一类级数求和的推广

借助收敛级数的简单运算,对一类简单级数及和数进行四种形式的推广.     

Class numbers of cyclic 2-extensions and Gross conjecture over Q

The Gross conjecture over Q was first claimed by Aoki in 1991.However,the original proof contains too many mistakes and false claims to be considered as a serious proof.This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki.We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of Q.     

On the Almost Everywhere Convergence of Wavelet Summation Methods

Let ψ be a rapidly decreasing one-dimensional wavelet. We show that the wavelet expansion of anyL^pfunction converges pointwise almost everywhere under the wavelet projection, hard sampling, and soft sampling summation methods, for 1 <p< ∞. In fact, the partial sums are uniformly dominated by the Hardy–Littlewood maximal function.     

Convergence for Summation Methods with Multipliers on the Sphere

In this article, we present convergence rates for summation methods with multipliers related to certain approximation methods on the sphere we previously introduced and discussed in Menegatto and Piantella [13 V.A. Menegatto and A.C. Piantella ( 2005 ). Approximation on the sphere by weighted Fourier expansions . J. Appl. Math. 2005 ( 4 ): 321 – 340 . [Google Scholar]]. The results are based upon spherical moduli of smoothness defined via the Laplace–Beltrami derivative.     

两类幂级数求和函数的一般方法

本文探讨了高等数学教材中的两类幂级数求和问题,并给出这两类幂级数求和函数的一般方法,同时进行了实例分析.     

Extreme Bloch Functions and Summation Methods for Bloch Functions

In this paper we construct Bloch functions F for which the set {z | e sup _{|ζ| < 1} |F'(ζ)| ( 1 - |ζ| ² ) = |F'(z)| ( 1 - |z| ² )} is an analytic Jordan curve tangential to the unit disk in some points. It is proved that, using such functions, we can derive analogs to the Taylor expansion for Bloch functions in cases where the Taylor expansion does not converge. October 15, 1997. Date revised: March 12, 1998. Date accepted: June 18, 1998.     

一类级数求和的推广之注记

通过对文献[1]中结论的分析,进一步阐述了拆项技巧在级数求和中的应用.     

On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space L 2

We prove a statement on exact inequalities between the deviations of functions from their linear methods (in the metric of L ₂) with multipliers defined by a continuous function and majorants determined as the scalar product of the squared modulus of continuity (of order r) in L ₂ for the lth derivative of the function and a certain weight function . We obtain several corollaries of the general theorem.     

2D Centroidal Voronoi Tessellations with Constraints

<正>We tackle the problem of constructing 2D centroidal Voronoi tessellations with constraints through an efficient and robust construction of bounded Voronoi diagrams, the pseudo-dual of the constrained Delaunay triangulation.We exploit the fact that the cells of the bounded Voronoi diagram can be obtained by clipping the ordinary ones against the constrained Delaunay edges.The clipping itself is efficiently computed by identifying for each constrained edge the(connected) set of triangles whose dual Voronoi vertices are hidden by the constraint.The resulting construction is amenable to Lloyd relaxation so as to obtain a centroidal tessellation with constraints.     

Q类亚纯函数的唯一性理论

主要讨论Q型亚纯函数的唯一性问题，推广并改进[1],[4]的有关结果。     

Summation of series

Three approaches are considered to the summation of some ‘standard’ series: an elementary analysis, an approach based on residues, and a technique employing the digamma function and partial fractions. This last procedure is the most convenient to use, but all three techniques have their limitations.     

一类广义W型李超代数

构造了一类有限维广义Cartan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

一类广义W型李超代数

构造了一类有限维广义Caxtan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

Class number one problem for the real quadratic fields $${{\mathbb {Q}({\sqrt{m^2+2r}})}}$$ Q ( m 2 + 2 r )

Archiv der Mathematik - We investigate the class number one problem for a parametric family of real quadratic fields of the form $$\mathbb {Q}( \sqrt{m^2+4r})$$ for certain positive integers m and r.     

Fourier级数的求和理论与方法—求和因子法求和

在 Fourier级数的线性求和中 ,通过构造求和因子 ,使得带有该求和因子的积分算子在全轴上一致地收敛到每个以 2 π为周期的连续函数 ,并对 Cj2π(0 j r)函数类的逼近均达到最佳收敛阶 ,参数 r为任意给定的奇自然数 .     

Q Curvature on a Class of 3‐Manifolds

Motivated by the strong maximum principle for the Paneitz operator in dimension 5 or higher found in a preprint by Gursky and Malchiodi and the calculation of the second variation of the Green's function pole's value on ??³ in our preprint, we study the Riemannian metric on 3‐manifolds with positive scalar and Q curvature. Among other things, we show it is always possible to find a constant Q curvature metric in the conformal class. Moreover, the Green's function is always negative away from the pole, and the pole's value vanishes if and only if the Riemannian manifold is conformal diffeomorphic to the standard ??³. Compactness of constant Q curvature metrics in a conformal class and the associated Sobolev inequality are also discussed. © 2016 Wiley Periodicals, Inc.     

一类Dogleg路径信赖域方法

本文提出一类折线搜索的信赖域方法，用于解无约束最优化问题，这些方法通过对一般对称矩阵的Bunch-Parlett分解来产生搜索路径，我们证明在一些较弱的条件下，算法是整体收敛的，对一致凸函数，是二次收敛的，并且在由算法得到的点列的任意聚点上，连续可微的目标函数的Hesse阵都是正定或半正定的，一些数值结果表明这种新的方法是非常有效的。     

求解无约束优化问题的一类新的下降算法

本文对求解无约束优化问题提出了一类新的下降算法,并且给出了HS算法与其相结合的两类杂交算法．在Wolfe线搜索下不需给定下降条件,即证明了它们的全局收敛性．数值实验表明新的算法十分有效,尤其是对求解大规模问题而言．