共查询到20条相似文献,搜索用时 250 毫秒
1.
Michael Frank 《Acta Appl Math》2001,68(1-3):227-242
Hilbert(ian) A-modules over finite von Neumann algebras with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared and a categorical equivalence is established. The correspondence between these two structures sheds new light on basic results in L
2-invariant theory providing alternative proofs. We indicate new invariants for finitely generated projective B-modules, where B is a unital C*-algebra (usually the full group C*-algebra C*() of the fundamental group =1(M) of a manifold M). 相似文献
2.
This paper, self-contained, deals with pseudo-unitary spin geometry. First, we present pseudo-unitary conformal structures
over a 2n-dimensional complex manifold V and the corresponding projective quadrics
for standard pseudo-hermitian spaces Hp,q. Then we develop a geometrical presentation of a compactification for pseudo-hermitian standard spaces in order to construct
the pseudo-unitary conformal group of Hp,q. We study the topology of the projective quadrics
and the “generators” of such projective quadrics. Then we define the space S of spinors canonically associated with the pseudo-hermitian scalar product of signature (2n−1, 2n−1). The spinorial group Spin U(p,q) is imbedded into SU(2n−1, 2n−1). At last, we study the natural imbeddings of the projective quadrics
相似文献
3.
Alexander Nabutovsky 《Geometric And Functional Analysis》1996,6(4):703-725
LetM be a compact manifold of dimension greater than four. Denote byRiem(M) the space of Riemannian structures onM (i.e. of isometry classes of Riemannian metrics onM) endowed with the Gromov-Hausdorff metric. LetRiem
(M) Riem(M) be its subset formed by all Riemannian structures such that vol()=1 andinj() , whereinj() denotes the injectivity radius of.We prove that for all sufficiently small positive the spaceRiem
(M) is disconnected. Moreover, if is sufficiently small, thenRiem
(M) is representable as the union of two non-empty subsetsA andB such that the Gromov-Hausdorff distance between any element ofA and any element ofB is greater than/9. We also prove a more general result with the following informal meaning: There exist two Riemannian structures of volume one and arbitrarily small injectivity radius onM such that any continuous path (and even any sequence of sufficiently small jumps) in the space of Riemannian structures of volume one onM connecting these Riemannian structures must pass through Riemannian structures of injectivity radius uncontrollably smaller than the injectivity radii of these two Riemannian structures.These results can be generalized for at least some four-dimensional manifolds. The technique used in this paper can also be used to prove the disconnectedness of many other subsets of the space of Riemannian structures onM formed by imposing various constraints on curvatures, volume, diameter, etc.This work was partially supported by the New York University Research Challenge Fund grant, by NSF grant DMS 9114456 and by the NSERC operating grant OGP0155879. 相似文献
4.
Dusa McDuff 《Inventiones Mathematicae》1991,103(1):651-671
Summary An example of a 4-dimensional symplectic manifold with disconnected boundary of contact type is constructed. A collection of other results about symplectic manifolds with contact-type boundaries are derived using the theory ofJ-holomorphic spheres. In particular, the following theorem of Eliashberg-Floer-McDuff is proved: if a neighbourhood of the boundary of (V, ) is symplectomorphic to a neighbourhood ofS
2n–1 in standard Euclidean space, and if vanishes on all 2-spheres inV, thenV is diffeomorphic to the ballB
2n.Oblatum 19-III-1990Partially supported by NSF grant no: DMS 8803056 相似文献
5.
Omegar Calvo-Andrade 《Bulletin of the Brazilian Mathematical Society》1995,26(1):67-83
LetM be a projective manifold of dimension 3 andH
1 (M, )=0. We will show that a deformation of a codimension one singular foliation arising from the fibers of a generic meromorphic map of the formf
p
/g
q
,p, q>0 has a meromorphic first integral of the same type.Supported by Conacyt: 3398 E9307. 相似文献
6.
Lutz Dümbgen 《Annals of the Institute of Statistical Mathematics》1995,47(1):155-165
Let (P
: R
p
) be a simple shift family of distributions onR
p
, and letK R
p
be a convex cone. Within the class of nonrandomized tests ofK versusR
p
K, whose acceptance regionA satisfiesA=A+K, a test with minimal bias is constructed. This minimax test is compared to a likelihood ratio type test, which is optimal with respect to a different criterion. The minimax test is mimicked in the context of linear regression and one-sided tests for covariance matrices. 相似文献
7.
Given then×p orthogonal matrixA and the convex functionf:R
nR, we find two orthogonal matricesP andQ such thatf is almost constant on the convex hull of ± the columns ofP, f is sufficiently nonconstant on the column space ofQ, and the column spaces ofP andQ provide an orthogonal direct sum decomposition of the column space ofA. This provides a numerically stable algorithm for calculating the cone of directions of constancy, at a pointx, of a convex function. Applications to convex programming are discussed.This work was supported by the National Science and Engineering Research Council of Canada (Grant No. A3388 and Summer Grant). 相似文献
8.
Mikhail Verbitsky 《Geometric And Functional Analysis》1996,6(4):601-611
We announce the structure theorem for theH
2(M)-generated part of cohomology of a compact hyperkähler manifold. This computation uses an action of the Lie algebra so(4,n–2) wheren=dimH
2(M) on the total cohomology space ofM. We also prove that every two points of the connected component of the moduli space of holomorphically symplectic manifolds can be connected with so-called twistor lines — projective lines holomorphically embedded in the moduli space and corresponding to the hyperkähler structures. This has interesting implications for the geometry of compact hyperkähler manifolds and of holomorphic vector bundles over such manifolds. 相似文献
9.
Let Agl(n, C) and let p be a positive integer. The Hessenberg variety of degree p for A is the subvariety Hess(p, A) of the complete flag manifold consisting of those flags S
1
S
n–1
in n which satisfy the condition AS
i
S
i+p
,for all i. We show that if A has distinct eigenvalues, then Hess(p, A) is smooth and connected. The odd Betti numbers of Hess(p, A) vanish, while the even Betti numbers are given by a natural generalization of the Eulerian numbers. In the case where the eigenvalues of A have distinct moduli, |1|<<|1|, these results are applied to determine the dimension and topology of the submanifold of U(n) consisting of those unitary matrices P for which A
0=P
-1
AP is in Hessenberg form and for which the diagonal entries of the QR-iteration initialized at A
0 converge to a given permutation of 1,n.Research partially supported by the National Science Foundation under Grant ECS-8696108. 相似文献
10.
A -symmetric spaceM is a complete connected regular Sasakian manifold, that fibers over an Hermitian symmetric spaceN, so that the geodesic involutions ofN lift to define global (involutive) automorphisms of the Sasakian structure onM. In the present paper the complete classification of -symmetric spaces is obtained. The groups of automorphisms of the Sasakian structures and the groups of isometries of the underlying Riemannian metrics are determined. As a corollary, the Sasakian space forms are also determined. 相似文献
11.
M. Raghavachari 《Mathematical Programming》1977,13(1):156-166
LetD
p
be the set of all doubly stochastic square matrices of orderp i.e. the set of allp × p matrices with non-negative entries with row and column sums equal to unity. The permanent of ap × p matrixA = (a
ij
) is defined byP(A) =
Sp
II
i=1
p
a
i(i)
whereS
p
is the symmetric group of orderp. Van der Waerden conjectured thatP(A) p !/p
p
for all A AD
p
with equality occurring if and only ifA = J
p
, whereJ
p
is the matrix all of whose entries are equal to 1/p.The validity of this conjecture has been shown for a few values ofp and for generalp under certain assumptions. In this paper the problem of finding the minimum of the permanent of a doubly stochastic matrix has been formulated as a reversed geometric program with a single constraint and an equivalent dual program is given. A related problem of reversed homogeneous posynomial programming problem is also studied. 相似文献
12.
Gilles Halbout 《Compositio Mathematica》2001,126(2):123-145
Let k be the field or let M be the space k
n and let A be the algebra of polynomials over M. We know from Hochschild and co-workers that the Hochschild homology H
·(A,A) is isomorphic to the de Rham differential forms over M: this means that the complexes (C
·(A,A),b) and (·(M), 0) are quasi-isomorphic. In this work, I produce a general explicit homotopy formula between those two complexes. This formula can be generalized when M is an open set in a complex manifold and A is the space of holomorphic functions over M. Then, by taking the dual maps, I find a new homotopy formula for the Hochschild cohomology of the algebra of smooth fonctions over M (when M is either a complex or a real manifold) different from the one given by De Wilde and Lecompte. I will finally show how this formula can be used to construct an homotopy for the cyclic homology. 相似文献
13.
LetX be a complex Lebesgue space with a unique duality mapJ fromX toX
*, the conjugate space ofX. LetA be a bounded linear operator onX. In this paper we obtain a non-linear eigenvalue problem for (A)=sup{Re: W(A} whereW(A)={J(x)A(x)) : x=1}, under the assumption that (A) and the convex hull ofW(A) for some linear operatorsA onl
p
, 2<p<. 相似文献
14.
N. K. Smolentsev 《Siberian Mathematical Journal》2001,42(6):1165-1169
Let A
M
be the space of all almost Kahlerian smooth metrics on a symplectic manifold M
2n
, such that the fundamental form of each metric coincides with . It is well known that A
M
is a retractor of the space M of all smooth metrics on M. We show that M is a smooth trivial bundle over A
M
. A similar fact holds also in the case of a contact manifold. 相似文献
15.
For a setA of non-negative numbers, letD(A) (the difference set ofA) be the set of nonnegative differences of elements ofA, and letD
k be thek-fold iteration ofD. We show that for everyk, almost every set of non-negative integers containing 0 arises asD
k
(A) for someA. We also give sufficient conditions for a setA to be the unique setX such that 0X andD
k
(X)=D
k
(A). We show that for eachm there is a setA such thatD(X)=D(A) has exactly 2
m
solutionsX with 0X.This work was supported by grants DMS 92-02833 and DMS 91-23478 from the National Science Foundation. The first author acknowledges the support of the Hungarian National Science Foundation under grants, OTKA 4269, and OTKA 016389, and the National Security Agency (grant No. MDA904-95-H-1045).Lee A. Rubel died March 25, 1995. He is very much missed by his coauthors. 相似文献
16.
Michel Weber 《Journal of Theoretical Probability》1996,9(1):105-112
Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL
2() such that
, whereA=sup{||sȒt||2
,s, tA} andN(A, u) is the smallest number ofL
2()-open balls of radiusu, centered inA, enough to coverA. Let
. We prove as a consequence of a more general result, thatC(A) is aGB subset ofL
2(). 相似文献
17.
John D. Dixon 《Numerische Mathematik》1982,40(1):137-141
Summary A method is described for computing the exact rational solution to a regular systemAx=b of linear equations with integer coefficients. The method involves: (i) computing the inverse (modp) ofA for some primep; (ii) using successive refinements to compute an integer vector
such that
(modp
m
) for a suitably large integerm; and (iii) deducing the rational solutionx from thep-adic approximation
. For matricesA andb with entries of bounded size and dimensionsn×n andn×1, this method can be implemented in timeO(n
3(logn)2) which is better than methods previously used.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (Grant No. A 7171) 相似文献
18.
Thomas Stehling 《Combinatorica》1992,12(4):475-479
We consider the numberN
A
(r) of subgroups of orderp
r
ofA, whereA is a finite Abelianp-group of type =1,2,...,
l
()), i.e. the direct sum of cyclic groups of order ii. Formulas for computingN
A
(r) are well known. Here we derive a recurrence relation forN
A
(r), which enables us to prove a conjecture of P. E. Dyubyuk about congruences betweenN
A
(r) and the Gaussian binomial coefficient
. 相似文献
19.
Ralph Greenberg 《Compositio Mathematica》2003,136(3):255-297
This paper concerns the Galois theoretic behavior of the p-primary subgroup Sel
A
(F)
p
of the Selmer group for an Abelian variety A defined over a number field F in an extension K/F such that the Galois group G(K/F) is a p-adic Lie group. Here p is any prime such that A has potentially good, ordinary reduction at all primes of F lying above p. The principal results concern the kernel and the cokernel of the natural map s
K/F Sel
A
(F)
p
Sel
A
(K)
p
G(K/F) where F is any finite extension of F contained in K. Under various hypotheses on the extension K/F, it is proved that the kernel and cokernel are finite. More precise results about their structure are also obtained. The results are generalizations of theorems of B.Mazurand M. Harris. 相似文献
20.
Mark C. Ho 《Integral Equations and Operator Theory》1997,29(3):301-312
In this paper, we will use the Birkhoff's ergodic theorem to do some finer analysis on the spectral properties of slant Toeplitz operators. For example, we will show that if is an invertibleL
function on the unit circle, then almost every point in (A
*
) is not an eigenvalue ofA
*
. More specifically, we will show that the point spectrum ofA
*
is contained in a circle with positive radius. 相似文献