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1.
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
2.
Judita Lihová 《Czechoslovak Mathematical Journal》1999,49(1):67-80
Let
be a partially ordered set, Int
the system of all (nonempty) intervals of
partially ordered by the set-theoretical inclusion
. We are interested in partially ordered sets
with Int
isomorphic to Int
. We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If
is a directed partially ordered set, the only
with Int
isomorphic to Int
are
corresponding to direct decompositions
of
(
denotes the dual of
. The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11]. 相似文献
3.
Let
be a reductive Lie algebra over C. We say that a
-module M is a generalized Harish-Chandra module if, for some subalgebra
, M is locally
-finite and has finite
-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when
is a Cartan subalgebra. We also review the recent determination of which reductive in
subalgebras
are essential to a classification. Finally, we present in detail the emerging picture for the case when
is a principal 3-dimensional subalgebra. 相似文献
4.
Introduce the notation:
, is the union of two segments [-1,1] and [-1 +
,1+
],
is a noninteger number,
is the Hölder class with exponent
on
The following result announced by the authors in [J. Math. Sci. 117 (2003), No. 3] is proved. There exist numbers a
1 (
) , b
1 (
)
0 depending only on
such that for any
there exists a polynomial
, such that
. Bibliography: 11 titles. 相似文献
5.
Let
be a polynomial with complex coefficients and define, for
,
where ||P|| is the euclidean norm of the polynomial P. By a theorem of Szegö
where
is the Mahler measure of F. Recently, J. Dégot proved an effective version of this result. In this paper we sharpen Dégot's result, under the additional hypotheses that F is a square-free polynomial with integer coefficients and without reciprocal factors. 相似文献
6.
We prove a local limit theorem for large deviations of the sums
, where
, is a Markov Gaussian random field,
is a bounded vector-valued function, and
. This paper generalizes the paper [13]. 相似文献
7.
Two numerical characteristics of a nonrectifiable arc
generalizing the notion of length are introduced. Geometrically, this notion can naturally be generalized as the least upper bound of the sums
, where
are the lengths of segments of a polygonal line inscribed in the curve
and
is a given function. On the other hand, the length of
is the norm of the functional
in the space
; its norms in other spaces can be considered as analytical generalizations of length. In this paper, we establish conditions under which the generalized geometric rectifiability of a curve
implies its generalized analytic rectifiability. 相似文献
8.
We prove the absolute continuity of the spectrum of the Schrödinger operator in
,
, with periodic (with a common period lattice
) scalar
and vector
potentials for which either
,
, or the Fourier series of the vector potential
converges absolutely,
, where
is an elementary cell of the lattice
,
for
, and
for
, and the value of
is sufficiently small, where
and
otherwise,
, and
. 相似文献
9.
E. P. Golubeva 《Journal of Mathematical Sciences》2003,118(1):4740-4752
Let h(d) be the class number of the field
and let
be the Lévy constant. A connection between these constants is studied. It is proved that if d is large, then the value h(d) increases, roughly speaking, at the rate
as
grows. A similar result is obtained in the case where the value
is close to
, i.e., to the least possible value. In addition, it is shown that the interval
contains no values of
for prime p such that p 3 (mod 4). As a corollary, a new criterion for the equality h(d)=1 is obtained. Bibliography: 14 titles. 相似文献
10.
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
11.
12.
E. G. Emelyanov 《Journal of Mathematical Sciences》2004,122(6):3648-3653
Let
be a finite Riemann surface. For a quadratic differential on
associated with a certain problem on extremal decomposition of
into n domains, a parametric family of quasiconformal mappings
, is defined. These mappings map the domains of the extremal decomposition of
onto the domains of the extremal decomposition of
.K This allows one to study the functional dependence of the problem on the parameters. Bibliography: 6 titles. 相似文献
13.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
14.
Let
be an entire function of finite type with respect to finite order
and let
be a subset of an open cone in a certain n-dimensional subspace
(the smaller
, the sparser
). We assume that this cone contains a ray
0} \right\}$$
" align="middle" border="0">
. It is shown that the radial indicator
of
at any point
may be evaluated in terms of function values at points of the discrete subset
. Moreover, if
tends to zero fast enough as
over
, then this function vanishes identically. To prove these results, a special approximation technique is developed. In the last part of the paper, it is proved that, under certain conditions on
and
, which are close to exact conditions, the function
bounded on
is bounded on the ray. 相似文献
15.
Tatsuya Maruta 《Designs, Codes and Cryptography》2001,22(2):165-177
There do not exist
codes over the Galois field GF
attaining the Griesmer bound for
for
andfor
for
. 相似文献
16.
On a Problem of the Theory of Multiply Local Formations 总被引:1,自引:0,他引:1
We describe the -closed n-multiply local formations
such that the lattice of all -closed n-multiply local formations between
and
is Boolean. 相似文献
17.
N. Yu. Galanova 《Algebra and Logic》2003,42(1):14-19
Let
be a field of formal power series with real coefficients, whose supports are well ordered subsets of an Abelian group
of cardinality strictly less than
. For
, we give criteria of a section being symmetric and of a symmetric section being Dedekind. It is proved that an
-saturated non-standard real line
is isomorphic to some field of the form
. For
, some consequences are inferred regarding symmetric sections, and the cofinality of banks of the sections. 相似文献
18.
We consider the Skyrme model using the explicit parameterization of the rotation group
through elements of its algebra. Topologically nontrivial solutions already arise in the one-dimensional case because the fundamental group of
is
. We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy. We propose a new class of projective models whose target spaces are arbitrary real projective spaces
. 相似文献
19.
We derive bosonic-type formulas for the characters of
2 coinvariants. 相似文献
20.
David A. Richter 《Acta Appl Math》2001,66(1):41-65
Starting from the commutation relations in a complex semisimple Lie algebra
, one may obtain a space
of vector fields on Euclidean space such that
and
are isomorphic when
is equipped with the usual Lie bracket between vector fields and the isotropy subalgebra of
is a Borel subalgebra
. Furthermore, one may adjoin to the vector fields in
multiplication operators to obtain an
-parameter family of distinct presentations of
as spaces of differential operators, where
is the dual of a Cartan subalgebra. Some of these presentations will preserve a space of polynomials on Euclidean space, and, in fact, all the finite-dimensional representations of
can be presented in this way. All of this is carried out explicitly for arbitrary
. In doing so, one discovers there is a Lie group of diffeomorphisms of the unipotent subgroup N complementary to B which acts on these presentations and preserves a certain notion of weight. 相似文献