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1.
In a semiabelian category, a strictly exact sequence 0ABC0 of cochain complexes gives rise to the cohomology sequence ...H n(A) H n(B) H n(C) H n+1 (A) .... We study conditions for exactness of the homology sequence at a given term.  相似文献   

2.
Summary A priori truncation error bounds are obtained for continued fractions of the formK(1/b n),b n complex. The error bounds are easily applied to the case whenb n0 asn. A numerical example involving the complex error function is given.  相似文献   

3.
It is proved that if the increasing sequence (np) of natural numbers satisfies the condition np+1/np 1 (p ) and all derivatives f(np) of the analytic function f in D=¦¦< 1 are univalent in D, then f is an entire function. At the same time, for each increasing sequence (np) natural numbers such that np+1/np (p ) there exists an analytic function f in D all of whose derivatives f(np) are univalent in D and D is the boundary for f. The growth of entire functions with derivatives univalent in the disc D is also studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 400–406, March, 1991.  相似文献   

4.
We describe all isometric immersionsf:S p n S p +1/n+m ,np 2m, whose first normal space is -parallel in the complement of totally geodesic points while the set of totally geodesic points does not disconnectS p n .  相似文献   

5.
LetK n n be a triangulatedn-ball. Examples are given to show that unlike in the two-dimensional case, the following hold for alln3: (1) there are nonconvexK n with no convex simplexwise linear embeddingsK n n , even though there are strictly convex simplexwise linear embeddings K n n ; (2) there are convexK n , with no spanning simplices, such that not every simplexwise linear embeddingf: K n n with convex image can be extended to a simplexwise linear embedding ofK n ; (3) there are convexK n such that the space of simplexwise linear homeomorphisms ofK n , fixed on K n , is not path connected.Partially supported by NSF Contract DMS-8503388.  相似文献   

6.
I. Moerdijk 《K-Theory》2003,28(3):207-258
We observe that any regular Lie groupoid G over a manifold M fits into an extension K G E of a foliation groupoid E by a bundle of connected Lie groups K. If F is the foliation on M given by the orbits of E and T is a complete transversal to F , this extension restricts to T, as an extension K T G T E T of an étale groupoid E T by a bundle of connected groups K T . We break up the classification problem for regular Lie groupoids into two parts. On the one hand, we classify the latter extensions of étale groupoids by (non-Abelian) cohomology classes in a new ech cohomology of étale groupoids. On the other hand, given K and E and an extension K T G T E T over T, we present a cohomological obstruction to the problem of whether this is the restriction of an extension K G E over M; if this obstruction vanishes, all extensions K G E over M which restrict to a given extension over the transversal together form a principal bundle over a group of bitorsors under K.  相似文献   

7.
We give a generalization of results obtained in [15]. LetK n denote the set of embedded hypersurfaces in n+1; for all xSn and MK n we denote by C x M the apparent contour ofM in the directionx. Then we give a sufficient condition on WSn such that the map W K n:K n P(T Sn) , defined by W K n (M)={C w M ¦ wW}, is injective.  相似文献   

8.
We construct an example of a finitely generated group G such that rank((G )n)=2 for all n1. For each n, we construct a finitely presented group G n such that rank((G n )n)=2. We conjecture that if G is a word-hyperbolic group then rank(G n ) as $ n. For each m we give an example of a residually finite group K m such that K m has exactly two relators, but K m has no proper subgroups of index $ m. We construct a finitely generated group D such that there is an epimorphism DD×D.  相似文献   

9.
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   

10.
S. A. Mitchell 《K-Theory》1990,3(6):607-626
Ifn2 the MoravaK-theoryK(n) * of an algebraicK-theory spectrumKX vanishes for any ring or schemeX. This is proved using thev n -complexes of Hopkins and Smith, together with the following theorem. The natural mapf:Q 0S0BGL+ factors through the space ImJ. In particularf *: * s K * annihilates CokerJ. These results are closely related to the Lichtenbaum-Quillen conjectures.Partially supported by an NSF grant.  相似文献   

11.
LetfL p( n ),n2, be a radial function and letS Rf be the spherical partial sums operator. We prove that if thenS Rf(x)f(x) a.e. asR. The result is false for and \frac{{2n}}{{n + 1}}$$ " align="middle" border="0"> .Partially supported by M.P.I.  相似文献   

12.
We consider a case in which n particles are distributed independently of one another in N cells. We examine the behavior of the number of empty cells, 0 (n), as a random function of the parameter n when n, N. We prove that for suitable variation of the time parameter, 0 (n) will converge to a Gaussian process in the following cases: a) n/N, n/N l nN; b) n/N0, n2/N.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp, 97–104, July, 1968.  相似文献   

13.
Summary Denote by E n the convex hull of n points chosen uniformly and independently from the d-dimensional ball. Let Prob(d, n) denote the probability that E n has exactly n vertices. It is proved here that Prob(d, 2 d/2 d -)1 and Prob(d, 2 d/2 d (3/4)+)0 for every fixed >0 when d. The question whether E n is a k-neighbourly polytope is also investigated.  相似文献   

14.
We extend and strengthen the result that, in the complete graphK n with independent random edge-lengths uniformly distributed on [0, 1], the expected length of the minimum spanning tree tends to(3) asn. In particular, ifK n is replaced by the complete bipartite graphK n, n then there is a corresponding limit of 2 (3).  相似文献   

15.
Givenf: R n R n* with some conditions, our aim is to compute a fixed pointx f(x) off; hereR n isn-dimensional Euclidean space andR n* is the collection of nonempty subsets ofR n . A typical application of the algorithm can be motivated as follows: Beginning with the constant mapf 0:R n {0} R n and its fixed pointx 0 = 0, we deformf t ast tof f and follow the pathx t of fixed points off t . Cluster points of thex t 's ast are fixed points off. This research was supported in part by Army Research Office-Durham Contract DAHC-04-71-C-0041 and by National Science Foundation Grant GK-5695.  相似文献   

16.
In 1992, Móricz, Schipp and Wade [MSW] proved for functions in L log+ L(I 2) (I 2 is the unit square) the a.e. convergence of the double (C, 1) means of the Walsh-Fourier series n f f as min(n 1, n 2) , n = (n 1, n 2 N 2). In the same paper, they also proved the restricted convergence of the (C, 1) means of functions in L(I 2): (2 n 1,2 n 2)f f a.e. as min (n 1, n 2) provided |n 1n 2| < C. The aim of this paper is to demonstrate the sharpness of these results of Móricz, Schipp and Wade with respect to both the space L log+ L(I 2) and the restrictedness |n 1n 2| < C.  相似文献   

17.
Let {S n} be a random walk, generated by i.i.d. increments X i which drifts weakly to in the sense that as n . Suppose k0, k1, and E|X 1|1\k = if k>1. Then we show that the probability that S. crosses the curve nan K before it crosses the curve nan k tends to 1 as a . This intuitively plausible result is not true for k = 1, however, and for 1/2 <k<1, the converse results are not true in general, either. More general boundaries g(n) than g(n) = n k are also considered, and we also prove similar results for first passages out of regions like { (n, y): n1, |y| (a + n) k } as a .  相似文献   

18.
This paper considers lazy random walks supported on a random subset of k elements of a finite group G with order n. If k=a log2 n where a>1 is constant, then most such walks take no more than a multiple of log2 n steps to get close to uniformly distributed on G. If k=log2 n+f(n) where f(n) and f(n)/log2 n0 as n, then most such walks take no more than a multiple of (log2 n) ln(log2 n) steps to get close to uniformly distributed. To get these results, this paper extends techniques of Erdös and Rényi and of Pak.  相似文献   

19.
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   

20.
Summary For a realization of lengthn from a covariance stationary discrete time process with spectral density which behaves like 1–2H as 0+ for 1/2<H<1 (apart from a slowly varying factor which may be of unknown form), we consider a discrete average of the periodogram across the frequencies 2j/n,j=1,..., m, wherem andm/n0 asn. We study the rate of convergence of an analogue of the mean squared error of smooth spectral density estimates, and deduce an optimal choice ofm.  相似文献   

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