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 836 毫秒
1.
Let Mn denote an n-dimensional Riemannian manifold. Its metric is called -strongly spherical if at every point Q Mn there exists a -dimensional subspace Q TQMn such that the curvature operator of the metric of Mn satisfies R(X, Y) Z = k(< Y, Z > X < X, Z > Y), where k = const > 0, Y Q , X, Z #x2208; TQMn. The number is called the index of sphericity and k the exponent of sphericity. The following theorems are proved in the paper.THEOREM 1. Let the Sasakian metric of T1Mn be -strongly spherical with exponent of sphericity k. The following assertions hold: a) = 1 if and only if M2 has constant Gaussian curvature K 1 and k = K2/4; b) = 3 if and only if M2 has constant curvature K = 1 and k = 1/4; c) = 0, otherwise.THEOREM 2. Let the Sasakian metric of T1Mn (n Mn) be -strongly spherical with exponent of sphericity k. If k > 1/3 and k 1, then = 0. Let us denote by (Mn, K) a space of constant curvatureK. THEOREM 3. Let the Sasakian metric of T1(Mn, K) (n 3) be -strongly spherical with exponent of sphericity k. The following assertions hold: a) = 1 if and only if K = 1/4; b) = 0, otherwise. In dimension n = 3 Theorem 2 is true for k {1/4, 1}.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 150–159, 1992.  相似文献   

2.
LetA be a subset of a balayage space (X,W) and a measure onX. It is shown that for every sequence n of measures such that limnn and limn n A = the limit measure is of the formf+[(1-f)]A for some (unique) Borel function 0f1Cb(A). Furthermore, conditions are given such that any such functionf occurs.  相似文献   

3.
Yarotskii  D. A. 《Mathematical Notes》2001,69(5-6):690-695
A spatially nonhomogeneous random walk t on the grid =m X n is considered. Let t 0 be a random walk homogeneous in time and space, and let t be obtained from it by changing transition probabilities on the set A= X n, || < , so that the walk remains homogeneous only with respect to the subgroup n of the group . It is shown that if >m 2 or the drift is distinct from zero, then the central limit theorem holds for t.  相似文献   

4.
The number of subgroups of type and cotype in a finite abelian p-group of type is a polynomialg with integral coefficients. We prove g has nonnegative coefficients for all partitions and if and only if no two parts of differ by more than one. Necessity follows from a few simple facts about Hall-Littlewood symmetric functions; sufficiency relies on properties of certain order-preserving surjections that associate to each subgroup a vector dominated componentwise by . The nonzero components of (H) are the parts of , the type of H; if no two parts of differ by more than one, the nonzero components of – (H) are the parts of , the cotype of H. In fact, we provide an order-theoretic characterization of those isomorphism types of finite abelian p-groups all of whose Hall polynomials have nonnegative coefficients.  相似文献   

5.
For a Cr,-immersion z:X E, r 2, 0 < < 1, of an n-dimensional (n 1) simply-connected Cr+2,-manifold X into Euclidean space E, the metric I(z) induced by z has a neighborhood in Cr,-topology in which every metric from a given subbundle of metrics is Cr,-immersible into E. In particular, it is proved that metric ds 0 2 of the Riemannian product of p spheres of dimensions 1, , p 2 has a neighborhood in C2,-topology from which any conformally equivalent metric to ds 0 2 , is immersible into E with dimE = 1 + + p + p. The proofs are based on the investigation of a varied system of Gauss—Codazzi—Ricci equations for an infinitely small deformation of surface z(X) in E with a prescribed variation of the metric.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 49–67, 1992.  相似文献   

6.
Dupoiron  K.  Mathieu  P.  San Martin  J. 《Potential Analysis》2004,21(1):7-33
Soit X une diffusion uniformément elliptique sur R d ,F une fonction dans H loc 1(R d ) et la loi initiale de la diffusion. On montre que si l'intégrale |F|2(x)U(x)dx est finie, oùU désigne le potentiel de la mesure , alors F(X) est un processus de Dirichlet. Si de plus, F appartient àH 2 loc(R d ) et si les intégrales |F|2(x)U(x)dx et |f k |2(x)U(x)dx sont finies, pour les dérivées faibles f k de F, alors on peut écrire une formule d'Itô. En particulier, on définit l'intégrale progressive F(X)dX et on prouve l'existence des covariations quadratiques [f k (X),X k ].  相似文献   

7.
Let the real functionsK(x) andL(x) be such thatM(x)=K(x)+iL(x)=eix g(x), whereg(x) is infinitely differentiable for all largex and is non-oscillatory at infinity. We develop an efficient automatic quadrature procedure for numerically computing the integrals a K(t)f(t) and a L(t)f(t)dt, where the functionf(t) is smooth and nonoscillatory at infinity. One such example for which we also provide numerical results is that for whichK(x)=J (x) andL(x)=Y (x), whereJ (x) andY (x) are the Bessel functions of order . The procedure involves the use of an automatic scheme for Fourier integrals and the modified W-transformation which is used for computing oscillatory infinite integrals.  相似文献   

8.
For every transnormal m-manifold V (see [3] or [7]) in n :VW, mapping pV into its normal plane (p) is a covering map onto a submanifold W of the open Grassmannian Hn,n–m of all (n–m)-dimensional planes in n. The transnormal frame T:=–1((p)) admits a transitive operation by a group J of isometries. The group action of the covering transformations of (V,,W) on T commutes with the action of J. The elements of J, which are restrictions of covering transformations to T, are exactly the elements of the centre of J. This property is applied to show the existence of nontrivial covering transformations of (V,,W) for n–m3.

Diese Arbeit faßt die Kapitel 5, 6 und 7 der von der Fakultät für Allgemeine Ingenieurwissenschaften der TU Berlin genehmigten Dissertation [6] zusammen.  相似文献   

9.
In this paper we consider the problem of determining and constructing E- and MV-optimal block designs to use in experimental settings where treatments are applied to experimental units occurring in b blocks of size k, k. It is shown that some of the well-known methods for constructing E- and MV-optimal unequally replicated designs having k fail to yield optimal designs in the case where . Some sufficient conditions are derived for the E- and MV-optimality of block designs having and methods for constructing designs satisfying these sufficient conditions are given.  相似文献   

10.
Conditions are found which must be imposed on a function g(x) in order that M g(1+2+ + v < if M g(i) < and M g(v) < ,, 1, 2, , n, ... being non-negative and independent, being integral, and {i} being identically distributed. The result is applied to the theory of branching processes.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 387–394, April, 1968.  相似文献   

11.
Let {Xi} be a sequence of random variables, E(Xi) 0. If 1, estimates for the -th moments can be derived from known estimates of the -th moment. Here we generalized the Men'shov-Rademacher inequality for =2 for orthonormal Xi, to the case 1 and dependent random variables. The Men'shov-Payley inequality >2 for orthonormal Xi) is generalized for >2 to general random variables. A theorem is also proved that contains both the Erdös -Stechkin theorem and Serfling's theorem withv > 2 for dependent random variables.Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 219–230, February, 1975.This article was written while the author was working in the V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR.  相似文献   

12.
An integral domain R provided with a non-archimedean valuation | | is called bald (kahl), if there exists a real number , 0<<1, such that the value set |R| does not meet the open interval (, 1). Bald rings are important in non-archimedean analysis because the method of iteration (classical and well known for fields with discrete valuation) is convergent in these rings. In this note it is shown that each valuated field contains big bald subrings, more precisely:Let K be a completely valuated field and let denote the valuation ring. Let {a}1 be a sequence in converging to zero. Then the smallest complete local subring of containing all a is bald.

Herrn Karl Stein zum 60. Geburtstag gewidmet  相似文献   

13.
In this paper we prove the existence and uniqueness of a solution u satisfying the equation- u – k2 y = f (k , k 0), homogeneous Dirichlet data on the boundary and a radiation condition at infinity. We consider this problem in some unbounded region with an infinite boundary for which the assumption (x) · (x) 0 holds; here denotes the exterior normal and a given field.  相似文献   

14.
A negative answer is given to Swinnerton-Dyer's question: Is it true that for any > 0 there exists a positive integer n such that for any planar closed strictly convex n-times differentiable curve , when it is blown up a sufficiently large number of times, the number of integral points on the resultant curve will be less than . An example has been constructed when this number for an infinite number is not less than 1/2, while is infinitely differentiable.Translated from Matematicheskie Zametki, Vol. 21, No. 6, pp. 799–805, June, 1977.The author thanks S. B. Stechkin for attention to the work.  相似文献   

15.
In the present work, necessary and sufficient conditions are given in terms of a nonnegative Borel measure which ensure the boundedness and compactness of operators with power-logarithmic kernels from L p (0, a) to L p (0, a) (or to L q (0, a)), where 0 < a < , 1 < p, q < , > 1/p and 0.  相似文献   

16.
p- . E R n -, f () p(R n)., ER n 2nq 0, E— - q 0(q 0-1). : q0>2 n1 E R n 2nq 0, p- p<0. , f-[-, ]n, f A p(R n) , p([-, ]n) (1 << ).  相似文献   

17.
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   

18.
The influence of natural six-month aging at 293 K of two kinds of epoxy resins with different network density on their dynamical properties was studied. All the samples were examined by forced resonance oscillations at a frequency of 200 Hz in the range of 120–520 K. The components of the complex Young's modulus E, E, tan , and low-frequency velocity of sound were measured. The basic temperature transitions including Tg and the network density were determined from the experimental data. It was established that after aging of epoxy resins cured by the cross-linking agent meta-phenylenediamine their network density decreased (cold degradation). By using the cross-linking agent 2,6-diaminopyridine, and Tg increased. An attempt is made to explain the nature of this phenomenon.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Moscow State Technical University, Russia. Translated from Mechanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 407–412, May–June, 1998.  相似文献   

19.
Let be a variety of groups defined by the set of laws V. In this paper we study the concept of -isologism of groups in terms of -extensions and their connections with the Baer-invariant of groups are also discussed.AMS Subject Classification (2000): primary 20F14, 20F19, secondary 20E10  相似文献   

20.
In this paper we study the eigenvalues of the Laplace operator u on some classes of unbounded regions G. The starting-point of our study is the paper [5] of Vogelsang. Among other things he has proved that the Laplace operator with zero boundary condition has no negative eigenvalues in unbounded regions the boundary of which satisfies (x) · x 0, where (x) is the exterior normal. We prove in this paper similar results of the spectrum, when the condition above is suitably disturbed. Because our main interest lies in replacing the geometric condition (x) · x 0 with another condition, we have studied neither equations with higher orders nor equations with variable coefficients.  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