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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.
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   

10.
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   

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.
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   

14.
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   

15.
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   

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.
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   

19.
We consider weakly p-harmonic maps (p2) from a compact connected Riemannian manifold Mm(m2) to the the standard sphere Sn with values in the closed hemisphere Sn+ = {x Sn : xn+1 0 } (n 2). We first prove that if u=(u1,...,un+1):MSn is a weakly p-harmonic map satisfying un+1(x)>0 a.e. on M, then it is a minimizing p-harmonic map. Next, we give a necessary and sufficient condition for the boundary data : M Sn+ to achieve uniqueness; and when this condition fails, we are able to describe the set of all minimizers. When M is without boundary, we obtain a Liouville type Theorem for weakly p-harmonic maps.Mathematics Subject Classification (2000): 58E20; 35J70  相似文献   

20.
Consider a centered Gaussian measure on a separable Banach spaceX. Denote byK the unit ball of the reproducing kernel of , and consider a symmetric convex setC ofX. We provide two-sided estimates of (C+tK). We determine in a very general setting at which rate for the gauge ofC the variablesY n (2 logn)–1/2 cluster toK, when (Y n ) is an i.i.d. sequence distributed like . The rate depends only on the behavior of the function (C) as 0.Partially supported by an NSF grant  相似文献   

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