学术报告

　　Dr. Liming Dai教授, 加拿大里贾纳大学（University of Regina）工业系统工程系(Industrial Systems Engineering)终身教授，担任近十年的系主任，美国机械工程师协会会士（ASME）Fellow，具有国际公认的创新研究成果，长期从事非线性动力学, 振动，混沌，高精度可靠性数值计算，现代设计，噪声控制理论及工业应用方向的研究，是连续26年加拿大自然科学基金（NSERC）的获得者，也是加拿大NSERC DAS奖的获得者。发表论文300余篇，专著12部。

　　Dr. Liming Dai教授有在4个加拿大高校工作的经历。曾任加拿大一家企业的厂长兼总工程师。担任过多个国际会议的大会主席及40余个ASME和其它国际会议分会的主席和组织者，也是多个国际科技杂志的编审。曾在14个国家的数十所大学和研究单位讲学和演讲介绍他的研究成果。

　　Most linear and nonlinear dynamic systems existing in nature, physics and engineering are continuous. Such systems are usually described by continuous governing equations, and the solutions of the systems are also continuous. Many systems in the world, however, are discrete or piecewise-constant or piecewise-linear. Numerous methods have been developed for describing and quantitatively solving these two types of systems. Nevertheless, there is still in lack of scientifically sound methods for relating or bridging the two systems which are different in nature and characteristics. A novel approach is thus developed by the presenter to face the challenge. An argument [Nt]/N utilizing a greatest integer function [.] is introduced. With this introduction and an approach proposed by the presenter, both continuous and piecewise-constant/linear systems can be described and solved with piecewise linear solutions. The two types of the systems are therefore seamlessly related. Existence and uniqueness of the solution such obtained are proved mathematically. Notably, the proposed approach provides advantages of higher efficiency, accuracy and reliability in analyzing and solving for linear and nonlinear continuous and discrete systems, in comparison with the other theoretical and numerical methods in the field.