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1.
There are exactlytwo non-equivalent [32,11,12]-codes in the binaryReed-Muller code
which contain
and have the weight set {0,12,16,20,32}. Alternatively,the 4-spaces in the projective space
over the vector space
for which all points have rank 4 fall into exactlytwo orbits under the natural action of PGL(5) on
. 相似文献
2.
J. A. Thas 《Designs, Codes and Cryptography》2001,23(2):249-258
If x is a regular point of the generalizedquadrangle
of order (s,t), s 1 t, then x defines a dual net
. If
contains a line L of regularpoints and if for at least one point x on Lthe automorphism group of the dual net
satisfies certain transitivityproperties, then
is a translation generalized quadrangle. Thisresult has many applications. We give one example. Ifs=t 1, then
is a dual affine plane. Let
be a generalizedquadrangle of orders,s odd and s 1, which contains a lineL of regular points. If for at least one pointx on L the plane
is Desarguesian, then
is isomorphic to the classical generalizedquadrangleW(s). 相似文献
3.
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
4.
Koen Thas 《Designs, Codes and Cryptography》2002,25(3):247-253
Suppose
is a generalized quadrangle (GQ) of order
, with a regular point. Then there is a net which arises from this regular point. We prove that if such a net has a proper subnet with the same degree as the net, then it must be an affine plane of order t. Also, this affine plane induces a proper subquadrangle of order t containing the regular point, and we necessarily have that
. This result has many applications, of which we give one example. Suppose
is an elation generalized quadrangle (EGQ) of order
, with elation point p. Then
is called a skew translation generalized quadrangle (STGQ) with base-point p if there is a full group of symmetries about p of order t which is contained in the elation group. We show that a GQ
of order s is an STGQ with base-point p if and only if p is an elation point which is regular. 相似文献
5.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
6.
Milan Jasem 《Mathematica Slovaca》2007,57(2):107-118
In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) there exists an internal direct decomposition
of
with
commutative such that
and
for each x ∈ A.
On the other hand, if
is an internal direct decomposition of a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) with
commutative, then the mapping g: A → A defined by
is an isometry in
and
.
相似文献
7.
Let
be a unital C*-algebra and G the group of units of
. A geometrical study of the action of G over the set
+ of all positive elements of
is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in 'components' which also have a rich geometrical structure. 相似文献
8.
Natalie M. Priebe 《Geometriae Dedicata》2000,79(3):239-265
In this paper, a technique for analyzing levels of hierarchy in a tiling
of Euclidean space is presented. Fixing a central configuration P of tiles in
, a `derived Voronoï' tessellation
P is constructed based on the locations of copies of P in
. A family of derived Voronoï tilings
is formed by allowing the central configurations to vary through an infinite number of possibilities. The family
will normally be an infinite one, but we show that for a self-similar tiling
it is finite up to similarity. In addition, we show that if the family
is finite up to similarity, then
is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided. 相似文献
9.
Let
be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra
so that for every 1 < p < 2, the Haagerup L
p
-space associated with
embeds isomorphically into
. We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if
is a semi-finite von Neumann algebra then every reflexive subspace of
embeds isomorphically into L
r
(
) for some r > 1.
Dedicated to Professor H. P. Rosenthal on the occasion of his sixty-fifth birthday
Research partially supported by NSF grant DMS-0456781. 相似文献
10.
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
11.
A. I. Budkin 《Algebra and Logic》2000,39(6):363-369
Let
be a class of all groups G for which the normal closure (x)
G
of every element x belongs to a class
.
is a Levi class generated by
. Let
and
0 be classes of finitely generated nilpotent groups and of torsion-free, finitely generated, nilpotent groups, respectively. We prove that
and
, and so
and
. It is shown that quasivarieties
and
are closed under free products, and that each contains at most one maximal proper subquasivariety. It is also proved that
is closed under free products if so is
. 相似文献
12.
For a discrete group G, we prove that a G-map between proper G–CW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K
*
G
(E(G,
in)), is isomorphic to K
*
G
(E(G,
)), where E(G,
) denotes the classifying space for the family of finite cyclic subgroups of G. Letting
be the family of virtually cyclic subgroups of G, we also establish that and related results. 相似文献
13.
Yu Qing Chen 《Designs, Codes and Cryptography》1998,13(3):247-250
In this paper, we will give a construction of a family of
-difference sets in thegroup
, where q is any power of 2, K is any group with
and G is an abelian 2-group of order
which contains anelementary abelian subgroup of index 2. 相似文献
14.
Given a unital C*-algebra
and a right C*-module
over
, we consider the problem of finding short smooth curves in the sphere
= {x ∈
: 〈x, x〉 = 1}. Curves in
are measured considering the Finsler metric which consists of the norm of
at each tangent space of
. The initial value problem is solved, for the case when
is a von Neumann algebra and
is selfdual: for any element x
0 ∈
and any tangent vector ν at x
0, there exists a curve γ(t) = e
tZ
(x
0), Z ∈
, Z* = −Z and ∥Z∥ ≤ π, such that γ(0) = x
0 and
(0) = ν, which is minimizing along its path for t ∈ [0, 1]. The existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the
boundary value problem: given x
0, x
1 ∈
, find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us
denote by f
0 the selfadjoint projection I − x
0 ⊗ x
0, if the algebra f
0
f
0 is finite dimensional, then there exists a curve γ joining x
0 and x
1, which is minimizing along its path.
相似文献
15.
Niels Jakob Laustsen 《K-Theory》2001,23(2):115-127
We prove that the K-groups of the Banach algebra
of bounded, linear operators on the pth James space
, where 1 < p < , are given by
and
. Moreover, for each Banach space
and each non-zero, closed ideal
contained in the ideal of inessential operators, we show that
and
. This enables us to calculate the K-groups of
for each Banach space
which is a direct sum of finitely many James spaces and
-spaces. 相似文献
16.
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
17.
For an algebra
with an action of a Hopf algebra
we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for
. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space
for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg's theorem relating
equivariant K-theory to ordinary K-theory of the C*-algebra crossed product, and characterize equivariant vector bundles on quantum homogeneous spaces. 相似文献
18.
A. J. van Zanten 《Designs, Codes and Cryptography》1997,10(1):85-97
Let
be a list of all words of
, lexicographically ordered with respect to some basis. Lexicodes are codes constructed from
by applying a greedy algorithm. A short proof, only based on simple principles from linear algebra, is given for the linearity of these codes. The proof holds for any ordered basis, and for any selection criterion, thus generalizing the results of several authors. An extension of the applied technique shows that lexicodes over
are linear for a wide choice of bases and for a large class of selection criteria. This result generalizes a property of Conway and Sloane. 相似文献
19.
We prove in this paper that the Hilbert geometry associated with a bounded open convex domain
in R
n
whose boundary
is a
2 hypersuface with nonvanishing Gaussian curvature is bi-Lipschitz equivalent to the n-dimensional hyperbolic space H
n
. Moreover, we show that the balls in such a Hilbert geometry have the same volume growth entropy as those in H
n
. 相似文献
20.
Ron M. Roth 《Designs, Codes and Cryptography》1996,9(2):177-191
Codes
of length 2
m
over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of
all have an rth order spectral null at zero frequency. Establishing the connection between
and the parity-check matrix of Reed-Muller codes, the minimum distance of
is obtained along with upper bounds on the redundancy of
. An efficient algorithm is presented for encoding unconstrained binary sequences into
. 相似文献