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1.
For suitable positive integers n and k let m(n, k) denote the maximum number of edges in a graph of order n which has a unique k-factor. In 1964, Hetyei and in 1984, Hendry proved
for even n and
, respectively. Recently, Johann confirmed the following conjectures of Hendry:
for
and kn even and
for n = 2kq, where q is a positive integer. In this paper we prove
for
and kn even, and we determine m(n, 3). 相似文献
2.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
3.
Andreas Rosenschon 《K-Theory》1999,16(2):185-199
Let X be a smooth projective variety over the complex numbers. We consider the cohomology of the sheaves
and
arising from Deligne–Beilinson cohomology and the Hodge filtration on the singular cohomology of X. We show that one can identify
with the image of the truncated regulator map c¯2,1. In particular, this implies that
is countable. Since this group is a direct summand of coker
, this gives a partial answer to Voisin's conjecture that cocker() is countable. In the case of X a surface, we prove that the Albanese kernel T(X) is isomorphic to the group of global sections of
if and only if pg=0. 相似文献
4.
Alina Iacob 《Archiv der Mathematik》2005,85(4):335-344
We consider two pairs of complete hereditary cotorsion theories
on the category of left R-modules, such that
We prove that for any left R-modules M, N and for any n ≧ 1, the generalized Tate cohomology modules
can be computed either using a left
of M and a left
of M or using a right
a right
of N.
Received: 17 December 2004 相似文献
5.
6.
Let
be a C*-algebra and X a Hilbert C*
-module. If
is a projection, let
be the p-sphere of X. For φ a state of
with support p in
and
consider the modular vector state φx of
given by
The spheres
provide fibrations
and
These fibrations enable us to examine the homotopy type of the sets of modular vector states, and relate it to the homotopy type of unitary groups and spaces of projections. We regard modular vector states as generalizations of pure states to the context of Hilbert C*-modules, and the above fibrations as generalizations of the projective fibration of a Hilbert space. 相似文献
7.
Stefan Gille 《Archiv der Mathematik》2007,88(4):333-343
Let
be a closed subscheme of the noetherian scheme X. We show that if X has a dualizing complex
then there exists a dualizing complex
of Z such that there is an isomorphism of coherent Witt groups
for all
.
Received: 3 March 2006 相似文献
8.
D. Jakubíková-Studenovská 《Algebra Universalis》2009,60(2):125-143
In the present paper we prove that the collection of all convexities of partial monounary algebras is finite; namely, it has exactly 23 elements. Further, we show that for
each element there exists a subset of such that is generated by and card .
This work was supported by the Science and Technology Assistance Agency under the contract No. APVT-20-004104. Supported by
Grant VEGA 1/3003/06. 相似文献
9.
Dong Zhe 《Czechoslovak Mathematical Journal》2006,56(2):287-298
In this paper we investigate finite rank operators in the Jacobson radical
of Alg(
), where
are nests. Based on the concrete characterizations of rank one operators in Alg(
) and
, we obtain that each finite rank operator in
can be written as a finite sum of rank one operators in
and the weak closure of
equals Alg(
) if and only if at least one of
is continuous. 相似文献
10.
Given an inclusion of (graded) local nets, we analyse the structure of the corresponding inclusion of scaling limit nets , giving conditions, fulfilled in free field theory, under which the unicity of the scaling limit of implies that of the scaling limit of . As a byproduct, we compute explicitly the (unique) scaling limit of the fixpoint nets of scalar free field theories. In
the particular case of an inclusion of local nets with the same canonical field net , we find sufficient conditions which entail the equality of the canonical field nets of .
Work supported by MIUR, GNAMPA-INDAM, the EU and SNS.
Submitted: August 29, 2008. Accepted: March 23, 2009. 相似文献
11.
Yi Hu 《Compositio Mathematica》1999,118(2):159-187
In this paper, certain natural and elementary polygonal objects in Euclidean space, the stable polygons, are introduced, and the novel moduli spaces
of stable polygons are constructed as complex analytic spaces. Quite unexpectedly, these new moduli spaces are shown to be projective and isomorphic to the moduli space
of the Deligne–Mumford stable curves of genus 0. Further, built into the structures of stable polygons are some natural data giving rise to a family of (classes of) symplectic (Kähler) forms. This, via the link to
, brings up a new tool to study the Kähler topology of
. A wild but precise conjecture on the shape of the Kähler cone of
is given in the end. 相似文献
12.
We consider Dirichlet spaces (
) in L
2 and more general energy forms
in L
p
,
. For the latter we introduce the notions of an extended ’Dirichlet’ space and a transient form. Under the assumption that
, resp.
, are compactly embedded in L
2, resp. L
p
, we prove a Poincaré inequality for transient (Dirichlet) forms. If both
and its adjoint
are sub-Markovian semigroups, we show that the transience of T
t
is independent of
) and that it is implied by the transience of the energy form
of
and the form
belonging to
. 相似文献
13.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
14.
We construct a determinantal resolution of singularities for the universal subscheme in
and prove that it is isomorphic to the variety of total pairs
. 相似文献
15.
A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. 相似文献
16.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
17.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
18.
The 3-local geometry
of the sporadic simple group Co1 has been known to have a cover
with a flag-transitive automorphism group which is a nonsplit extension of an elementary Abelian 2-group of rank 24 (the Leech lattice modulo 2) by Co1. It was conjectured that
was simply connected. We disprove this conjecture by constructing a double cover
of
. The automorphism group of
is of the shape
. However, it is not isomorphic to the involution centralizer of the Monster sporadic simple group. 相似文献
19.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 相似文献
20.
Let
be the set of all coloured permutations on the symbols 1, 2, . . . , n
with colours 1, 2, . . . , r, which is the analogous of the
symmetric group when r = 1, and the hyperoctahedral
group when r = 2. Let
be a subset of d colours; we define
to be the set of all coloured permutations
.
We prove that the number of
-avoiding coloured permutations in
.
We then prove that for any
,
the number of coloured permutations in
which avoid all patterns in
except for and contain exactly once equals
.
Finally, for any
,
this number equals
.
These results generalize recent results due to Mansour, Mansour and West, and Simion.AMS Subject Classification: 05A05, 05A15. 相似文献