共查询到20条相似文献,搜索用时 31 毫秒
1.
Necdet Güner 《Geometriae Dedicata》1996,63(1):17-23
Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra
. Let I* (
) denote the invariant differential forms on
.If I* (
) H* (
) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (
) H* (
) is injective. 相似文献
2.
Let G be an additive group and C
k
be the additive group of the ring Z
k
of residues modulo k. If there exist a (G, k, ) difference family and a (G, k, ) perfect Mendelsohn difference family, then there also exists a
difference family. If the (G, k, ) difference family and the (G, k, ) perfect Mendelsohn difference family are further compatible, then the resultant
difference family is elementary resolvable. By first constructing several series of perfect Mendelsohn difference families, many
difference families and elementary resolvable
difference families are thus obtained. 相似文献
3.
Let (,G, U) be a continuous representation of a Lie groupG by bounded operatorsg U (g) on the Banach space and let (,
,dU) denote the representation of the Lie algebra
obtained by differentiation. Ifa
1, ...,a
d
is a Lie algebra basis of
,A
i
=dU (a
i
) and
whenever =(i
1, ...,i
k
) we reconsider the operators
相似文献
4.
Renate Jaritz 《Geometriae Dedicata》1997,64(3):365-372
An ordered plane is an incidence structure (
) with an order function , which satisfies the axioms (G), (V) and (S), but no continuation--axiom is required. Points a, b E are said to be in distinct sides of a line
iff
and in the same side if
, respectively. For any lines
,
and
we prove that if b,c are in the same side of line A and a,c are in the same side of B , then a and b are in distinct sides of C. As conclusions we deduce that is harmonic and that in each complete quadrangle the intersection points of the diagonals are never collinear, which is known as the axiom of Fano. So the Fano-axiom holds in each ordered plane, and also in those with boundary points. 相似文献
5.
Asymptotic properties of partitions of the unit interval are studied through the entropy for random partition
6.
In this paper we investigate functorial properties of the Segal algebra
which consists of all functionsf in Wiener's algebra onG with Fourier transform
in Wiener's algebra on the dual group
. Especially
may serve as a very large and natural domain for Poisson's formula. Moreover, there is introduced a Segal algebraE
0(G) containing
as a subspace, but still eachfE
0(S) satisfies Poisson's formula. 相似文献
7.
The largest Fischer 3-transposition group M(24) acts flag-transitively on a 3-local incidence geometry
(M(24)) which is a c-extension of the dual polar space associated with the group O
7(3). The action of the simple commutator subgroup M(24) is still flag-transitive. We show that
(M(24)) is characterized by its diagram under the flag-transitivity assumption. The result implies in particular that
(M(24)) is simply connected. The geometry
(M(24)) appears as a subgeometry in the Buekenhout-Fischer 3-local geometry
(F
1) of the Monster group. The simple connectedness of
(M(24)) has played a crucial role in the characterization of
(F
1), which has been achieved recently. When determining the possible structure of the parabolic subgroups we have used an unpublished pushing-up result by U. Meierfrankenfeld.Dedicated to Professor B. Fischer on the occasion of his sixtieth birthday 相似文献
8.
For a graphG, the switched graphS
v
(G) ofG at a vertexv is the graph obtained fromG by deleting the edges ofG incident withv and adding the edges of
incident withv. Properties of graphs whereS
v
(G) G or
are studied. This concept is extended to the partial complementS
H
(G) where H
. The investigation here centers around the existence of setsH for whichS
H
(G) G. A parameter is introduced which measures how near a graph is to being self-complementary. 相似文献
9.
L. Pyber 《Combinatorica》1996,16(4):521-525
By a well-known result of Nash-Williams if a graphG is not edge reconstructible, then for all
,|A||E(G)| mod 2 we have a permutation ofV(G) such thatE(G)E(G)=A. Here we construct infinitely many graphsG having this curious property and more than
edges.Research (partially) supported by Hungarian National Foundation for Scientific Research Grant No.T016389. 相似文献
10.
By removing the components of at-spread
of a finite projective spacePG(d, q) from each hyperplane ofPG(d, q), the blocks of a regular group divisible design
are obtained We characterize geometrict-spreads as thoset-spreads
which are such that the dual of
is also a group divisible design. 相似文献
11.
B. N. Cooperstein 《Designs, Codes and Cryptography》2001,23(2):185-196
The projective plane
is embedded as a variety of projective points
in
, where M is a nine dimensional
-module for the groupG=GL(3,q
2). The hyperplane sections of thisvariety and their stabilizers in the group G aredetermined. When q 2 (mod 3) one such hyperplanesection is a member of the family of Kantor's unitary ovoids.We furtherdetermine all sections
whereD has codimension two in M and demonstratethat these are never empty. Consequences are drawn for Kantor'sovoids. 相似文献
12.
Negami and Kawagoe has already defined a polynomial
associated with each graphG as what discriminates graphs more finely than the polynomialf(G) defined by Negami and the Tutte polynomial. In this paper, we shall show that the polynomial
includes potentially the generating function counting the independent sets and the degree sequence of a graphG, which cannot be recognized fromf(G) in general, and discuss on
of treesT with observations by computer experiments. 相似文献
13.
14.
Matching Polynomials And Duality 总被引:2,自引:0,他引:2
Let G be a simple graph on n vertices. An r-matching in G is a set of r independent edges. The number of r-matchings in G will be denoted by p(G, r). We set p(G, 0) = 1 and define the matching polynomial of G by
and the signless matching polynomial of G by
.It is classical that the matching polynomials of a graph G determine the matching polynomials of its complement
. We make this statement more explicit by proving new duality theorems by the generating function method for set functions. In particular, we show that the matching functions
and
are, up to a sign, real Fourier transforms of each other.Moreover, we generalize Foatas combinatorial proof of the Mehler formula for Hermite polynomials to matching polynomials. This provides a new short proof of the classical fact that all zeros of µ(G, x) are real. The same statement is also proved for a common generalization of the matching polynomial and the rook polynomial. 相似文献
15.
S. A. Shakhova 《Algebra and Logic》2005,44(2):132-139
Let M be any quasivariety of Abelian groups,
(H) be the dominion of a subgroup H of a group G in M, and Lq(M) be the lattice of subquasivarieties of M. It is proved that
(H ) coincides with a least normal subgroup of the group G containing H, the factor group with respect to which is in M. Conditions are specified subject to which the set L(G,H,M) = {
(H) | N Lq(M)} forms a lattice under set-theoretic inclusion and the map : Lq(M) L(G,H,M) such that (N) =
(H) for any quasivariety N Lq(M)is an antihomomorphism of the lattice L
q
(M) onto the lattice L(G, H, M).__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 238–251, March–April, 2005. 相似文献
16.
A bijective mapping
defined on a finite group G is complete if the mapping defined by
,
, is bijective. In 1955 M. Hall and L. J. Paige conjectured that a finite group G has a complete mapping if and only if a Sylow 2-subgroup of G is non-cyclic or trivial. This conjecture is still open. In this paper we construct a complete mapping for the projective groups PSL
and PGL(2,q),q odd. As a consequence, we prove that in odd characteristic the projective groups PGL(n,q GL
, admit a complete mapping. 相似文献
17.
Alexander A. Ivanov 《Journal of Algebraic Combinatorics》1992,1(1):45-69
The sporadic simple group F
2 known as Fischer's Baby Monster acts flag-transitively on a rank 5 P-geometry
. P-geometries are geometries with string diagrams, all of whose nonempty edges except one are projective planes of order 2 and one terminal edge is the geometry of the Petersen graph. Let
be a flag-transitive P-geometry of rank 5. Suppose that each proper residue of
is isomorphic to the corresponding residue in
. We show that in this case
is isomorphic to
. This result realizes a step in classification of the flag-transitive P-geometries and also plays an important role in the characterization of the Fischer–Griess Monster in terms of its 2-local parabolic geometry. 相似文献
18.
We consider the spaceL(D) consisting of Lipschitz continuous mappings fromD to the Euclideann-space
n
,D being an open bounded subset of
n
. LetF belong toL(D) and suppose that
solves the equationF(x) = 0. In case that the generalized Jacobian ofF at
is nonsingular (in the sense of Clarke, 1983), we show that forG nearF (with respect to a natural norm) the systemG(x) = 0 has a unique solution, sayx(G), in a neighborhood of
Moreover, the mapping which sendsG tox(G) is shown to be Lipschitz continuous. The latter result is connected with the sensitivity of strongly stable stationary points in the sense of Kojima (1980); here, the linear independence constraint qualification is assumed to be satisfied. 相似文献
19.
Let (G, H) be an irreducible semisimple symmetric pair,P
G a parabolic subgroup. Suppose that theL-orbit of the base point in the flag manifoldG/P is open and writeS(L,P)={gG:gL
LP} for the compression semigroup of this orbit. We show that ifP is minimal andS(L, P)=G, then (G, H) is Riemannian and we give a geometric characterization of those cases whereS(L, P) has non-empty interior different fromG. IfG/H is a symmetric space of regular type, then we show under certain additional assumptions thatS(L, Q) is an Ol'shanskiî semigroup.Supported by a DFG Heisenberg-grant. 相似文献
20.
Newton's binomial theorem is extended to an interesting noncommutative setting as follows: If, in a ring,ba=ab with commuting witha andb, then the (generalized) binomial coefficient
arising in the expansion
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