1, ,n } such thatx i() ands j () as fori B , andj N , andx N (),s B () converge to weighted analytic centers of certain polytopes. For allk 1, we show that thekth order derivativesx (k) () ands (k) () converge when 0 and . Consequently, the derivatives of each order are bounded in the interval (0, ). We calculate the limiting derivatives explicitly, and establish the surprising result that all higher order derivatives (k 2) converge to zero when .  相似文献   

6.
The following statement is proved. Letu be a subharmonic function in the region and u the associated measure. Then there exists a functionf holomorphic in and such that if f is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for= u and for= f . In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.

. . .  相似文献   

7.
Given a bounded linear operatorA in an infinite dimensional Banach space and a compact subset of a connected component of its semi-Fredholm domain, we construct a finite rank operatorF such that –A+F is bounded below (or surjective) for each ,F 2=0 and rankF=max min{dimN(–A), codimR(–A)}, if ind(–A)0 (or ind(–A)0, respectively) for each .  相似文献   

8.
LetB,B be bases of a matroid, withX B, X B. SetsX,X are asymmetric exchange if(B – X) X and(B – X) X are bases. SetsX,X are astrong serial B-exchange if there is a bijectionf: X X, where for any ordering of the elements ofX, sayx i ,i = 1, , m, bases are formed by the sets B0 = B, Bi = (Bi–1 – xi) f(x i), fori = 1, , m. Any symmetric exchangeX,X can be decomposed by partitioning X = i=1 m Yi, X = i=1 m Yi, X, where (1) bases are formed by the setsB 0 =B, B i = (B i–1 Y i ) Y i ; (2) setsY i ,Y i are a strong serialB i–1 -exchange; (3) properties analogous to (1) and (2) hold for baseB and setsY i ,Y i .  相似文献   

9.
We investigate the multidimensional equations j=1 q Aj(x)y(x+e j )=f(x),e j n wherex n andA j : n Hom( p , m ),f : n m are given maps. Sufficient conditions for smooth and analytic solvability for anyf C k ,k are found.Research partially supported by the Israel Ministry of ScienceAMS classification 39B Functional equations  相似文献   

10.
Over the past several decades, the optimization over the efficient set has seen a substantial development. The aim of this paper is to provide a state-of-the-art survey of the development. Given p linear criteria c 1x,,cp x and a feasible region X of R n, the linear multicriteria problem is to find a point x of X such that no point x' of X satisfies (c1 x',,cp x')(c1 x,,cp x) and (c1x',,cp x')q (c1 x ,,cp x). Such a point is called an efficient point. The optimization over the efficient set is the maximization of a given function over the set of efficient points. The difficulty of this problem is mainly due to the nonconvexity of this set. The existing algorithms for solving this problem could be classified into several groups such as adjacent vertex search algorithm, nonadjacent vertex search algorithm, branch-and-bound based algorithm, Lagrangian relaxation based algorithm, dual approach and bisection algorithm. In this paper we review a typical algorithm from each group and compare them from the computational point of view.  相似文献   

11.
Let E be a linear space, let K E and f:K . We formulate in terms of the lower Dini directional derivative problem GMVI (f ,K ), which can be considered as a generalization of MVI (f ,K ), the Minty variational inequality of differential type. We investigate, in the case of K star-shaped (SS), the existence of a solution x * of GMVI (f K ) and the property of f to increase-along-rays starting at x *, fIAR (K,x *). We prove that the GMVI (f ,K ) with radially l.s.c. function f has a solution x * ker K if and only if fIAR (K,x *). Further, we prove that the solution set of the GMVI (f ,K ) is a convex and radially closed subset of ker K. We show also that, if the GMVI (f ,K ) has a solution x *K, then x * is a global minimizer of the problem min f(x), xK. Moreover, we observe that the set of the global minimizers of the related optimization problem, its kernel, and the solution set of the variational inequality can be different. Finally, we prove that, in the case of a quasiconvex function f, these sets coincide.  相似文献   

12.
It is proved that for every sequence of points n from the unit circle, n1, and for an arbitrary sequence of positive numbers An, An, there exists a continuous real function u, such that for the Toeplitz operator T (acting in the Hardy space H2) with the symbol =e iu we have the estimates (T–nI)–1>An, n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 157, pp. 175–177, 1987.  相似文献   

13.
In this paper we study the question of uniqueness for an inverse problem, arising in the (thermal) linear and/or non-linear potential theory. The overdetermined problem we shall study is represented by(div(|u| p–2u)–D t u+)u=0where supp()R n ×(0,), 1<p<, L and {t=} is bounded for >0.The problem has applications in shape-recognition in underground water/oil recovery, subject to shape-change during time intervals. The particular case u0, D t u0, and p=2, is an example of the well-known Stefan.  相似文献   

14.
A distribution is said to have regularly varying tail with index – (0) if lim x(kx,)/(x,)=k for each k>0. Let X and Y be independent positive random variables with distributions and , respecitvely. The distribution of product XY is called Mellin–Stieltjes convolution (MS convolution) of and . It is known that D() (the class of distributions on (0,) that have regularly varying tails with index –) is closed under MS convolution. This paper deals with decomposition problem of distributions in D() related to MS convolution. A representation of a regularly varying function F of the following form is investigated: F(x)= k=0 n–1 b k f(a k x), where f is a measurable function and a and b k (k=1,...,n–1) are real constants. A criterion is given for these constants in order that f be regularly varying. This criterion is applicable to show that there exist two distributions and such that neither nor belongs to D() (>0) and their MS convolution belongs to D().  相似文献   

15.
Summary Given a Brownian motionB, we consider the filtration ( x xR ), where x is defined as the -field generated by the excursions ofB belowx. In this paper we prove a conjecture of Walsh which says that all -martingales are continuous.  相似文献   

16.
New oscillation criteria are given for the second order sublinear differential equation
where a C 1 ([t 0, )) is a nonnegative function, , f C() with (x) 0, xf(x) / (x) > 0 for x 0, , f have continuous derivative on \ {0} with [f(x) / #x03C8;(x)] 0 for x 0 and q C([t 0, )) has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients q and a and extend known oscillation criteria for the equation x (t) + q(t)x(t) = 0.  相似文献   

17.
Let 1, 2, ... be a sequence of independent identically distributed random variables with zero means. We consider the functional n = k=o n (S k ) where S1=0, Sk= i=1 k i (k1) and(x)=1 for x0,(x) = 0 for x<0. It is readily seen that n is the time spent by the random walk Sn, n0, on the positive semi-axis after n steps. For the simplest walk the asymptotics of the distribution P (n = k) for n and k, as well as for k = O(n) and k/n<1, was studied in [1]. In this paper we obtain the asymptotic expansions in powers of n–1 of the probabilities P(hn = nx) and P(nx1 n nx2) for 0<1, x = k/n 2<1, 0<1x122<1.Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 613–620, April, 1974.The author wishes to thank B. A. Rogozin for valuable discussions in the course of his work.  相似文献   

18.
Summary Let {X t } be a 1 process with stationary independent increments and its Lévy measurev be given byv{yy>x}=x –L 1 (x), v{yy<–x}=x –L 2 (x) whereL 1,L 2 are slowly varying at 0 and and 0<1. We construct two types of a nondecreasing functionh(t) depending on 0<<1 or =1 such that lim inf a.s. ast 0 andt for some positive finite constantC.This research is partialy supported by a grant from Korea University  相似文献   

19.
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   

20.
In this note we shall prove that there exist infinitely many cyclic biquadratic fieldsK whose integral bases are neither {1, , 2, } nor {1, , , 3) for any numbers , inK. Next, we shall construct infinitely many cyclic biquadratic fieldsK which have the index 1, but still have not the integral basis {1, , 2, 3) for every inK. Finally we shall give a class of biquadratic fields for a problem of Hasse concerning an integral basis.  相似文献   

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