共查询到20条相似文献,搜索用时 15 毫秒
1.
Jianqiang Zhao 《The Ramanujan Journal》2007,14(2):189-221
For every positive integer d we define the q-analog of multiple zeta function of depth d and study its properties, generalizing the work of Kaneko et al. who dealt with the case d=1. We first analytically continue it to a meromorphic function on ℂ
d
with explicit poles. In our Main Theorem we show that its limit when q
↑1 is the ordinary multiple zeta function. Then we consider some special values of these functions when d=2. At the end of the paper we also propose the q-analogs of multiple polylogarithms by using Jackson’s q-iterated integrals and then study some of their properties. Our definition is motivated by those of Koornwinder and Schlesinger
although theirs are slightly different from ours.
Partially supported by NSF grant DMS0139813 and DMS0348258. 相似文献
2.
Xueyan Xiang Qian He Wenshan Yang 《分析论及其应用》2007,23(3):243-254
Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein polynomials and their Boolean sum are estimated. Moreover, the saturation of {Bn(., qn)} when n → ∞ and convergence rate of Bn(f,q;x) when f ∈ C^n-1 [0, 1], q → ∞ are also presented. 相似文献
3.
We prove a new relation for the multiple q-zeta values (MqZV’s). It is a q-analogue of the Ohno-Zagier relation for the multiple zeta values (MZV’s). We discuss the problem of determining the dimension
of the space spanned by MqZV’s over ℚ, and present an application to MZV.
The first author is supported by Grant-in-Aid for Young Scientists (B) No. 17740026 and the second author is supported by
Grant-in-Aid for Young Scientists (B) No. 17740089. 相似文献
4.
Jianqiang Zhao 《数学学报(英文版)》2008,24(10):1593-1616
In this paper, we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq (s1,..., Sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (Renormalization of Multiple Zeta Values, arxiv: math/0606076v3). We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζq(S1,..., sd) (i.e., s1 ≤ 1). Moreover, when q ↑ 1 our renormalizations agree with those of Guo and Zhang. 相似文献
5.
Sofiya Ostrovska 《Numerical Algorithms》2007,44(1):69-82
Since in the case q > 1, q-Bernstein polynomials are not positive linear operators on C[0,1], the study of their approximation properties is essentially more difficult than that for 0<q<1. Despite the intensive research conducted in the area lately, the problem of describing the class of functions in C[0,1] uniformly approximated by their q-Bernstein polynomials (q > 1) remains open. It is known that the approximation occurs for functions admit ting an analytic continuation into a disc
{z:|z| < R}, R > 1. For functions without such an assumption, no general results on approximation are available. In this paper, it is shown
that the function f(x) = ln (x + a), a > 0, is uniformly approximated by its q-Bernstein polynomials (q > 1) on the interval [0,1] if and only if a ≥ 1.
相似文献
6.
Let n,p and k be three non negative integers. We prove that the apparently rational fractions of q:
are actually polynomials of q with non negative integer coefficients. This generalizes a recent result of Lassalle (Ann. Comb. 6(3–4), 399–405, 2002),
in the same way as the classical q-binomial coefficients refine the ordinary binomial coefficients.
相似文献
7.
Helmut Prodinger 《Annals of Combinatorics》2007,11(2):213-225
Salié permutations are defined to be first alternating, and then monotone. We q-enumerate them by considering words (instead of permutations), equipped with geometric probabilities.
Received May 26, 2005 相似文献
8.
Yu Can ZHU 《数学学报(英文版)》2007,23(9):1707-1718
In this paper, we introduce the concepts of q-Besselian frame and (p, σ)-near Riesz basis in a Banach space, where a is a finite subset of positive integers and 1/p+1/q = 1 with p 〉 1, q 〉 1, and determine the relations among q-frame, p-Riesz basis, q-Besselian frame and (p, σ)-near Riesz basis in a Banach space. We also give some sufficient and necessary conditions on a q-Besselian frame for a Banach space. In particular, we prove reconstruction formulas for Banach spaces X and X^* that if {xn}n=1^∞ C X is a q-Besselian frame for X, then there exists a p-Besselian frame {y&*}n=1^∞ belong to X^* for X^* such that x = ∑n=1^∞ yn^*(x)xn for all x ∈ X, and x^* =∑n=1^∞ x^*(xn)yn^* for all x^* ∈ X^*. Lastly, we consider the stability of a q-Besselian frame for the Banach space X under perturbation. Some results of J. R. Holub, P. G. Casazza, O. Christensen and others in Hilbert spaces are extended to Banach spaces. 相似文献
9.
Using the theory of Macdonald polynomials, a number of q-integrals of Selberg type are proved.
2000 Mathematics Subject Classification: Primary—33D05, 33D52, 33D60 相似文献
10.
Hiro-aki Narita 《Mathematische Zeitschrift》2008,259(3):591-615
Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by “Kudla lifting”, i.e. a theta lifting from elliptic modular forms to holomorphic
automorphic forms on SU(1,q). We prove that the images of Arakawa’s theta lifting belong to the space of bounded automorphic forms generating quaternionic
discrete series, which are non-holomorphic forms. In the appendix we provide the construction of Eisenstein series and Poincaré series generating such discrete series.
The author was partially supported by JSPS Research Fellowships for Young Scientist for April 2002 to March 2005. The results
of this paper were obtained in this period. 相似文献
11.
Norman L. Johnson 《Designs, Codes and Cryptography》2008,46(2):127-136
New subgeometry partitions of PG(n − 1, q
m
) by subgeometries isomorphic to PG(n − 1, q) are constructed.
相似文献
12.
The paper deals with positive linear operators based on q-integer. The rate of convergence of these operators is established. For these operators, we present Voronovskaya-type theorems
and apply them to q-Bernstein polynomials and q-Stancu operators. 相似文献
13.
Wolter Groenevelt 《Constructive Approximation》2009,29(1):85-127
Big q-Jacobi functions are eigenfunctions of a second-order q-difference operator L. We study L as an unbounded self-adjoint operator on an L
2-space of functions on ℝ with a discrete measure. We describe explicitly the spectral decomposition of L using an integral transform ℱ with two different big q-Jacobi functions as a kernel, and we construct the inverse of ℱ.
相似文献
14.
Nazim Mahmudov 《Numerical Algorithms》2010,53(4):439-450
In this note we give the estimates of the central moments for q-Bernstein operators (0 < q < 1) which can be used for studying the approximation properties of the operators. 相似文献
15.
Zhi Yuan HUANG Pei Yan LI Ying WU 《数学学报(英文版)》2008,24(2):201-214
The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters: c1, c2,γ and β. In this paper, for-1 〈q〈 1, we obtain a unified explicit form of q-deformed Levy-Meixner polynomials and their generating functions in term of c1, c2, γand β, which is shown to be a reasonable interpolation between classical case (q=1) and fermionic case (q=-1).In particular, when q=0 it's also compatible with the free case. 相似文献
16.
Let Bn( f,q;x), n=1,2,… be q-Bernstein polynomials of a function f : [0,1]→C. The polynomials Bn( f,1;x) are classical Bernstein polynomials. For q≠1 the properties of q-Bernstein polynomials differ essentially from those in the classical case. This paper deals with approximating properties of q-Bernstein polynomials in the case q>1 with respect to both n and q. Some estimates on the rate of convergence are given. In particular, it is proved that for a function f analytic in {z: |z|<q+} the rate of convergence of {Bn( f,q;x)} to f(x) in the norm of C[0,1] has the order q−n (versus 1/n for the classical Bernstein polynomials). Also iterates of q-Bernstein polynomials {Bnjn( f,q;x)}, where both n→∞ and jn→∞, are studied. It is shown that for q(0,1) the asymptotic behavior of such iterates is quite different from the classical case. In particular, the limit does not depend on the rate of jn→∞. 相似文献
17.
In this paper, we propose approximations to compute the steady-state performance measures of the M/GI/N+GI queue receiving Poisson arrivals with N identical servers, and general service and abandonment-time distributions. The approximations are based on scaling a single
server M/GI/1+GI queue. For problems involving deterministic and exponential abandon times distributions, we suggest a practical way to compute
the waiting time distributions and their moments using the Laplace transform of the workload density function. Our first contribution
is numerically computing the workload density function in the M/GI/1+GI queue when the abandon times follow general distributions different from the deterministic and exponential distributions.
Then we compute the waiting time distributions and their moments. Next, we scale-up the M/GI/1+GI queue giving rise to our approximations to capture the behavior of the multi-server system. We conduct extensive numerical
experiments to test the speed and performance of the approximations, which prove the accuracy of their predictions.
相似文献
18.
By using two operators representable by Jacobi matrices, we introduce a family of q-orthogonal polynomials, which turn out to be dual with respect to alternative q-Charlier polynomials. A discrete orthogonality relation and the completeness property for these polynomials are established.
__________
Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 614–621, May, 2005. 相似文献
19.
Jian-Wen Peng 《Journal of Global Optimization》2007,39(3):441-457
In this paper, we introduce and study a new system of variational inclusions with (A, η, m)-accretive operators which contains variational inequalities, variational inclusions, systems of variational inequalities
and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (A, η, m)-accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multi-step iterative
algorithm for this system of variational inclusions in real q-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature.
相似文献
20.
Thomas Vougiouklis 《数学学报(英文版)》2008,24(7):1067-1078
The hyperoperations, called theta-operations (δ), are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures. 相似文献