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991.
In this paper we consider the biorthogonal polynomials with respect to the measure e-x4-y2+2τxydxdy, and show that their roots interlace. The proof involves showing total nonnegativity of matrices related to Jacobi type matrices. 相似文献
992.
Guangxing Jiang Hongbo Zhu Wei Cao 《International Journal of Infrared and Millimeter Waves》2007,28(8):677-688
The complete electromagnetic responses from conducting objects in time and frequency domains are generated by using their
early time and low frequency information. Utilizing two kinds of Hermite polynomials and their Fourier transform, the time-domain
signal and its corresponding frequency response can be expressed as a weighted sum of these quantities in an efficient way.
The general properties of these two families of Hermite functions are studied, which greatly affect the performance of the
proposed method. Due to the performance of the algorithm being sensitive to the choice of the origin and the scaling factor,
how to properly choose the initial values of these parameters is considered. An optimal algorithm is also developed to find
the above parameters so as to achieve the best performance. A criterion is also provided to assess the sensitivity of the
performance. The excellent agreement between the computed results by the proposed method and those obtained by earlier approaches
is demonstrated in each case.
This work was supported in part by natinal nature science foundatin of China (NO. 60432040). 相似文献
993.
先引入了由一列Orlicz空间生成的Ba空间(LMBa)的定义,然后用分数阶α的连续模给出一类广义插值在LBMa空间中逼近阶. 相似文献
994.
In this paper, we discuss properties of the ω,q-Bernstein polynomials introduced by S. Lewanowicz and P. Woźny in [S. Lewanowicz, P. Woźny, Generalized Bernstein polynomials, BIT 44 (1) (2004) 63–78], where fC[0,1], ω,q>0, ω≠1,q−1,…,q−n+1. When ω=0, we recover the q-Bernstein polynomials introduced by [G.M. Phillips, Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1997) 511–518]; when q=1, we recover the classical Bernstein polynomials. We compute the second moment of , and demonstrate that if f is convex and ω,q(0,1) or (1,∞), then are monotonically decreasing in n for all x[0,1]. We prove that for ω(0,1), qn(0,1], the sequence converges to f uniformly on [0,1] for each fC[0,1] if and only if limn→∞qn=1. For fixed ω,q(0,1), we prove that the sequence converges for each fC[0,1] and obtain the estimates for the rate of convergence of by the modulus of continuity of f, and the estimates are sharp in the sense of order for Lipschitz continuous functions. 相似文献
995.
996.
B. Z. Shavarovskii 《Computational Mathematics and Mathematical Physics》2006,46(8):1283-1292
A certain standard form is found for a complex matrix with respect to equivalent transformations by quasi-diagonal matrices. The solvability of certain matrix equations in the rings of quasi-diagonal matrices is examined using this standard form. 相似文献
997.
A multiplication theorem for the Lerch zeta function ?(s,a,ξ) is obtained, from which, when evaluating at s=−n for integers n?0, explicit representations for the Bernoulli and Euler polynomials are derived in terms of two arrays of polynomials related to the classical Stirling and Eulerian numbers. As consequences, explicit formulas for some special values of the Bernoulli and Euler polynomials are given. 相似文献
998.
Sheng-liang Yang 《Discrete Mathematics》2008,308(4):550-554
The main purpose of this paper is to prove an identity of symmetry for the higher order Bernoulli polynomials. It turns out that the recurrence relation and multiplication theorem for the Bernoulli polynomials which discussed in [F.T. Howard, Application of a recurrence for the Bernoulli numbers, J. Number Theory 52 (1995) 157-172], as well as a relation of symmetry between the power sum polynomials and the Bernoulli numbers developed in [H.J.H. Tuenter, A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001) 258-261], are all special cases of our results. 相似文献
999.
An integrable chain connected to the isospectral evolution of the polynomials of type R–I introduced by Ismail and Masson is presented. The equations of motion of this chain generalize the corresponding equations of the relativistic Toda chain introduced by Ruijsenaars. We study simple self-similar solutions to these equations that are obtained through separation of variables. The corresponding polynomials are expressed in terms of the Gauss hypergeometric function. It is shown that these polynomials are stable (up to shifts of the parameters) against Darboux transformations of the generalized chain. 相似文献
1000.
John R. Stembridge 《Journal of Algebraic Combinatorics》1992,1(1):71-95
Let B
n denote the centralizer of a fixed-point free involution in the symmetric group S
2n
. Each of the four one-dimensional representations of B
n induces a multiplicity-free representation of S
2n
, and thus the corresponding Hecke algebra is commutative in each case. We prove that in two of the cases, the primitive idempotents can be obtained from the power-sum expansion of Schur's Q-functions, from which follows the surprising corollary that the character tables of these two Hecke algebras are, aside from scalar multiples, the same as the nontrivial part of the character table of the spin representations of S
n. 相似文献