共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
Let
be an
-filtered category in the sense of Karoubi. This is the categorical analogue of an ideal
in a ring
. Pedersen and Weibel constructed a fibration of K-theory spectra associated with the sequence
. We present a new easier proof based on Waldhausen' generic fibration. 相似文献
4.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 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.
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
7.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):651-663
Let Int
be the lattice of all intervals of an MV-algebra
. In the present paper we investigate the relations between direct product decompositions of
and (i) the lattice Int
, or (ii) 2-periodic isometries on
, respectively. 相似文献
8.
We construct a supersymmetric analogue of the Calogero operator
, which depends on the parameter k. This analogue is related to the root system of the Lie superalgebra
. It becomes the standard Calogero operator for m = 0 and becomes the operator constructed by Veselov, Chalykh, and Feigin up to changing the variables and the parameter k for m = 1. For k = 1 and 1/2, the operator
is the radial part of the second-order Laplace operator for the symmetric superspaces corresponding to the respective pairs
. We show that for any m and n, the supersymmetric analogues of the Jack polynomials constructed by Kerov, Okounkov, and Olshanskii are eigenfunctions of the operator
. For k = 1 and 1/2, the supersymmetric analogues of the Jack polynomials coincide with the spherical functions on the above superspaces. We also study the algebraic analogue of the Berezin integral. 相似文献
9.
Demidov S. V. Dubovsky S. L. Rubakov V. A. Sibiryakov S. M. 《Theoretical and Mathematical Physics》2004,138(2):269-283
The solution-generating technique originally suggested for gauge theories on the noncommutative plane is generalized to the noncommutative cylinder. For this, we construct partial isometry operators and a complete set of orthogonal projection operators in the algebra
C of the cylinder, and an isomorphism between the free module
C and its direct sum
C
C with the Fock module on the cylinder. We explicitly construct the gauge theory soliton and evaluate the spectrum of perturbations about this soliton. 相似文献
10.
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
11.
The concepts of an annihilator and a relative annihilator in an autometrized l-algebra are introduced. It is shown that every relative annihilator in a normal autometrized l-algebra
is an ideal of
and every principal ideal of
is an annihilator of
. The set of all annihilators of
forms a complete lattice. The concept of an I-polar is introduced for every ideal I of
. The set of all I-polars is a complete lattice which becomes a two-element chain provided I is prime. The I-polars are characterized as pseudocomplements in the lattice of all ideals of
containing I. 相似文献
12.
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
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.
Juraj Činčura 《Applied Categorical Structures》1998,6(4):527-530
Let
be an epireflective subcategory of the category Top of topological spaces which is not contained in the category of indiscrete spaces (e.g. Top, the category of Hausdorff spaces, the category of Tychonoff spaces) and
be a coreflective subcategory of
. In this paper we prove that the coreflector
preserves regular epimorphisms if and only if
or
is contained in the category of discrete spaces. 相似文献
15.
Let X be a complex analytic manifold,
a C
2 submanifold,
an openset with C
2 boundary
.Denote by
(resp.
) the microlocalization along M (resp.
) of the sheaf
of holomorphic functions.In the literature (cf. [A-G], [K-S 1,2])one encounters two classical results concerning the vanishing of the cohomology groups
.The most general gives the vanishing outside a range of indices j whose length is equal to
(with
being the number of respectively positive, negative and null eigenvalues for themicrolocal Levi form
).The sharpest result gives the concentration in a single degree, provided that the difference
is locally constant for
near p (with
for z the base point of p).The first result was restated for the complex
in [D'A-Z 2], in the case codim
We extend it here to any codimension and moreover we also restate for
the second vanishing theorem.We also point out that the principle of our proof, related to a criterion for constancy of sheaves due to [K-S 1], is a quite new one. 相似文献
16.
17.
We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献
18.
In the open disk
of the complex plane, we consider the following spaces of functions: the Bloch space
; the Hardy--Sobolev space
; and the Hardy--Besov space
. It is shown that if all the poles of the rational function R of degree n,
, lie in the domain
, then
, where
and
depends only on
. The second of these inequalities for the case of the half-plane was obtained by Semmes in 1984. The proof given by Semmes was based on the use of Hankel operators, while our proof uses the special integral representation of rational functions. 相似文献
19.
Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius
-homomorphism. For
, this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space,
the
th symmetric power of X, and
the algebra of continuous complex-valued functions on X with the sup-norm; then the evaluation map
defined by the formula
identifies the space
with the space of all Frobenius
-homomorphisms of the algebra
into
with the weak topology. 相似文献
20.
We obtain the decomposition of the tensor space
as a module for
, find an explicit formula for the multiplicities of its irreducible summands, and (when n 2k) describe the centralizer algebra
=
(
) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of
is given by the number of derangements of a set of 2k elements. 相似文献