共查询到20条相似文献,搜索用时 31 毫秒
1.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
where dx denotes theLebesgue measure on
and > 0. Let T
be the convolution operator
and let
Assume that, for x 0, the followingtwo conditions hold:
vanishes only at h = 0 and
. In this paper we show that if
then E
is the empty set and if
then E
is the closed segment withendpoints
and
. Also, we give some examples. 相似文献
2.
Let
be a semisimple Lie algebra overk, an algebraically closed field of characteristic zero, and let
be a Cartan subalgebra inside a Borel subalgebra of
. LetU be the enveloping algebra of
. For
letM() denote the corresponding Verma modúle and letU
u=U/AnnM(). LetW be the Weyl group and letW
0
be the stabiliser of inW. We prove the following theorem, which affirms a conjecture of T.J. Hodges.Oblatum 16-XII-1994 相似文献
3.
Let
be a continuous semimartingale and let
be a continuous function of bounded variation. Setting
and
suppose that a continuous function
is given such that F is C1,2 on
and F is
on
. Then the following change-of-variable formula holds:
where
is the local time of X at the curve b given by
and
refers to the integration with respect to
. A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping. 相似文献
4.
Wilhelm Forst 《Numerische Mathematik》1978,30(2):137-147
Summary Letx
0<x
1<...<x
n–1<x
0+2 be nodes having multiplicitiesv
0,...,v
n–1, 1v
k
r (0k<n). We approximate the evaluation functional
,x fixed, and the integral respectively by linear functionals of the form
and determine optimal weights
for the Favard classesW
r
C
2. In the even case
of optimal interpolation these weights are unique except forr=1,x(x
k
+x
k–1)/2 mod 2. Moreover we get periodic polynomial splinesw
k, j
(0k<n, 0j<v
k
) of orderr such that
are the optimal weights. Certain optimal quadrature formulas are shown to be of interpolatory type with respect to these splines. For the odd case
of optimal interpolation we merely have obtained a partial solution.
Bojanov hat in [4, 5] ähnliche Resultate wie wir erzielt. Um Wiederholungen zu vermeiden, werden Resultate, deren Beweise man bereits in [4, 5] findet, nur zitiert 相似文献
5.
Helena Ferreira 《Extremes》2000,3(4):385-392
Let
be a sequence of identically distributed variables. We study the asymptotic distribution of
, where Y
[r:n] denotes the concomitant of the rth order statistic X
r:n
, corresponding to
, and
is held fixed while
. Conditions are given for the
and
to have the same asymptotic behavior as that we would apply if
were i.i.d. The result is illustrated with a simple linear regression model
, where
is a stationary sequence with extremal index
. 相似文献
6.
Yu. V. Nagrebetskaya 《Algebra and Logic》2000,39(6):396-406
We study into the question of whether some rings and their associated matrix rings have equal decidability boundaries in the scheme and scheme-alternative hierarchies. Let
be a decidability boundary for an algebraic system A; w.r.t. the hierarchy H. For a ring R, denote by
an algebra with universe
. On this algebra, define the operations + and in such a way as to extend, if necessary, the initial matrices by suitably many zero rows and columns added to the underside and to the right of each matrix, followed by ordinary addition and multiplication of the matrices obtained. The main results are collected in Theorems 1-3. Theorem 1 holds that if R is a division or an integral ring, and R has zero or odd characteristic, then the equalities
hold for any n1. And if R is an arbitrary associative ring with identity then
for any n 1 and i,j { 1,..., n}, where e
ij
is a matrix identity. Theorem 2 maintains that if R is an associative ring with identity then
. Theorem 3 proves that
for any n 1. 相似文献
7.
Let
be the j-fold iterated function of
. Let
and > 0 be fixed, Q be a prime, and let N
k(Q|x) denote the number of those nx for which Q
. We give the asymptotics of N
k(Q|x) in the range
. 相似文献
8.
H. Fiedler 《Numerische Mathematik》1987,51(5):571-581
Summary Interpolatory quadrature formulae consist in replacing
by
wherep
f
denotes the interpolating polynomial off with respect to a certain knot setX. The remainder
may in many cases be written as
wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP
X
(t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis. 相似文献
9.
Let = (1,...,d) be a vector with positive components and let D be the corresponding mixed derivative (of order j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that
and
for all
Moreover, if
is the least possible value of the exponent in this inequality, then
Deceased.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 579–594, May, 2004. 相似文献
10.
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
11.
We obtain new unimprovable Kolmogorov-type inequalities for differentiable periodic functions. In particular, we prove that, for r = 2, k = 1 or r = 3, k = 1, 2 and arbitrary q, p [1, ], the following unimprovable inequality holds for functions
:
where
and
r
is the perfect Euler spline of order r. 相似文献
12.
Let w() be a positive weight function on the unit circle of the complex plane. For a sequence of points {
k
}
k = 1
included in a compact subset of the unit disk, we consider the orthogonal rational functions
n
that are obtained by orthogonalization of the sequence { 1, z / 1, z
2 / 2, ... } where
, with respect to the inner product
In this paper we discuss the behaviour of
n
(t) for t = 1 and n under certain conditions. The main condition on the weight is that it satisfies a Lipschitz–Dini condition and that it is bounded away from zero. This generalizes a theorem given by Szeg in the polynomial case, that is when all
k
= 0. 相似文献
13.
We present some comments on the behavior of solutions of the difference equation
where p
i 0, i = 1,..., k, k N, and x
–k
,..., x
–1 R. 相似文献
14.
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
15.
Noboru Hamada 《Designs, Codes and Cryptography》1997,10(1):41-56
Let k and d be any integers such that k 4 and
. Then there exist two integers and in {0,1,2} such that
. The purpose of this paper is to prove that (1) in the case k 5 and (,) = (0,1), there exists a ternary
code meeting the Griesmer bound if and only if
and (2) in the case k 4 and (,) = (0,2) or (1,1), there is no ternary
code meeting the Griesmer bound for any integers k and d and (3) in the case k 5 and
, there is no projective ternary
code for any integers k and such that 1k-3, where
and
for any integer i 0. In the special case k=6, it follows from (1) that there is no ternary linear code with parameters [233,6,154] , [234,6,155] or [237,6,157] which are new results. 相似文献
16.
Define
, where
is a symmetric U-type statistic, H
k() is the Hermite polynomial of degree k, and {X, X
n, n1} are independent identically distributed binary random variables with Pr(X{–1, 1}})=1. We show that
according as EX=0 or EX0, respectively. 相似文献
17.
Let G be a finite group,
a normal subgroup, p a prime,
a finite splitting field of characteristic p for
G and
We prove that
is a splitting field for N, using the action
of the Galois group of the field extension
on the irreducible representations of N.
As
is a splitting field for the symmetric group
Sn
we get as a corollary that
is a splitting field for the alternating group
An.
Received: 31 July 2003 相似文献
18.
S. L. Ma 《Graphs and Combinatorics》1989,5(1):355-361
LetG be a group of finite order andD
0 = {e},D
1,...,D
d
be a partition ofG. Suppose{d
–1|d D
i
} =D
i, i {0, 1,..., d}, for eachi {0, 1,..., d}; and
for alli, j where
. Then the subalgebra spanned by
is called a Schur ring overG. It is known that such a partitionD
0,D
1,...,D
d
can be used to construct an association scheme of classd. In this paper, we obtain a complete classification for the case whenG is cyclic andd = 3. The result corresponds to a complete classification of cyclic association schemes of class three. 相似文献
19.
Vladimir I. Koltchinskii 《Journal of Theoretical Probability》1998,11(3):645-699
Let H be a map from a set SR
d
to R
d
. For tR
d
let
H
(t) denote the distance from t to the set H(S). Consider sequences {s
n}
n1 in S such that
. Any limit point of any such sequence (finite or infinite) is considered as a possible value of the inverse H
–1(t). Any map
defined in such a way will be called an SC-inverse (a selected closest inverse) to H. In the paper we study differentiability of the nonlinear operator
at H=G, where G is a one-to-one map from S onto a set TR
d
with good analytic properties (specifically, a diffeomorphism). We establish compact differentiability of this operator tangentially to continuous functions and introduce a family of norms such that it is Fréchet differentiable with respect to them. We also obtain optimal bounds for the remainder of the differentiation, extending to the multivariate case recent results of Dudley. These differentiability results are applied to random maps
, which could be statistical estimators of an unknown map G. For a function J on R
d
, let (J)
T
be its restriction to T. It is shown that for a diffeomorphism G and for an increasing sequence of positive numbers {a
n
}
n1 weak convergence of the sequence {a
n
(G
n
– G)}
n1 (locally in S) is equivalent to weak convergence of the sequence
(locally in T) along with the convergence of the sequence
to 0 in probability (locally uniformly in S). The equivalence holds for all SC-inverses
and all double SC-inverses
and it extends to the multivariate case a theorem of Vervaat. Moreover, each of these equivalent statements implies a kind of Taylor expansion of the SC-inverse
at G (locally uniformly in T)
where inv(A) denotes the inverse of a nonsingular linear transformation A in R
d
. Such limit theorems for functional inverses can be used to study asymptotic behavior of statistical estimators defined implicitly (as solutions of equations involving the empirical distribution P
n
). We show how to apply this approach to get asymptotic normality of M-estimators in the multivariate case under minimal assumptions. We consider an extension of the quantile function to the multivariate case related to M-parameters of a distribution P in R
d
(an M-quantile function)and use limit theorems for functional inverses to study limit behavior of the empirical M-quantile process. We also show how to use these theorems to study asymptotics of regression quantiles. 相似文献
20.
It is shown that the set [G,] of immersed linear networks in
that are parallel to a given immersed linear network
and have the same boundary as is a convex polyhedral subset of the configuration space of movable vertices of the graph G. The dimension of [G,] is calculated, and the number of its maximal faces is estimated. As an application, the spaces of all locally minimal and weighted minimal networks with fixed boundary and topology in
are described. Bibliography: 21 titles. 相似文献