共查询到20条相似文献,搜索用时 31 毫秒
1.
Slowly convergent infinite products
are considered, where
is a sequence of numbers, or a sequence of linear operators. Using an asymptotic expansion for the “remainder” of the infinite
product a method for convergence acceleration is suggested. The method is in the spirit of the d-transformation for series. It is very simple and efficient for some classes of sequences
. For complicated sequences
it involves the solution of some linear systems, but it is still effective.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
We show that the zeros of the hypergeometric polynomials
,
, cluster on the loop of the lemniscate
as
. We also state the equations of the curves on which the zeros of
, lie asymptotically as
. Auxiliary results for the asymptotic zero distribution of other functions related to hypergeometric polynomials are proved,
including Jacobi polynomials with varying parameters and associated Legendre functions. Graphical evidence is provided using
Mathematica.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
Let
denote the unit sphere in
and
the geodesic distance in
. A spherical‐basis function approximant is a function of the form
, where
are real constants,
is a fixed function, and
is a set of distinct points in
. It is known that if
is a strictly positive definite function in
, then the interpolation matrix
is positive definite, hence invertible, for every choice of distinct points
and every positive integer M. The paper studies a salient subclass of such functions
, and provides stability estimates for the associated interpolation matrices.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
Let ℂ denote the complex numbers and
denote the ring of complex-valued Laurent polynomial functions on ℂ\{0}. Furthermore, we denote by
the subsets of Laurent polynomials whose restriction to the unit circle is real, nonnegative, respectively. We prove that
for any two Laurent polynomials
, which have no common zeros in ℂ\{0} there exists a pair of Laurent polynomials
satisfying the equation Q
1
P
1 + Q
2
P
2 = 1. We provide some information about the minimal length Laurent polynomials Q
1 and Q
2 with these properties and describe an algorithm to compute them. We apply this result to design a conjugate quadrature filter
whose zeros contain an arbitrary finite subset Λ⊂ℂ\{0} with the property that for every
implies
and
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
E. S. Dubtsov 《Journal of Mathematical Sciences》2001,107(4):4002-4021
Let K be a compact space, let X be a closed subspace of C(K), and let
be a positive measure on K. The triple
is said to be regular if, for any positive function
and for any
, there exists a function
such that
on K and
. The case where K is the unit sphere in
and the subspace X is invariant with respect to the unitary group is investigated. Sufficient spectral conditions and a necessary condition for the regularity of a triple are obtained. Connections with compactness of certain Hankel operators and applications to interpolation problems are presented. Bibliography: 16 titles. 相似文献
6.
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
7.
The following assertion is proved. Let
be the set of integers the number of the prime power of which is
. Let
be the size of
. Then for each irrational
, uniformly in
, \begin{equation*} \frac{1}{\pi_k(x)} \bigg|\sum _{\alul{n\le x}{n\in\cN_k}} f(n) e^{2\pi in\alpha}\bigg|\to 0, \end{equation*}
where
is an arbitrary multiplicative function with
,
is a positive constant.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
8.
We consider a Skorohod map
which takes paths in
to paths which stay in the positive orthant
. We let
be the domain of definition of
. A convex and lower semi-continuous function
and a set
are given. We are concerned with the calculation of the infimum of the value
for t ⩾ 0 and absolutely continuous
subject to the conditions
and
. We show that such minimization problems characterize large deviation asymptotics of tail probabilities of the steady-state
distribution of certain reflected processes. We approximate the infimum by a sequence of finite-dimensional minimization problems.
This approximation allows to formulate an algorithm for the calculation of the infimum and to derive analytical bounds for
its value. Several applications are discussed including large deviations of generalized processor sharing and large deviations
of heavily loaded queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
§1 Introduction and preliminariesA set T Rn×Rnis called a monotone operator on Rn,if T has the property(x,y) ,(x′,y′)∈T 〈x -x′,y -y′〉≥0 ,where〈·,·〉denotes the inner product on Rn.T is maximal if(considered as a graph) itis not strictly contained in any other monotone operator on Rn.It is well known that thetheory of maximal monotone operators plays an important role in the study of convexprogramming and variational inequalities since itcan provide a powerful general framework… 相似文献
10.
Suppose that
,
, and
are three discrete probability distributions related by the equation (E):
, where
denotes the k-fold convolution of
In this paper, we investigate the relation between the asymptotic behaviors of
and
. It turns out that, for wide classes of sequences
and
, relation (E) implies that
, where
is the mean of
. The main object of this paper is to discuss the rate of convergence in this result. In our main results, we obtain O-estimates and exact asymptotic estimates for the difference
. 相似文献
11.
Crossed Modules and Quantum Groups in Braided Categories 总被引:2,自引:0,他引:2
Yu. N. Bespalov 《Applied Categorical Structures》1997,5(2):155-204
Let A be a Hopf algebra in a braided category
. Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category
of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group
the corresponding braided category of modules
is identified with a full subcategory in
. The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized. 相似文献
12.
A. N. Petrov 《Journal of Mathematical Sciences》2001,107(4):4067-4072
A new numerical inequality for average power means is presented. Let
and let
be a sequence of positive numbers. Consider the operator
. We denote by
the superposition of these operators. The following assertion is proved: if
. Bibliography: 2 titles. 相似文献
13.
Let Δ(1) be the uniform three direction mesh of the plane whose vertices are integer points of
.Let
(respectively
of degree d=3r (respectively d=3r+1 ) for r odd (respectively even) on the triangulation
, and of degree d=2r (respectively d=2r+1) for r odd (respectively even) on the triangulation
. Using linear combinations of translates of these splines we obtain Lagrange interpolants whose corresponding order of approximation
is optimal.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
14.
Let n be a positive integer, let
be complex numbers and let
be a nonsingular n × n complex Toeplitz matrix. We present a superfast algorithm for computing the determinant of T. Superfast means that the arithmetic complexity of our algorithm is
, where N denotes the smallest power of 2 that is larger than or equal to n. We show that det T can be computed from the determinant of a certain coupled Vandermonde matrix. The latter matrix is related to a linearized
rational interpolation problem at roots of unity and we show how its determinant can be calculated by multiplying the pivots
that appear in the superfast interpolation algorithm that we presented in a previous publication.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
We show that every sub-weak embedding of any singular (degenerate or not) orthogonal or unitary polar space of non-singular rank at least 3 in a projective space PG
,
a commutative field, is the projection of a full embedding in some subspace PG
of PG
, where PG
contains PG
and
is a subfield of
. The same result is proved in the symplectic case under the assumption that the field over which the polarity is defined is perfect if the characteristic is 2 and if each secant line of the embedded polar space contains exactly two points of . This completes the classification of all sub-weak embeddings of orthogonal, symplectic and unitary polar spaces (singular or not; degenerate or not) of non-singular rank at least 3 and defined over a commutative field
, where in the characteristic 2 case
is perfect if the polar space is symplectic and the degree of the embedding is 2. 相似文献
16.
Dražen Adamović 《Algebras and Representation Theory》2004,7(4):457-469
Let
be the affine Lie algebra associated to the simple finite-dimensional Lie algebra
. We consider the tensor product of the loop
-module
associated to the irreducible finite-dimensional
-module V() and the irreducible highest weight
-module L
k,. Then L
k, can be viewed as an irreducible module for the vertex operator algebra M
k,0. Let A(L
k,) be the corresponding
-bimodule. We prove that if the
-module
is zero, then the
-module
is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras. 相似文献
17.
We prove new pointwise inequalities involving the gradient of a function
, the modulus of continuity
of the gradient
, and a certain maximal function
and show that these inequalities are sharp. A simple particular case corresponding to
and
is the Landau type inequality
, where the constant 8/3 is best possible and
. 相似文献
18.
O. M. Fomenko 《Journal of Mathematical Sciences》2003,118(1):4910-4917
Let
be the Hecke eigenbasis of the space
of
-cusp forms of weight 2. Let p be a prime. Let
be the Hecke L-series of form
. The following statements are proved:
and
We also give a correct proof of a previous author's theorem on automorphic L-functions. Bibliography: 12 titles. 相似文献
19.
Jet Wimp 《Numerical Algorithms》2000,24(1-2):179-193
In this paper we investigate Hankel determinants of the form
, where c
n
(t) is one of a number of polynomials of combinatorial interest. We show how some results due to Radoux may be generalized,
and also show how “stepped up” Hankel determinants of the form
may be evaluated.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
Solutions
of a semilinear elliptic boundary value problem,
(with
bounded below) can be put into a one-to-one correspondence with zeros
of a function
. Often d is small. The function
is called the bifurcation function. It can also be shown that the eigenvalues of the matrix
characterize the stability properties of the solutions of the elliptic problem as rest points of
. A finite element method that can be used for computing B and B
c has recently been proposed. An overview of these results and the finite element method is given.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献