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1.
Let E be a normed space,
and
. Let
. We give some exact formulas for 7#x03C4;. 相似文献
2.
Let
be i.i.d. random variables and let, for each
and
. It is shown that
a.s. whenever the sequence of self-normalized sums S
n
/V
n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if
相似文献
3.
Suppose that
(j) is the lag-j autocorrelation of the squared residuals computed from a realization of length n under the assumption that the observations follow a GARCH(1,1) model. We study the asymptotic distribution of the statistics of the form
, where the j are nonnegative summable weights and the matrix
, can be estimated from the data. We show that, under weak assumptions on model errors, the statistic Q
n converges in distribution to
, where the N
i are iid standard normal. We discuss choices of the weights j for which the distribution of Q is tabulated. Our results lead to and provide a rigorous justification for Portmanteau goodness-of-fit tests for GARCH(1,1) specification. 相似文献
4.
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
5.
In this paper we show that if X is an s-distance set in
m
and X is on
p concentric spheres then
Moreover if
X is antipodal, then
. 相似文献
6.
In this paper we prove that if
is a set of
k positive integers and
{A
1,
..., A
m
} is a family of subsets
of an n-element set
satisfying
, for all 1
i <
j m, then
. The case
k = 1 was proven 50 years ago
by Majumdar. 相似文献
7.
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
8.
A. N. Frolov 《Journal of Mathematical Sciences》2002,109(6):2229-2240
Let
be a sequence of independent equidistributed random vectors with
. Let
, where
and
denotes the indicator function of the event in brackets. If, for example,
are the gains and
are the indicators of success in repetitions of a game of chance, then
is the maximal gain along head runs (sequences of successes without interruptions) of length j. We investigate the asymptotic behavior of the values
,
, where
is the length of the longest head run in
. We show that the asymptotics of the values
depend significantly on the growth rate of j and that these asymptotics vary from the strong noninvariance (as in the ErdsRéenyi law of large numbers) to the strong invariance (as in the CsöorgRévész strong approximation laws). We also consider the Shepp-type statistics. Bibliography: 17 titles. 相似文献
9.
Soichi Okada 《Journal of Algebraic Combinatorics》1993,2(2):155-176
An alternating sign matrix is a square matrix whose entries are 1, 0, or –1, and which satisfies certain conditions. Permutation matrices are alternating sign matrices. In this paper, we use the (generalized) Littlewood's formulas to expand the products
and
2 as sums indexed by sets of alternating sign matrices invariant under a 180° rotation. If we put t = 1, these expansion formulas reduce to the Weyl's denominator formulas for the root systems of type B
n and C
n. A similar deformation of the denominator formula for type D
n is also given. 相似文献
10.
Václav Tryhuk 《Czechoslovak Mathematical Journal》2000,50(3):509-518
The paper describes the general form of an ordinary differential equation of the order n + 1 (n 1) which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form
where
are given functions,
is solved on
. 相似文献
11.
We consider the quadratic formsQ
X
j
X
k+
(X
j
2
-E
X
j
2
)where X
j
are i.i.d. random variables with finite sixth moment. For a large class of matrices (a
jk
) the distribution of Q can be approximated by the distribution of a second order polynomial in Gaussian random variables. We provide optimal bounds for the Kolmogorov distance between these distributions, extending previous results for matrices with zero diagonals to the general case. Furthermore, applications to quadratic forms of ARMA-processes, goodness-of-fit as well as spacing statistics are included. 相似文献
12.
By combinatorial means the authors show the existence of thin sub-sets of primes, useful for Goldbach decompositions. For example, there is a set
of primes with
, such that all butO(x(ln x)–A) even integersnx can be written as
. 相似文献
13.
For a non-decreasing integer sequence a=(a1,...,an) we define La to be the set of n-tuples of integers = (1,...,n) satisfying
. This generalizes the so-called lecture hall partitions corresponding to ai=i and previously studied by the authors and by Andrews. We find sequences a such that the weight generating function for these a-lecture hall partitions has the remarkable form
In the limit when n tends to infinity, we obtain a family of identities of the kind the number of partitions of an integer m such that the quotient between consecutive parts is greater than is equal to the number of partitions of m into parts belonging to the set P, for certain real numbers and integer sets P. We then underline the connection between lecture hall partitions and Ehrhart theory and discuss some reciprocity results. 相似文献
14.
This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any
-minihyper, with
, where
, is the disjoint union of
points,
lines,...,
-dimensional subspaces. For q large, we improve on this result by increasing the upper bound on
non-square, to
non-square,
square,
, and (4) for
square, p prime, p<3, to
. In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry
. For the coding-theoretical problem, our results classify the corresponding
codes meeting the Griesmer bound. 相似文献
15.
E. P. Golubeva 《Journal of Mathematical Sciences》2004,122(6):3603-3607
A number of results on the average values of the class numbers of indefinite binary quadratic forms with discriminants divisible by a large square are proved. The main result is as follows. Let d = 4n
2 + 1. Then
where h(d) is the class number for the discriminant d and
means that the summation is performed over the square-free d only. Bibliography: 9 titles. 相似文献
16.
A celebrated result of Johnson, Maurey, König and Retherford from 1977 states that for
every complex
matrix
satisfies the following eigenvalue estimate:
Based on the concept of entropy numbers and a simple product trick we give a selfcontained elementary proof. 相似文献
17.
Markov- and Bernstein-Type Inequalities for Polynomials with Restricted Coefficients 总被引:1,自引:0,他引:1
The Markov-type inequality
is proved for all polynomials of degree at most n with coefficients from {-1,0,1} with an absolute constant c. Here ·[0,1] denotes the supremum norm on [0,1]. The Bernstein-type inequality
is shown for every polynomial p of the form
The inequality
is also proved for every analytic function p on the open unit disk D that satisfies the growth condition
相似文献
18.
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
19.
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
20.
J. Sunklodas 《Lithuanian Mathematical Journal》2001,41(3):292-305
We derive lower bounds for Lp norms
, in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments. 相似文献