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1.
Let {V(k) :K1} be a sequence of independent, identically distributed random vectors in d with mean vector . The mappingg is a twice differentiable mapping from d to 1. Setr=g(). A bivariate central limit theorem is proved involving a point estimator forr and the asymptotic variance of this point estimate. This result can be applied immediately to the ratio estimation problem that arises in regenerative simulation. Numerical examples show that the variance of the regenerative variance estimator is not necessarily minimized by using the return state with the smallest expected cycle length.This research was supported by Army Research Office Contract DAAG29-84-K-0030. The first author was also supported by National Science Foundation Grant ECS-8404809 and the second author by National Science Foundation Grant MCS-8203483.  相似文献   

2.
Summary Fix a curve X of genus g and L Pic d (X). Let L(X) be the image of X through the complete linear system H0(X, L). Here we prove that a general projection of L(X) intoP N has maximal rank if either (a) N4, 0gN–1, dg+N, or (b) dd (g, N) for suitable d(g, N).  相似文献   

3.
Let (K(s,t), 0s1, t1) be a Kiefer process, i.e., a continuous two-parameter centered Gaussian process indexed by [0,1]×+ whose covariance function is given by (K(s1,t1) K(s2,t2))=(s1s2-s1s2)t1t2, 0s1, s21, t1, t2 0. For each t>0, the process K(·,t) is a Brownian bridge on the scale of . Let M 1 * (t) M 2 * (t) M j * (t) 0 be the ranked excursion heights of K(,t). In this paper, we study the path properties of the process tM j * (t). Two laws of the iterated logarithm are established to describe the asymptotic behaviors of M j * (t) as t goes to infinity.  相似文献   

4.
Let {n} be a sequence of identically distributed independent random variables,M1=<0,M 1 2 <;S 0=0,S n =1+2,+...+ n, n1;¯ S=sup {S n n=0.} The asymptotic behavior ofP(¯ St) as t is studied. If t P (1x dx=0((t)), thenP(¯ St)– 1/¦¦ t P (1x dx=0((t)) (t) is a positive function, having regular behavior at infinity.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 763–770, November, 1977.The author thanks B. A. Rogozin for the formulation of the problem and valuable remarks.  相似文献   

5.
Summary We say that a curve C in P 3 has maximal rank if for every integer k the restriction map rc(k):H 0(P 3, OP3(k)) H0 (C, OC(k))has maximal rank. Here we prove the following results. Theorem 1Fix integers g, d with 0g3,dg+3.Fix a curve X of genus g and L Picd (X).If g=3and X is hyperelliptic, assume d8. Let L(X)be the image of X by the complete linear system H 0(X, L). Then a general projection of L(X)into P 3 has maximal rank. Theorem 2For every integer g0,there exists an integer d(g, 3)such that for every dd(g, 3),for every smooth curve X of genus g and every LPicd (X) the general projection of L(X)into P 3 has maximal rank.  相似文献   

6.
Automorphisms of unitary linear groups u (n,,q) over the ring are found to be standard on an elementary unitary subgroup in the case when the hyperbolic rank of the form q is strictly greater than one and n5 (for a commutative ring, n4).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im V. A. Steklova AN SSSR, Vol. 132, pp. 97–109, 1983.  相似文献   

7.
Suppose an integral function (|A|)q1 defined on the subsets of edges of a hypergraph (X,u,) satisfies the following two conditions: 1) any set W u such that |A|(|A|) for any AW is matroidally independent; 2) if W is an independent set, then there exists a unique partitionW=T1+ T2+...+Tv such that |T i |=(|T i |),i1:v, and for any AW, |A|(|A|) there exists a Ti such that ATi. The form of such a function is found, in terms of parameters of generalized connected components, hypercycles, and hypertrees.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 196–204, 1982.  相似文献   

8.
The parametric linear complementarity problem is given by the conditions:q + p + Mz 0, 0,z 0,z T (q + p + Mz) = 0. Under the assumption thatM is a P-matrix, Cottle proved that the solution mapz() of the above problem is montonically nondecreasing in the parameter for every nonnegativeq and everyp if and only ifM is a Minkowski matrix. This paper examines whether a similar result holds in various other settings including a nonlinear case.  相似文献   

9.
Summary In this paper, the object of study is reflected Brownian motion in a cone ind-dimensions (d3) with nonconstant oblique reflection on each radial line emanating from the vertex of the cone. The basic question considered here is When is this process a semimartingale?. Conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter depending on the cone and the direction of reflection. It is shown that starting from any point of the cone, the process is a semimartingale if < 1, + 0 and not a semimartingale if < < 2.This research is supported by KOSEF grant 941-0100-011-1  相似文献   

10.
One investigates the asymptotic normality of integrals over unboundedly increasing sets of a random field, describing a shot noise in d ,d1. One shows how important here are roles played by the growth character of the considered sets and by the dimension d.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 28–36, 1989.  相似文献   

11.
One considers the total scattering cross section on the potential gV(x), xm, m3, for large values of the coupling constant g and of the wave number k. One assumes that V(x)(x/|1x|)|x|, 2>m+1, as ¦x¦. It is shown that for gk–1 , g3–ak2(a–2) the scattering cross section is equal asymptotically to a(gk–1), x=(m–1)(–1)–1. Here the coefficient a is determined only by the function and the number . Under the additional conditions >0, V>0, the indicated asymptotic behavior holds in the large domain gk–1 , gka–z c(gk–1), >0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 105–136, 1986.  相似文献   

12.
This work will be concerned with a Krasnosel'skii theorem for nonclosed bounded sets in Rd, and the following theorem will be obtained: For each d 2, define f(d) = d2 – 2d+3 if d 3 and f(d)=2d+1 if d = 3. Let S be a nonempty bounded set in Rd, d 2, and assume that cl S S is a finite union of convex components, each having closure a polytope. If every f(d) points of S see via S a common point, then there is a point p in cl S such that Bp s:s in S and (p,s] S is nowhere dense in S.  相似文献   

13.
We study the minimality of elementsx h,j,k of canonical systems of root vectors. These systems correspond to the characteristic numbers k of operator functionsL() analytic in an angle; we assume that operators act in a Hilbert space . In particular, we consider the case whereL()=I+T()c, >0,I is an identity operator,C is a completely continuous operator, (I- C)–1c for ¦arg¦, 0<<, the operator functionT() is analytic, and T()c for ¦arg¦<. It is proved that, in this case, there exists >0 such that the system of vectorsC v x h,j,k is minimal in for arbitrary positive <1+, provided that ¦k¦>.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 545–566, May, 1994.This research was partially supported by the Ukrainian State Committee of Science and Technology.  相似文献   

14.
We will establish the following improved Krasnosel'skii theorems for the dimension of the kernel of a starshaped set: For each k and d, 0 k d, define f(d,k) = d+1 if k = 0 and f(d,k) = max{d+1,2d–2k+2} if 1 k d.Theorem 1. Let S be a compact, connected, locally starshaped set in Rd, S not convex. Then for a k with 0 k d, dim ker S k if and only if every f(d, k) lnc points of S are clearly visible from a common k-dimensional subset of S.Theorem 2. Let S be a nonempty compact set in Rd. Then for a k with 0 k d, dim ker S k if and only if every f (d, k) boundary points of S are clearly visible from a common k-dimensional subset of S. In each case, the number f(d, k) is best possible for every d and k.  相似文献   

15.
Summary Let X=Cn / be a toroidal group of rank =n+m. If X is compact, then it is a complex torus. In the compact case, we have the theorem of Lefschetz which asserts that if L is a positive line bundle over a complex torus X, then gives an embedding of X for any integer l3. This theorem is generalized to noncompact toroidal groups in this paper. In fact, we prove the following: (I) In the case of rank =n+1, H0(X, (Ll)) gives an embedding of a toroidal group X for l3, if L is positive. (II) In the case of rank =n+m, 2m相似文献   

16.
Blocking sets in symmetric BIBD's with 2 are defined and bounds for their sizes are found. Thus, some results known in projective planes are generalized to symmetric BIBD's.  相似文献   

17.
If A and B are operators in the spaces X and Y, respectively, and if the operator B has many sets , , such that the manifolds p is a polynomial are dense in the space Y, then Here a=(the multiplicity of the spectrum of the operator A)=mindimL: span (AnL:n0)}=X. For example, if B=Tg is a Toeplitz operator in the space H2 with antianalytic symbol) and if g (the polynomial convex hull of the spectrum (A)) , then. Conversely, if and, then (under some assumptions on the regularity of the function f we have. One also gives examples of univalent and essentially univalent functions f (f H), for which Tf>1.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 150–158, 1983.  相似文献   

18.
A. V. Pazhitnov 《K-Theory》1996,10(4):323-412
Let M be a closed connected smooth manifold with dim M=n6, and : 1(M) Z be an epimorphism. Denote by the group ring of 1(M) and let be its Novikov completion. Let D * be a free-based finitely generated chain complex over . Assume that D ii=0 for i1 and in–1 and that D * has the same simple homotopy type as the Novikov-completed simplicial chain complex of the universal covering M. Let N be an integer. We prove that D * can be realized, up to the terms of of degree N as the Novikov complex of a Morse map : M S 1, belonging to . Applications to Arnold's conjectures and to the theory of fibering of M over S 1 are given.  相似文献   

19.
Let S be a semi-integral, symmetric, positive-definite m x m matrix; mn1. By the Siegel fundamental formula we mean the identity between the Siegel theta series of genus n, associated with the genus of the matrix S, and the correspond ing Eisenstein-Siegel series (C. L. Siegel, Lectures on the Analytical Theory of Quadratic Forms, 3rd rev. edition, Peppmüller, Göttingen, 1963). The validity of the mentioned formula for m/2n+1 is an open problem in the general case. In this paper we prove Siegel's formula for n=2, m=6.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 76, pp. 210–215, 1978.  相似文献   

20.
Summary Forf ( C n() and 0 t x letJ n (f, t, x) = (–1)n f(–x)f (n)(t) +f(x)f (n) (–t). We prove that the only real-analytic functions satisfyingJ n (f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ 0 (f, x, x) 0 and 0 x (x – t)n – 1Jn(f, t, x)dt 0 (n 1).  相似文献   

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