Mathematical Sciences: Wavelets Based on Several Scaling Functions and Related Applications

数学科学：基于多个标度函数的小波及相关应用

• 批准号: 9503282
• 负责人: Jianzhong Wang
• 金额: $ 12万
• 依托单位: Sam Houston State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503282&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Wavelets; Based; Several

9503282 Wang This project will involve research in the theory and applications of wavelets. The problems to be considered include: (1) the construction and characterization of wavelets of Battle-Federbush type and their associated wavelet packets; (2) the general construction of multiwavelets from an orthogonal multiresolution analysis generated by scaling vectors; (3) determining properties of certain classes of solutions of matrix refinement equations; (4) applications of fractal multiwavelets to second order hyperbolic partial differential equations; and (5) adaptations of fast wavelet transformations by incorporating multiwavelets in order to study nonlinear integral equations. This project is being supported under the Research in Undergraduate Institutions (RUI) activity. The RUI activity is part of the Foundation's effort to help assure a broad base for science and engineering research, and thereby enhance the scientific and technical training of students in undergraduate institutions. The specific objectives of the RUI program are to: (1) support high quality research by faculty with active involvement of undergraduate students, (2) strengthen the research environment in academic departments that are oriented primarily toward undergraduate instruction, and (3) promote the integration of research and education at predominantly undergraduate institutions. This project will involve research on the theory of multiwavelets. Multiwavelet theory involves replacing the classical dilation equation of wavelet theory by a matrix dilation equation. The relationship of the dilation equation and the various features of the wavelet bases generated will be investigated. The use of wavelets for the numerical solution of partial differential and integral equations will also be studied; these techniques will be compared to more classical algorithms.

小行星9503282 本计画将研究小波的理论与应用。 要考虑的问题包括：（1）建设和 Battle-Federbush型小波的特征及其相关 小波包的一般构造方法;（2）基于 由尺度向量产生的正交多分辨分析;（3） 某些矩阵加细解类的判定性质 （4）分形多小波在二阶非线性系统中的应用 双曲型偏微分方程;（5）快速小波的自适应 变换，以研究非线性 积分方程 该项目得到了本科生研究项目的支持。 机构（RUI）活动。 RUI活动是基金会 努力帮助确保科学和工程研究的广泛基础， 从而加强学生的科学技术训练， 本科院校。 RUI计划的具体目标是 （1）支持教师积极参与高质量的研究 （2）加强本科生的科研环境， 主要面向本科生的学术部门 教学，（3）促进研究与教育的融合， 主要是本科院校。 该项目将涉及 多小波理论的研究。 多小波理论涉及到 用矩阵代替小波理论中经典的伸缩方程， 膨胀方程 膨胀方程和各种 将研究所产生的小波基的特征。 使用 小波在偏微分和偏积分数值解中的应用 方程也将进行研究;这些技术将被比较， 经典算法