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1.
A (k,n)-arc in PG(2,q) is usually defined to be a set
of k points in the plane such that some line meets
in n points but such that no line meets
in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow
to be a multiset, that is, permit
to contain multiple points. The case k=q
2+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q
2+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q
2+q+2 and minimum distance q
2. Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q
2+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem. 相似文献
2.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
3.
Sufficient conditions are established for the oscillation of proper solutions of the system
where f
i
:+ × 2m (i=1,2) satisfy the local Carathéodory conditions and
i
,
i
:+ +(i=1,...,m) are continuous functions such that
i
(t) t for
. 相似文献
4.
Let p>q and let G be the group U(p, q) or Spin0(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup
where
Let be a one-dimensional character of M and an irreducible representation of U with highest weight . Let
be the representation of P which is trivial on N and
. Let I
p,q be the Harish-Chandra module of the induced representation
. In this paper, we shall determine (i) the reducibility of I
p,q, (ii) the K-types of all the irreducible subquotients of I
p,q when it is reducible, where K is the maximal compact subgroup of G, (iii) the module diagram of I
p,q (from which one can read off the composition structure), and (iv) the unitarity of I
p,q and its subquotients. Except in the cases q=p–1 and q=1, I
p,q is not K-multiplicity free. 相似文献
5.
We study Banach spaces of the form
We call such a space a p-space, p[1,), if for every k the space
is isomorphic to pk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces r in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that i ni
1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c
0 is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if nkm1/pkm-1/pkm-1 increases to infinity for a subsequence (nkm) , then 1 embeds into X. We also investigate complemented minimality for the class of spaces
where
is either a subsequence of the sequence of Schreier classes (
n)n N or a subsequence of (
n)n N. 相似文献
6.
Sjoerd E. Crans 《K-Theory》2003,28(1):39-105
Let
be n-dimensional teisi, i.e., higher-dimensional Gray-categorical structures. The following questions can be asked. Does a left q-transfor
, i.e., a functor 2
q
, induce a right q-transfor
, i.e., a functor
More generally, does a functor
induce a functor
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a q-transfor
, for appropriate k-arrows
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a (q + k + 1)-transfor
, for appropriate k-arrows
I give answers to these questions in the cases where n-dimensional teisi and their tensor product have been defined, i.e., for n 3, and for n up to 5 in some cases that do not need all data and axioms of n-dimensional teisi.I apply the above to compositions in teisi, in particular to braidings and syllepses. One of the results is that a braiding on a monoidal 2-category induces a pseudo-natural transformation
, where
is the reverse of ? –, which is almost, but not quite, equal to – ?. However, in higher dimensions need not be reversible, so a braiding on a higher-dimensional tas can not be seen as a transfor A B B A. 相似文献
7.
Takuya Hara 《Integral Equations and Operator Theory》1992,15(4):551-567
Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. 相似文献
8.
For 1/p+1/q1, we study the closed ideal
formed by the (c
o
,p,q)-summing operators. It turns out thatT:XY does not belong to
if and only if it factors the mapId:l
p
*l
q
. By localization, we get the ideal
that consists of those operatorsT for which all ultrapowersT
u
are contained in
. Operators in the complement of
are characterized by the property that they factor the mapsId:l
p
*n
l
q
n
uniformly. Our main tools are ideal norms.Supported by DFG grant PI 322/1-2 相似文献
9.
Joseph Rosenblatt 《Mathematische Annalen》1977,230(3):245-272
For a mean zero norm one sequence (f
n
)L
2[0, 1], the sequence (f
n
{nx+y}) is an orthonormal sequence inL
2([0, 1]2); so if
, then
converges for a.e. (x, y)[0, 1]2 and has a maximal function inL
2([0, 1]2). But for a mean zerofL
2[0, 1], it is harder to give necessary and sufficient conditions for theL
2-norm convergence or a.e. convergence of
. Ifc
n
0 and
, then this series will not converge inL
2-norm on a denseG
subset of the mean zero functions inL
2[0, 1]. Also, there are mean zerofL[0, 1] such that
never converges and there is a mean zero continuous functionf with
a.e. However, iff is mean zero and of bounded variation or in some Lip() with 1/2<1, and if |c
n
| = 0(n
–) for >1/2, then
converges a.e. and unconditionally inL
2[0, 1]. In addition, for any mean zerof of bounded variation, the series
has its maximal function in allL
p[0, 1] with 1p<. Finally, if (f
n
)L
[0, 1] is a uniformly bounded mean zero sequence, then
is a necessary and sufficient condition for
to converge for a.e.y and a.e. (x
n
)[0, 1]. Moreover, iffL
[0, 1] is mean zero and
, then for a.e. (x
n
)[0, 1],
converges for a.e.y and in allL
p
[0, 1] with 1p<. Some of these theorems can be generalized simply to other compact groups besides [0, 1] under addition modulo one. 相似文献
10.
Let
be an i.i.d. sequence of rotationally invariant random vectors in
. If X
12 is dominated (in the sense defined below) by Z2 for a rotationally invariant normal random vector Z in
, then for each k and
for p3 or p,n2 (resp. for 1p2, n3). The constant (
Zp)1/p is the best possible. The result applies, in particular, for variables uniformly distributed on the sphere S
n-1 or the ball B
n. In the case of the sphere, the best constant is
With this constant, the Khintchine type inequality in this case also holds for 1p2,n=2. 相似文献
11.
Let (, , ) be a complete measure space, L0 the vector lattice of -measurable real functions on , : L0 [0, )] a lattice semimodular,
the corresponding modular space, S0 the ideal generated by
and
0,{\text{ }}\exists {\text{ }}s \in {\text{ }}S_{\text{0}} {\text{ such that }}\rho \left( {\frac{{x - s}}{\user1{\lambda }}} \right) < \infty } \right\}$$
" align="middle" border="0">
. In X consider the distance
0:\rho \left( {\frac{{x - y}}{\user1{\lambda }}} \right) \leqq \user1{\lambda }} \right\}$$
" align="middle" border="0">
and, if is convex, the distances dL, do subordinated to the Luxemburg and Amemiya-Orlicz norms, respectively. We give necessary and sufficient conditions for H(So) in order to be proximinal in X with the distances d, dL and do. 相似文献
12.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
13.
We compare the two recently introduced semidirect product operations
*r and
*rr within the lattice of e-varieties of locally inverse
semigroups. For each e-variety
which
contains all rectangular bands and is properly contained in the e-variety of all completely
simple semigroups, the inclusions
are proved where
is the e-variety of all semilattices and
the variety of all abelian
groups of exponent dividing q where q is any
integer greater than one. Some consequences for the class of finite locally inverse semigroups are also obtained. 相似文献
14.
Yutaka Hiramine 《Geometriae Dedicata》1993,48(2):139-189
In this paper we consider finite nets of orderq
2 and degreeq + 1 which admit GL(2,q). Our main result says that if a net
of orderq
2 and degreeq + 1 admits a collineation group with a point-regular normal subgroupT such that /T GL(2,q), then
is isomorphic to a regulus net, a twisted regulus net, a Hering net, or
. Except in the last one, each of them corresponds to a surface in PG(3,q) obtained from a homogeneous polynomial in two variables. 相似文献
15.
E. Getzler 《Compositio Mathematica》2002,132(2):121-135
We calculate the Euler characteristics of the local systems S
k
S
2
on the moduli space
2 of curves of genus 2, where
is the rank 4 local system R
1 *
. 相似文献
16.
Ganikhodzhaev N. N. Mukhamedov F. M. Rozikov U. A. 《Theoretical and Mathematical Physics》2002,130(3):425-431
We consider the Potts model on the set in the field Q
p of p-adic numbers. The range of the spin variables (n),
, in this model is
. We show that there are some values q=q(p) for which phase transitions occur. 相似文献
17.
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
18.
We consider the parabolic SPDE
with the Neuman boundary condition
and some initial condition.We use the Malliavin calculus in order to prove that, if the coefficients and are smooth and > 0, then the law of any vector (X(t,x1),..., X(t,xd)), 0 x1 ... xd 1, has a smooth, strictly positive density with respect to Lebesgue measure. 相似文献
19.
Letf be analytic in a hyperbolic region . The Bloch constant
f
off is defined by
, where (z)|dz| is the Poincaré metric in . Suppose is hyperbolic and
where
. Then for allf withf() , we have
f
1/(). In this paper we study the extremal functions defined by
f
=1/() and the existence of those functions.Supported by the National Natural Science Foundation of China. 相似文献
20.
V. Ostrik 《Transformation Groups》1997,2(3):279-287
We study the tensor category
of tilting modules over a quantum groupU
q
with divided powers. The setX
+ of dominant weights is a union of closed alcoves
numbered by the elementswW
f
of a certain subset of affine Weyl groupW. G. Lusztig and N. Xi defined a partition ofW
f
into canonical right cells and the right order
R
on the set of cells. For a cellAW
f
we consider a full subcategory
formed by direct sums of tilting modulesQ() with highest weights
. We prove that
is a tensor ideal in
, generalizing H. Andersen's theorem about the ideal of negligible modules which in our notations is nothing else then
. The proof is an application of a recent result by W. Soergel who has computed the characters of tilting modules.This material is based upon work supported by the U.S. Civilian Research and Development Foundation under Award No. RM1-265. 相似文献