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61.
For a strictly decreasing sequence an
n=0 of nonnegative real numbers converging to zero, we construct a continuous 2-periodic function f such that RT
n(f) = an, n=0,1,2,..., where RT
n(f) are best approximations of the function f in uniform norm by trigonometric rational functions of degree at most n. 相似文献
62.
Dunkl Operators for Complex Reflection Groups 总被引:3,自引:0,他引:3
Dunkl operators for complex reflection groups are defined inthis paper. These commuting operators give rise to a parameterizedfamily of deformations of the polynomial De Rham complex. Thisleads to the study of the polynomial ring as a module over therational Cherednik algebra, and a natural contravariantform on this module. In the case of the imprimitive complexreflection groups G(m, p, N), the set of singular parametersin the parameterized family of these structures is describedexplicitly, using the theory of non-symmetric Jack polynomials.2000 Mathematical Subject Classification: 20F55 (primary), 52C35,05E05, 33C08 (secondary). 相似文献
63.
This paper concerns the cubic smoothing spline approach to nonparametric regression. After first deriving sharp asymptotic formulas for the eigenvalues of the smoothing matrix, the paper uses these formulas to investigate the efficiency of different selection criteria for choosing the smoothing parameter. Special attention is paid to the generalized maximum likelihood (GML), C
p
and extended exponential (EE) criteria and their marginal Bayesian interpretation. It is shown that (a) when the Bayesian model that motivates GML is true, using C
p
to estimate the smoothing parameter would result in a loss of efficiency with a factor of 10/3, proving and strengthening a conjecture proposed in Stein (1990); (b) when the data indeed come from the C
p
density, using GML would result in a loss of efficiency of ; (c) the loss of efficiency of the EE criterion is at most 1.543 when the data are sampled from its consistent density family. The paper not only studies equally spaced observations (the setting of Stein, 1990), but also investigates general sampling scheme of the design points, and shows that the efficiency results remain the same in both cases.This work is supported in part by NSF grant DMS-0204674 and Harvard University Clark-Cooke Fund.
Mathematics Subject Classification (2000):Primary: 62G08; Secondary: 62G20 相似文献
64.
V. P. Lexin 《Acta Appl Math》2003,75(1-3):105-115
A special class of integrable Fuchsian systems on C
n
related to KZ equations is considered. We survey the construction of such systems and the list of the structural properties their monodromy representations. The relation of the Fuchsian systems obtained by the Veselov construction assosiated with a deformation of the A
n–1-type root system and the Gauss–Manin connection of the natural projection C
n
C
n–1 is described. In this case, we prove that the monodromy representation is equivalent to the Burau representation of the Artin braid group. For a deformations of the other root system, we introduce generalized Burau representations. We conjecture that the integrable Fuchsian systems related to essential new finite sets of the vectors described by Veselov and Chalykh are the result of the Klares–Schlesinger isomonodromic deformations (or transformation) of the integrable Fuchsian system related to the Coxeter root systems. 相似文献
65.
Piecewise quadratic trigonometric polynomial curves 总被引:6,自引:0,他引:6
Xuli Han. 《Mathematics of Computation》2003,72(243):1369-1377
Analogous to the quadratic B-spline curve, a piecewise quadratic trigonometric polynomial curve is presented in this paper. The quadratic trigonometric polynomial curve has continuity, while the quadratic B-spline curve has continuity. The quadratic trigonometric polynomial curve is closer to the given control polygon than the quadratic B-spline curve.
66.
Cindy de Volder 《Geometriae Dedicata》2001,85(1-3):237-251
We consider the blowing-up Y
k
of the projective plane along k general points P
1,...,P
k
. Let
k
: Y
k
2 be the projection map and E
i
the exceptional divisor corresponding to P
i
for 1ik. For m2 and km(m+3)/2–4 let
k
be the invertible sheaf
k
*(
2(m))
Y
k
(–E
1–···–E
k
) on Y
k
, and let k: Y
k
N
be the morphism corresponding to
k
. As
k
is a local embedding, the Gauss map
k
corresponding to
k
is defined on Y
k
by
k
(x)=(d
x
k
)(T
x
(Y
k
)) for all xY
k
. We prove that this Gauss map
k
is injective. 相似文献
67.
Ragheb M. Abu-Sarris 《Journal of Computational Analysis and Applications》2000,2(1):103-109
In this paper, we are concerned with the global behavior ofthe solutions of the difference equation
where
and
. Necessary and sufficient conditions for boundedness, persistence,and periodicity of all solutions will be established. The oscillatorybehavior will be investigated. 相似文献
68.
69.
有理插值问题不适定的根本原因 总被引:2,自引:2,他引:0
盛中平 《高等学校计算数学学报》2001,23(3):227-236
1 在 Rm,n中的有理插值问题本文记 Pn为次数不超过 n的一元多项式函数类 ,约定零多项式的次数为 -∞ ,即deg(0 ) =-∞ ;记 Rm,n为分子属于 Pm,分母属于 Pn\{ 0 }的一元有理函数类 .对既约分式Am/Bn∈Rm,n,如果 Bn满足尾项规范条件 (即 Wuytack条件 ) [2 ] ,则称其为标准既约分式 .引进一个新的有理函数类 ,记Rl =Rl- 1 ,0 ∪ Rl- 2 ,1 ∪…∪ R0 ,l- 1 .称 Rl 是自由度为 l的一元有理函数类 .并称其中有理函数类 Rl- 1 - i,i为有理函数类 Rl 的基本子类 ,(i=0 ,1 ,… ,l-1 ) .我们约定 :本文中“有理插值问题”如不特殊声明 ,系指文… 相似文献
70.
We give a Newton type rational interpolation formula (Theorem 2.2). It contains as a special case the original Newton interpolation, as well as the interpolation formula of Liu, which allows to recover many important classical q-series identities. We show in particular that some bibasic identities are a consequence of our formula. 相似文献