Constructing pairs of dual bandlimited framelets with desired time localization

For sufficiently small translation parameters, we prove that any bandlimited function ψ, for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame with a dual frame also having the wavelet structure. This dual frame is generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose generators have compact support in the Fourier domain and desired time localization. The construction is based on characterizing equations for dual wavelet frames and relies on a technical condition. We exhibit a general class of function satisfying this condition; in particular, we construct piecewise polynomial functions satisfying the condition.      

Designing unity magnitude input shaping by using PWM technique

This paper proposes a method for reducing vibrations in flexible systems by using the input shaping. A new input shaper technique based on Pulse Width Modulation (PWM) is used to shape the input.Since unity magnitude (UM) input shaping is easy to implement and provides less control duration, it has been preferred for many application areas. An analytical solution to time locations of the UM shaper requires very complex mathematical expressions due to involving in dependent constraint equations. This paper presents a simple PWM based input shaping method. The proposed technique allows designing UM shapers without analytical solution especially for the shapers having higher order impulse sequence. The method requires only the estimated value of system natural frequency and damping ratio. Desired numbers of impulses can be obtained by comparing reference signal amplitude and carrier wave frequency of a PWM. Analysis and experimental results demonstrate the effectiveness of the proposed method.     

A novel virtual node method for polygonal elements

A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.     

物理实验教学与中学生辩证逻辑思维能力的培养

阐述了如何在辩证逻辑基本规律——对立统一规律指导下，通过挖掘物理实验中蕴涵的辩证逻辑思维素材，在物理实验教学中有意识地培养学生的辩证逻辑思维能力。     

一类特殊级数的和函数

利用k次单位根及其正交性得到级数∑∞n=0xkn+l/(kn+l)!的和函数.它与利用微分方程理论来求级数的和有很大区别.作为应用,得到了一些特殊级数的和.     

Tilings,packings, coverings,and the approximation of functions

A packing (resp. covering) ? of a normed space X consisting of unit balls is called completely saturated (resp. completely reduced) if no finite set of its members can be replaced by a more numerous (resp. less numerous) set of unit balls of X without losing the packing property (resp. covering property) of ?. We show that a normed space X admits completely saturated packings with disjoint closed unit balls as well as completely reduced coverings with open unit balls, provided that there exists a tiling of X with unit balls. Completely reduced coverings by open balls are of interest in the context of an approximation theory for continuous real‐valued functions that rests on so‐called controllable coverings of compact metric spaces. The close relation between controllable coverings and completely reduced coverings allows an extension of the approximation theory to non‐compact spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

New solvable lattice models in three dimensions

In this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models. The first is the Zamolodchikov model, which is the only nontrivial model on a three-dimen-sional lattice so far solved. The second is the chiral Potts model on the square lattice and its generalization associated with theU _q(sl(n)) algebra, which is of current interest due to its connections with high-genus algebraic curves and with representations of quantum groups at roots of unity. We show that this last sl(n)-generalized chiral Potts model can be interpreted as a model on a threedimensional simple cubic lattice consisting ofn square-lattice layers with anN- valued (N2) spin at each site. Further, in theN=2 case this three-dimen-sional model reduces (after a modification of the boundary conditions) to the Zamolodchikov model we mentioned above.     

策略三十六计和算法三十六计

本着文化自信的精神,深入学习具有三千多年历史的《易经》,挖掘《易经》形象思维的抽象和推理的理念,结合现代计算机学科的发展和作者本身的专业经历,给出了计算机系统设计策略三十六计和算法三十六计的初步成果.本文提出了计算机学科的四个基本对立统一关系,即四个基本科学问题：集分定位、刚柔相摩、供需相应、串并转换.从集分定位出发,在策略三十六计中提出了架构设计十八计,它包括了时空转换和多种计算模式的计策.从刚柔相摩出发,在策略三十六计中提出了系统特性十八计,它包括了八类特性设计的计策,例如,可控性、效率性、安全性、可变性等方面的计策.供需相应和串并转换所涉及的科学问题,主要体现在资源管理和任务调度的算法三十六计中.这些算法计策中包含了计算机学科的经典和热点问题,例如,可计算性、多目标优化、云计算、软件定义系统、大数据思维和人工智能等.策略三十六计和算法三十六计可以为计算机专业人员在学习和系统研发工作中提供思维框架、策略辩证思路和需要的计策及实例,更为重要的是可以进一步理解事物的哲学道理.     

网络化超高清制作岛的设计与实施

随着4K技术的全面应用,中央广播电视总台4K超高清频道开播,对于4K后期制作需求快速增加,网络化的超高清制作岛必然成为发展趋势,4K后期制作全面融入全台文件化制播流程体系中。本文以超高清制作岛3为例从系统架构、素材管理、后期制作及调色流程、4K制作岛特点等,多角度、全方位介绍网络化超高清制作岛的优势。     

一种改进的无单元伽辽金方法

使用单位分解积分,对传统的无单元伽辽金方法进行改进.有限覆盖和单位分解是单位分解积分的数学基础,对单位分解积分进行了严格证明,并指出使用Shepard函数作为单位分解函数是一个很好的选择.数值实例表明,使用单位分解积分进行数值求积的无单元伽辽金方法是一种真正的无网格方法,与经典的背景网格积分相比具有更高的精度.