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81.
对复指数多项式在Bamch空间Hpa(1≤ρ≤2)中的完备性给出了充要条件,其中Hρa为开半带形Ia={z=x iy:x>0,│y│<a}(a>0)中的Hardy空间. 相似文献
82.
The exact solutions to a class of differential equation are studied. Some special cases are discussed for the central potentials, single ring-shaped potential and the angular Teukolsky equation. A new expression to the associated Legendre polynomials is found. Some new properties of the universal associated-Legendre polynomials (UALPs) including the generating function, Rodrigues’ formula, parity, some special values and the recurrence relations are presented. A new different Rodrigues’ formula of associated Legendre polynomials is also obtained. 相似文献
83.
New representation and factorizations of the higher-order ultraspherical-type differential equations
The paper deals with the class of linear differential equations of any even order 2α+4, α∈N0, which are associated with the so-called ultraspherical-type polynomials. These polynomials form an orthogonal system on the interval [−1,1] with respect to the ultraspherical weight function (1−x2)α and additional point masses of equal size at the two endpoints. The differential equations of “ultraspherical-type” were developed by R. Koekoek in 1994 by utilizing special function methods. In the present paper, a new and completely elementary representation of these higher-order differential equations is presented. This result is used to deduce the orthogonality relation of the ultraspherical-type polynomials directly from the differential equation property. Moreover, we introduce two types of factorizations of the corresponding differential operators of order 2α+4 into a product of α+2 linear second-order operators. 相似文献
84.
In this article, boundary characteristic orthogonal polynomials have been implemented in the Rayleigh–Ritz method to investigate free vibration of non-uniform Euler–Bernoulli nanobeams based on nonlocal elasticity theory. Non-uniform cross section of nanobeams has been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinate. Detailed analysis has been reported for all the possible cases of such variations. The objective of the present study is to analyze the effects of nonlocal parameter, boundary condition, length-to-diameter ratio and non-uniform parameter on the frequency parameters. It is found that clamped nanobeams are having highest frequency parameters than other types of boundary conditions for a particular set of parameters. It is also observed that frequency parameters decrease with increase in scaling effect parameter. First four deflection shapes of non-uniform nanobeams have also been incorporated. In this analysis, some of the new results in terms of boundary conditions have also been included. 相似文献
85.
m·K1∪T(1,2,n)及其补图的匹配刻画 总被引:1,自引:1,他引:0
申世昌 《河南师范大学学报(自然科学版)》2011,39(5):13-15
研究了图的匹配刻画问题,利用匹配根的信息,根据匹配多项式的性质,给出了m·K1∪ T(1,2,n)及其补图匹配刻画的充分必要条件是n≠1,2,5,9. 相似文献
86.
Cauchy多项式与高阶Cauchy多项式 总被引:1,自引:0,他引:1
高泽图 《海南大学学报(自然科学版)》2006,24(3):217-221
给出了Cauchy多项式与高阶Cauchy多项式及高阶Cauchy数的定义,导出了它们的生成函数,利用第2类Stirling数得到了它们的递推公式,获得它们与高阶Bernou lli多项式、高阶退化Bernou lli多项式的关系式. 相似文献
87.
88.
89.
M. Morh 《Mathematical and Computer Modelling》1994,19(12):85-93
The paper presents an error-free algorithm to solve a system of linear equations with polynomial coefficients. Modular arithmetic in residual polynomial class and in residual numeric class is employed. The algorithm is iterative and well suited for implementation for computers with vector operations and fast and error-free convolutors. 相似文献
90.
Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of p(Rz)-βp(rz) + α (R+1/r+1)n-|β | p(rz) s on p(z) s for every α, β∈ C with |α|≤ 1, |β | ≤ 1, R > r 1, and s > 0. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure. 相似文献