共查询到20条相似文献,搜索用时 46 毫秒
1.
2.
Benjamin M. S. Martin 《Geometriae Dedicata》2001,86(1-3):19-27
Let be the fundamental group of a closed orientable surface of genus g 1, and let R(, G)/G be the space of conjugacy classes of representations of into a connected real reductive Lie group G. Motivated by the theory of geometric quantization, we define a map ¯ on R(, G)/G and investigate whether the fibres of ¯ are isotropic with respect to the natural symplectic structure on R(, G)/G. If g = 2 and G = SU(2), then the foliation given by the fibres of ¯ is equivalent to a real polarization defined by Weitsman, and we reprove his result that the fibres are isotropic in this case. If g = 1 then the fibres of ¯ are also isotropic, but we give an example to show that in general they are not. 相似文献
3.
Existence and uniqueness of a doubly -derived translation plane of order 49 are proved. Furthermore, we give a complete classification of those translation planes of order 49 which can be obtained from the desarguesian plane of order 49 by a mixed double derivation, namely by applying a -derivation on and a classical derivation (also called Ostrom's derivation or -derivation) on . 相似文献
4.
Let be a translation plane of odd order p2R for p a prime. Let admit at least two p-groups, Bi, i=1, 2, B1B2 of orders > pR/2 which fix Baer subplanes i, i = 1,2, 12 pointwise. It is shown that under these assumptions must be a Hall plane. 相似文献
5.
Shmuel Onn 《Journal of Algebraic Combinatorics》1994,3(2):187-206
Each matrix representation :G GLn() of a finite Group G over a field induces an action of G on the module n over the polynomial algebra
The graded -submodule M() of n generated by the orbit of
is studied. A decomposition of M() into generic modules is given. Relations between the numerical invariants of and those of M(), the latter being efficiently computable by Gröbner bases methods, are examined. It is shown that if is multiplicity-free, then the dimensions of the irreducible constituents of can be read off from the Hilbert series of M(Pi;). It is proved that determinantal relations form Gröbner bases for the syzygies on generic matrices with respect to any lexicographic order. Gröbner bases for generic modules are also constructed, and their Hilbert series are derived. Consequently, the Hilbert series of M(Pi;) is obtained for an arbitrary representation. 相似文献
6.
LetV
n
={1, 2, ...,n} ande
1,e
2, ...,e
N
,N=
be a random permutation ofV
n
(2). LetE
t={e
1,e
2, ...,e
t} andG
t=(V
n
,E
t
). If is a monotone graph property then the hitting time() for is defined by=()=min {t:G
t
}. Suppose now thatG
starts to deteriorate i.e. loses edges in order ofage, e
1,e
2, .... We introduce the idea of thesurvival time =() defined by t = max {u:(V
n, {e
u,e
u+1, ...,e
T
}) }. We study in particular the case where isk-connectivity. We show that
相似文献
7.
We define (n) to be the largest number such that for every setP ofn points in the plane, there exist two pointsx, y P, where every circle containingx andy contains (n) points ofP. We establish lower and upper bounds for (n) and show that [n/27]+2(n)[n/4]+1. We define
for the special case where then points are restricted to be the vertices of a convex polygon. We show that
. 相似文献
8.
Jeremy M. Dover 《Journal of Geometry》2000,69(1-2):58-67
Asemioval in a projective plane is a setS of points such that for every pointP S, there exists a unique line of such thatS={P}. In other words, at every point ofS, there exists a unique tangent line.In this paper, we consider semiovals such that some line has a large intersection withS. In a finite plane it is shown that no semioval can contain a full line, and that apart from two small cases, no semioval can contain all but one point of some line. We then consider semiovals which contain all but two points of some line, providing some examples and characterizations. 相似文献
9.
U. Raitums 《Journal of Optimization Theory and Applications》1997,92(3):633-660
This paper considers analogues of the Helmholtz projections of the set of selections of a piecewise smooth multivalued map
, n2. It is shown that, for mn–1 (m=1), the closure of the projection of on the subspace of gradient fields (solenoidal vector fields) is a convex set. For the general case, there are given point-wise conditions on the values of the map which ensure that the closure of the projection of contains the zero element. Possible applications to optimal control problems are discussed. 相似文献
10.
Let
be a probability space and a partition of . A necessary and sufficient condition is given for the existence of a -additive and measurable disintegration of P on . It is also shown that P admits a -additive (but not measurable) disintegration on whenever
is a standard space and the set (1, 2):1 and 2 are in the same element of } is coanalytic in ×. Finally, sufficient statistics (in the classical Fisherian sense) are investigated by using -additive disintegrations as conditional probabilities. 相似文献
11.
Axel Hultman 《Journal of Algebraic Combinatorics》2002,16(1):83-96
Let
n,k,k
and
n,k,h
, h < k, denote the intersection lattices of the k-equal subspace arrangement of type
n
and the k,h-equal subspace arrangement of type
n
respectively. Denote by
the group of signed permutations. We show that (
n,k,k
)/
is collapsible. For (
n,k,h
)/
, h < k, we show the following. If n 0 (mod k), then it is homotopy equivalent to a sphere of dimension
. If n h (mod k), then it is homotopy equivalent to a sphere of dimension
. Otherwise, it is contractible. Immediate consequences for the multiplicity of the trivial characters in the representations of
on the homology groups of (
n,k,k
) and (
n,k,h
) are stated.The collapsibility of (
n,k,k
)/
is established using a discrete Morse function. The same method is used to show that (
n,k,h
)/
, h < k, is homotopy equivalent to a certain subcomplex. The homotopy type of this subcomplex is calculated by showing that it is shellable. To do this, we are led to introduce a lexicographic shelling condition for balanced cell complexes of boolean type. This extends to the non-pure case work of P. Hersh (Preprint, 2001) and specializes to the CL-shellability of A. Björner and M. Wachs (Trans. Amer. Math. Soc.
4 (1996), 1299–1327) when the cell complex is an order complex of a poset. 相似文献
12.
Let and be two hyperbolic simply connected domains in the extended complex plane C¯ = C¯ {}. We derive sharp upper bounds for the modulus of the nth derivative of a holomorphic, resp. meromorphic function f: at a point z
0 . The bounds depend on the densities (z
0) and (f(z
0)) of the Poincaré metrics and on the hyperbolic distances of the points z
0 and f(z
0) to the point . 相似文献
13.
Micheline Vigué-Poirrier 《manuscripta mathematica》1986,56(2):177-191
Let X be a nilpotent space such that it exists k1 with Hp (X,) = 0 p > k and Hk (X,) 0, let Y be a (m–1)-connected space with mk+2, then the rational homotopy Lie algebra of YX (resp.
is isomorphic as Lie algebra, to H* (X,) (* (Y) ) (resp.+ (X,) (* (Y) )). If X is formal and Y -formal, then the spaces YX and
are -formal. Furthermore, if dim * (Y) is infinite and dim H* (Y,Q) is finite, then the sequence of Betti numbers of
grows exponentially. 相似文献
14.
15.
Necessary and sufficient conditions for interpolation with functions having monotoner-th derivatives
Gy. Sonnevend 《Analysis Mathematica》1988,14(4):273-285
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