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1.
Let
and
be Hausdorff topological vector spaces over the field
, let
be a bilinear functional, and let
be a non-empty subset of
. Given a set-valued map
and two set-valued maps
, the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point
and a point
such that
and
for all
and for all
or to find a point
a point
and a point
such that
and
for all
. The generalized bi-quasi-variational inequality was introduced first by Shih and Tan [8] in 1989. In this paper we shall obtain some existence theorems of generalized bi-quasi-variational inequalities as application of upper hemi-continuous operators [4] in locally convex topological vector spaces on compact sets. 相似文献
2.
A. Cossidente J. W. P. Hirschfeld G. Korchmáros F. Torres 《Compositio Mathematica》2000,121(2):163-181
The number N of rational points on an algebraic curve of genus g over a finite field
satisfies the Hasse–Weil bound
. A curve that attains this bound is called maximal. With
and
, it is known that maximalcurves have
. Maximal curves with
have been characterized up to isomorphism. A natural genus to be studied is
and for this genus there are two non-isomorphic maximal curves known when
. Here, a maximal curve with genus g
2 and a non-singular plane model is characterized as a Fermat curve of degree
. 相似文献
3.
E. G. Emel'yanov 《Journal of Mathematical Sciences》2002,110(6):3078-3090
An extension of a theorem on extremal decomposition of a Riemann surface is obtained. The problem of extremal decomposition is extended from the case of a Riemann surface
with a prescribed set
of distinguished points to the case of the Teichmüller space
corresponding to
under quasiconformal homeomorphisms f. For the functional
of our problem on extremal decomposition of a surface
, we consider a function
expressing the dependence of the extremal value of
on a point
. Differentiation formulas for the function
are derived. These formulas are different and depend on the genus g of the surface
. The case where the function
is pluriharmonic is considered. Bibliography: 8 titles. 相似文献
4.
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
5.
A. M. Protopopov 《Algebra and Logic》2003,42(4):279-286
We study into the question of whether a partial order can be induced from a partially right-ordered group
onto a space
of right cosets of
w.r.t. some subgroup
of
. Examples are constructed showing that the condition of being convex for
in
is insufficient for this. A necessary and sufficient condition (in terms of a subgroup
and a positive cone
of
) is specified under which an order of
can be induced onto
. Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups
for which
is partially ordered for every convex subgroup
, and properties of the class of groups such that
is partially ordered for every partial right order
on
and every subgroup
that is convex under
. 相似文献
6.
Masayuki Uchida 《Annals of the Institute of Statistical Mathematics》1998,50(4):655-671
Let X
, X
, ... be a sequence of independent and identically distributed random variables, which take values in a countable set S = {0, 1, 2, ...}. By a pattern we mean a finite sequence of elements in S. For every i = 0, 1, 2, ..., we denote by P
= "a
a
... a
" the pattern of some length k
, and E
denotes the event that the pattern P
occurs in the sequence X
, X
, .... In this paper, we have derived the generalized probability generating functions of the distributions of the waiting times until the r-th occurrence among the events
. We also have derived the probability generating functions of the distributions of the number of occurrences of sub-patterns of length l(l < k) until the fiurrence of the pattern of length k in the higher order Markov chain. 相似文献
7.
V.G. Osmolovskii 《Journal of Mathematical Sciences》2004,122(3):3278-3289
We consider the energy functional of a two-phase elastic medium
with quadratic energy densities
defined for
such that
,where
is a measurable characteristic function. Under some natural conditions on the data of the problem, we prove the existence of an interval (t
-,t
+) of the change of temperature
such that the energy functional has only a minimizer
such that
for
or
such that
t^ + $$
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. The energy functional has no minimizers
such that
or
if
. We derive two-sided estimates for the numbers
in terms of the characteristics of the two-phase elastic medium and the boundary condition. Bibliography: 3 titles. 相似文献
8.
Hiroshi Suzuki 《Journal of Algebraic Combinatorics》1998,7(2):165-180
It is well known that imprimitive P-polynomial association schemes
with
are either bipartite or antipodal, i.e., intersection numbers satisfy either
for all
for all
. In this paper, we show that imprimitive
-polynomial association schemes
with
are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either
. 相似文献
9.
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
10.
Qi S. Zhang 《Journal of Computational Analysis and Applications》2000,2(4):277-292
We study the inhomogeneous semilinear wave equations
on
with initial values
and
,where
is a noncompact, complete manifold. We founda new critical behavior in the following sense. There exists ap* > 0. When 1 < p p*, the above problem hasno global solution for any nonnegative
not identicallyzero and for any
and
; when
the problem has a global solution for some
and some
and
. If
, which is equipped with the Euclideanmetric, then
. If
we show that
belongs to the blow upcase. Although homogeneous semilinear wave equations are known to exhibit acritical behavior for a long time, this seems to be the first result oninhomogeneous ones. 相似文献
11.
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
12.
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
13.
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
14.
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
15.
Izu Vaisman 《Annals of Global Analysis and Geometry》2001,19(3):209-234
The transversal twistor space of a foliation
of an even codimension is the bundle
of the complex structures of the fibers of the transversalbundle of
. On
there exists a foliation
by covering spaces of the leaves of
, and any Bottconnection of
produces an ordered pair
of transversal almost complex structures of
. The existence of a Bott connection which yields a structure
1 that is projectable to the space of leaves isequivalent to the fact that
is a transversallyprojective foliation. A Bott connection which yields a projectablestructure
2 exists iff
isa transversally projective foliation which satisfies a supplementarycohomological condition, and, in this case,
1is projectable as well.
2 is never integrable.The essential integrability condition of
1 isthe flatness of the transversal projective structure of
. 相似文献
16.
We study a version of the Gauss map
for a surface
immersed in
and prove an analog of the Ruh--Vilms theorem which states that this map is harmonic iff
has a constant mean curvature. As a corollary, we conclude that an embedded flat torus
with constant mean curvature is a spherical Delonay surface. 相似文献
17.
We consider the extremal problem to determine the maximal number
of columns of a 0-1 matrix with
rows and at most
ones in each column such that each
columns are linearly independent modulo
. For fixed integers
and
, we shall prove the probabilistic lower bound
=
; for
a power of
, we prove the upper bound
which matches the lower bound for infinitely many values of
. We give some explicit constructions. 相似文献
18.
We obtain necessary and sufficient conditions for the solvability of the augmentation and modification problems of order
for Hermitian matrices. The augmentation problem consists in the construction of a Hermitian
-matrix with a given
-block
in block
-representation and with the prescribed eigenvalues. The modification problem consists in the construction of a Hermitian
-matrix
of rank not greater than
so that the obtained matrix, being added to a given Hermitian
-matrix
, will have the required spectrum. We give an estimate for the minimal number of different eigenvalues of the solutions to these problems. 相似文献
19.
If a regular graph of valence
and diameter
has
vertices, then
, which was proved by Moore (cf. [1]). Graphs for which this non-strict inequality turns into an equality are called Moore graphs. Such have an odd girth equal to
. The simplest example of a Moore graph is furnished by a
-triangle. Damerell proved that a Moore graph of valence
has diameter 2. In this case
, the graph is strongly regular with
and
, and the valence
is equal to 3 (Peterson's graph), to 7 (Hoffman–Singleton's graph), or to 57. The first two graphs are of rank 3. Whether a Moore graph of valence
exists is not known; yet, Aschbacher proved that the Moore graph with
will not be a rank 3 graph. We call the Moore graph with
the Aschbacher graph. Cameron showed that such cannot be vertex transitive. Here, we treat subgraphs of fixed points of Moore graph automorphisms and an automorphism group of the hypothetical Aschbacher graph for the case where that group contains an involution. 相似文献
20.
S. Yu. Orevkov 《Mathematical Notes》2000,68(5-6):588-593
Dehornoy constructed a right invariant order on the braid group B
n uniquely defined by the condition
1{\text{ if }}\beta _0 ,\beta _1$$
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are words in
. A braid is called strongly positive if
1$$
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for any
. In the present paper it is proved that the braid
is strongly positive if the word
does not contain
. We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity. 相似文献