Mathematical Sciences: Analysis of Two-Scale Dilation Equations
Mathematical Sciences: Analysis of Two-Scale Dilation Equations
批准号:
9307601
负责人:
Yang Wang
金额:
$5.27万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1993
资助国家:
美国
项目状态:
已结题
起止时间:
1993-08-15 至 1997-01-31
中文摘要
9307601王本研究涉及描述尺度函数的双尺度行为特征的双尺度膨胀方程。这些方程出现在广泛的应用中,包括小波,用于计算机生成曲线和曲面的细分方案,以及分形几何(迭代函数系统)。主要研究人员将开发基于无限矩阵乘积展开形式的尺度函数表示的技术,该技术可用于建立构造尺度函数的算法,并分析其正则性、可积性和维度。到目前为止,为了确保无穷矩阵乘积的收敛,施加了一个对比性假设。这一假设比必要的更强,PI正在调查涉及有界半群矩阵的较弱假设,以及由Lyapunov指数确定的平均收缩系数。这也引出了关于矩阵的有界半群的结构的问题。PI还开发了研究自相似晶格平铺的技术,这种格子平铺源于多维正交子波。PI主要研究如下问题:(1)曲面生成:滑动窗方法;(2)可积解的存在性;(3)具有非负系数的膨胀方程;(4)自相似格子拼接;(5)Daubechies和Lagarias的有限猜想。这项活动在许多领域都有很大的应用潜力,包括压缩算法。***
英文摘要
9307601 Wang This research concerns two-scale dilation equations, which describe the two-scale behavior characteristic of scaling functions. These equations arise in a wide variety of applications, including wavelets, sub-division schemes for computer generation of curves and surfaces, and fractal geometry (iterated function systems - IFS). The principal investigator will develop techniques based on representations of the scaling function in terms of an infinite matrix product expansion, which can be used to establish an algorithm for constructing scaling functions, and to analyze their regularity, integrability, and dimensionality. Thus far, in order to ensure convergence of the infinite matrix product,a Contractivity Assumption has been imposed. This Assumption is stronger than necessary, and the PI is investigating weaker assumptions involving bounded semi-groups of matrices, and an average contractivity factor as determined by the Lyapunov exponent. This also leads to questions regarding the structure of bounded semi-groups of matrices. The PI has also developed techniques to study self-similar lattice tilings, which arises from multi-dimensional orthonormal wavelets. The PI intends to study the following: (1) surface generation: sliding window method; (2) existence of integrable solutions; (3) dilation equations with non-negative coefficients; (4) self-similar lattice tilings; (5) the Finiteness Conjecture of Daubechies and Lagarias. This activity had substantial potential for application in many areas, including compression algorithms. ***
期刊论文(0)
专著(0)
科研奖励(0)
会议论文
Characterizing the Physical, Chemical, and Toxicological Properties of Secondhand Aerosols Generated from Electronic Nicotine Delivery Systems in Indoor Environments
-
批准号:2324142
-
项目类别:Standard Grant
-
资助金额:$42.0万
-
财政年份:2023
-
负责人:Yang Wang
-
依托单位:
Frequency-Domain Model Updating through Branch and Bound with Convex Relaxation
-
批准号:2211343
-
项目类别:Standard Grant
-
资助金额:$64.98万
-
财政年份:2023
-
负责人:Yang Wang
-
依托单位:
Characterizing the Physical, Chemical, and Toxicological Properties of Secondhand Aerosols Generated from Electronic Nicotine Delivery Systems in Indoor Environments
-
批准号:2204659
-
项目类别:Standard Grant
-
资助金额:$42.0万
-
财政年份:2022
-
负责人:Yang Wang
-
依托单位:
Collaborative Research: PPoSS: LARGE: ScaleStuds: Foundations for Correctness Checkability and Performance Predictability of Systems at Scale
-
批准号:2118745
-
项目类别:Continuing Grant
-
资助金额:$62.47万
-
财政年份:2021
-
负责人:Yang Wang
-
依托单位:
Collaborative Research: SaTC: CORE: Medium: Novel Algorithms and Tools for Empowering People Who Are Blind to Safeguard Private Visual Content
-
批准号:2126314
-
项目类别:Standard Grant
-
资助金额:$31.59万
-
财政年份:2021
-
负责人:Yang Wang
-
依托单位:
Collaborative Research: EAGER: SaTC-EDU: Teaching High School Students about Cybersecurity and Artificial Intelligence Ethics via Empathy-Driven Hands-On Projects
-
批准号:2114991
-
项目类别:Standard Grant
-
资助金额:$15.48万
-
财政年份:2021
-
负责人:Yang Wang
-
依托单位:
Collaborative Research: Gateway to North America--the Great American Biotic Interchange (GABI) in Mexico and Origin of C4 Grassland
-
批准号:1949814
-
项目类别:Standard Grant
-
资助金额:$14.21万
-
财政年份:2020
-
负责人:Yang Wang
-
依托单位:
Collaborative Research: Element: Development of MuST, A Multiple Scattering Theory based Computational Software for First Principles Approach to Disordered Materials
-
批准号:1931525
-
项目类别:Standard Grant
-
资助金额:$27.0万
-
财政年份:2019
-
负责人:Yang Wang
-
依托单位:
CAREER: Inclusive Privacy: Effective Privacy Management for People with Visual Impairments
-
批准号:2028387
-
项目类别:Continuing Grant
-
资助金额:$34.15万
-
财政年份:2019
-
负责人:Yang Wang
-
依托单位:
CNS Core: SMALL: Clarifying Experimenter Bias by Identifying and Visualizing Experiment Bottlenecks
-
批准号:1908020
-
项目类别:Standard Grant
-
资助金额:$49.69万
-
财政年份:2019
-
负责人:Yang Wang
-
依托单位:
CAREER: Inclusive Privacy: Effective Privacy Management for People with Visual Impairments
-
批准号:1652497
-
项目类别:Continuing Grant
-
资助金额:$49.79万
-
财政年份:2017
-
负责人:Yang Wang
-
依托单位:
CRII: CSR: Efficient and Available Replication in Large-scale Datacenters
-
批准号:1566403
-
项目类别:Standard Grant
-
资助金额:$17.5万
-
财政年份:2016
-
负责人:Yang Wang
-
依托单位:
Collaborative Research: Reconstruction of Paleo-Storm History Using Geochemical Proxies in Coastal Lake Sediments
-
批准号:1566134
-
项目类别:Continuing Grant
-
资助金额:$29.24万
-
财政年份:2016
-
负责人:Yang Wang
-
依托单位:
CRII: SaTC: Privacy-Enhancing User Interfaces Based on Individualized Mental Models
-
批准号:1464347
-
项目类别:Standard Grant
-
资助金额:$15.96万
-
财政年份:2015
-
负责人:Yang Wang
-
依托单位:
CAREER: Decentralized Monitoring and Control for Large-Scale Smart Structures with Wireless and Mobile Sensor Networks
-
批准号:1150700
-
项目类别:Standard Grant
-
资助金额:$40.0万
-
财政年份:2012
-
负责人:Yang Wang
-
依托单位:
ATD: Collaborative Research: MULTISCALE AND STOCHASTIC METHODS FOR INVERSE SOURCE PROBLEMS AND SIGNAL ANALYSIS
-
批准号:1043034
-
项目类别:Standard Grant
-
资助金额:$20.22万
-
财政年份:2010
-
负责人:Yang Wang
-
依托单位:
Collaborative Research: Late Cenozoic Vertebrate Paleontology and Paleoenvironments of the Tibetan Plateau (China)
-
批准号:0958602
-
项目类别:Standard Grant
-
资助金额:$10.7万
-
财政年份:2010
-
负责人:Yang Wang
-
依托单位:
Technician Support for the Stable Isotope Laboratory at Florida State University
-
批准号:0824628
-
项目类别:Continuing Grant
-
资助金额:$8.95万
-
财政年份:2009
-
负责人:Yang Wang
-
依托单位:
Adaptive Mobile Sensor Networks for Structural Health Monitoring
-
批准号:0928095
-
项目类别:Standard Grant
-
资助金额:$23.99万
-
财政年份:2009
-
负责人:Yang Wang
-
依托单位:
Midwest Conference on Mathematical Methods for Biomedical Images and Biological Surfaces; September 2008
-
批准号:0813502
-
项目类别:Standard Grant
-
资助金额:$2.5万
-
财政年份:2008
-
负责人:Yang Wang
-
依托单位:
国内基金
海外基金
登录
查看更多内容
Handbook of the Mathematics of the Arts and Sciences的中文翻译
-
批准号:12226504
-
项目类别:数学天元基金项目
-
资助金额:20.0万元
-
批准年份:2022
-
负责人:黄朝凌
-
依托单位:
SCIENCE CHINA: Earth Sciences
-
批准号:41224003
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2012
-
负责人:魏建晶
-
依托单位:
Journal of Environmental Sciences
-
批准号:21224005
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2012
-
负责人:冯庆彩
-
依托单位:
SCIENCE CHINA Information Sciences
-
批准号:61224002
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2012
-
负责人:宋扉
-
依托单位:
SCIENCE CHINA Technological Sciences
-
批准号:51224001
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2012
-
负责人:安梅
-
依托单位:
SCIENCE CHINA Life Sciences (中国科学 生命科学)
-
批准号:81024803
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2010
-
负责人:李纪元
-
依托单位:
Journal of Environmental Sciences
-
批准号:21024806
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2010
-
负责人:冯庆彩
-
依托单位:
SCIENCE CHINA Earth Sciences(中国科学:地球科学)
-
批准号:41024801
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2010
-
负责人:魏建晶
-
依托单位:
SCIENCE CHINA Technological Sciences
-
批准号:51024803
-
项目类别:专项基金项目
-
资助金额:24.0万元
-
批准年份:2010
-
负责人:安梅
-
依托单位: