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In this paper, two identities involving a function defined by the complete elliptic integrals of the first and second kinds are proved. Some functional inequalities and elementary estimates for this function are also derived from the properties of monotonicity and convexity of this function. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied. 相似文献
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Yilmaz Simsek 《Applied mathematics and computation》2011,218(3):1072-1076
Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties of this generating functions are given. By applying this generating function, not only derivative of these polynomials but also recurrence relations of these polynomials are found. Interpolation function of these polynomials is also constructed by Mellin transformation. This function interpolates these polynomials at negative integers which are given explicitly. Moreover, relations between these polynomials, the Stirling numbers of the second kind and Bernoulli polynomials of higher order are given. Furthermore some remarks associated with the Bezier curves are given. 相似文献
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D. V. Trushchin 《Moscow University Mathematics Bulletin》2012,67(4):158-163
A set of functions of the three-valued logic is considered and upper estimates for the Shannon function in the class of formulas of special form are obtained for this set. Some examples of sequences of functions from this set are considered and exponential lower estimates of complexity are obtained. In this case the values of the Shannon function are obtained for the considered class with the accuracy up to an additive constant. 相似文献
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以 2 l为周期的函数 f(x)也可看作周期为 2 kl(k=1 ,2 ,3 ,… ) .设 f(x)满足 Dirichlet充分条件 ,[2 ]证明了按 [1 ]方法展开的以 2 l为周期的 Fourier级数和以 4l为周期的 Fourier级数对应的不同表达形式是一致的 .本文则在 [2 ]的基础上 ,进一步证明了按 [1 ]方法展开的以 2 l为周期的 Fourier级数和以 2 kl(k=1 ,2 ,3 ,… )为周期的 Fourier级数对应的表达式的一致性 ,从而得出结论 :任一周期函数 f(x)按 [1 ]方法展开的Fourier级数是唯一的 . 相似文献
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考虑一类非线性不等式约束的非光滑minimax分式规划问题;目标函数中的分子是可微函数与凸函数之和形式而分母是可微函数与凸函数之差形式,且约束函数是可微的.在Arrow- Hurwicz-Uzawa约束品性下,给出了这类规划的最优解的Kuhn-Tucker型必要条件.所得结果改进和推广了已有文献中的相应结果. 相似文献
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基于g函数的多元copula的构造 总被引:1,自引:0,他引:1
针对目前多元copula的构造方法存在的局限性,提出了构造多元copula的新方法.本文首先定义的一类新的函数-g函数,基于g函数建立了2-copula的构造方法,并讨论了该方法的存在性与唯一性问题,然后将2-copula的构造方法直接扩展到n-copula构造的情形.最后给出了g函数的一种寻求方法,从而说明此copula构造方法的可行性. 相似文献
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CES生产函数与投资控制模型 总被引:12,自引:9,他引:3
本文讨论了 C-D生产函数和 CES生产函数模型 ,同时针对边界条件用 CES生产函数表示的投资控制模型进行了分析 ,证明了该投资控制模型解的存在性和唯一性 相似文献
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Banach空间的型与独立Banach空间值随机变量序列的不等式 总被引:3,自引:0,他引:3
本文建立了独立B值随机变量序列部分和的极大值函数S*与p方根函数S(p,X)的分布函数不等式与矩不等式,讨论了这些不等式的成立与Banach空间的p型与q余型的关系,同时给出了与Hilbert空间同构的Banach空间的特征。 相似文献
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Lu-Ming Shen 《Journal of Mathematical Analysis and Applications》2007,329(2):1440-1445
We introduce the error-sum function of Lüroth series. Some elementary properties of this function are studied. We also determine the Hausdorff dimension of the graph of this function. 相似文献
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通过构造一个Riemann Zeta函数ζ(k)的部分和ζ_n(k)的幂级数函数,利用牛顿二项式展开及柯西乘积公式可以计算出一些重要的和式.再将该幂级数函数由一元推广到二元甚至多元,由此得到Riemann Zeta函数的高次方和式之间的关系.并利用对数函数与第一类Stirling数之间的关系式及ζ(k)函数满足的相关等式,可得出Riemann Zeta函数的18个七阶和式,以及其它一些高次方的和式. 相似文献
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B-空间上凸函数的若干指数性质 总被引:1,自引:0,他引:1
本文引入且用次梯度集该划Banach空间上凸函数的上、下指数,得到共轭凸函数上、下指数间的完整共轭关系、正齐次凸函数是Minkovski规函数的幂等结果,已有的一维相关结果是本文的特例。 相似文献
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A characterization of the multivariate excess wealth ordering 总被引:1,自引:0,他引:1
J.M. Fernández-Ponce F. Pellerey M.R. Rodríguez-Griñolo 《Insurance: Mathematics and Economics》2011,49(3):410-417
In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate right-spread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the excess wealth ordering by Shaked and Shanthikumar (1998) and Fernández-Ponce et al. (1998). The multivariate excess wealth function enable us to define a new stochastic comparison which is weaker than the multivariate dispersion orderings. Also, some properties relating the multivariate excess wealth order with stochastic dependence are described. 相似文献
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O. S. Rothaus 《Israel Journal of Mathematics》1974,18(1):75-96
In this paper, for some of the results which were announced in we define, for every convex polytope, a function generalizing the permanent; we study the growth of the function, the behavior of its minimum and determine a lower bound for the minimum. Some of the results are new even for the permanent. A related function whose properties are strongly linked to the permanent is also studied, and will be described in greater detail in a sequel to this paper. 相似文献
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李高明 《纯粹数学与应用数学》2010,26(3):363-366
在X^*可分的条件下,首先讨论了集值Pramart有关支撑函数和距离函数的性质,利用支撑函数和距离函数研究了集值Pramart鞅逼近,在此基础上,给出了集值Pramart的一类鞅分解. 相似文献
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The second order properties of a process are usually characterized by the autocovariance function. In the stationary case, the parameterization by the partial autocorrelation function is relatively recent. We extend this parameterization to the nonstationary case. The advantage of this function is that it is subject to very simple constraints in comparison with the auto- covariance function which must be nonnegative definite. As in the stationary case, this parameterization is well adapted to autoregressive models or to the identification of deterministic processes. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(5):1400-1416
In this study, we present a multifunctional indicator system for the performance evaluation of crop production system by set pair analysis method. Five functions were summarized to represent the multifunctionality of crop production system, including production function, supply function, ecological function, security function and economic function. Setting a case study of 31 provincial regions in mainland China, this paper conducted a comparison of each function in different regions, divided into 9 groups by cluster analysis. The results show that: the levels of multifunction in most regions are under a low degree balance; the production function has a high coordination with the economic function and security function in China; the supply function is lowly correlated with the other functions, especially the economic function has negative correlation with the supply function to some extent; some relevant policies and suggestions are deduced for multifunctional improvement. It is concluded that the multifunctional indicators and the set pair analysis method can serve as an effective method for the assessment of crop production system. 相似文献