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The Borel measure of sequences with bounded run-length

Control Theory and Technology 2022年第3期20卷 316-322页

作者： Alisa DeStefano clyde martin Department of Mathematics and Computer Science College of the Holy Cross1 College StWorcesterMA01610USA Department of Mathematics and Statistics Texas Tech University1108 Memorial CircleLubbockTX79409USA

Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel *** sequences arise in many applications including digitization of certain linear systems involving flows on the circle and 2-torus,large scale simulation,and *** are basic objects of study in ergodic theory.

关键词： Digitization Borel measure Binary sequences Bounded run-length Irrational flow Torus

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OBSERVING THE HEAT EQUATION ON A TORUS ALONG A DENSE GEODESIC

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Systems Science and Mathematical Sciences 1991年第2期4卷 186-192页

作者： Lance D.Drager Robert L.Foote clyde F.martin Department of Mathematics Texas Tech.University.LubbockTX 79409USA Department of Mathematics Wabash CollegeCrawfordsvilleIN 47933USA Department of Mathematics Texas Tech.UniversityLubbockTX 79409USA

Several authors have considered observability problems for the heat equation and relatedpartial differential equations.A basic problem is to determine what kinds of sampling providesufficient information to uniquely determine the initial heat *** address the case wherethe temperature is measured while travelling along a *** consider the special case where the space is a flat torus(of arbitrary dimension)and thecurve is a *** is shown that,in this case,the observed temperature is sufficient informationto uniquely determine the initial heat distribution if and only if the geodesic is dense in the *** the case of a torus,Fourier analysis techniques can be used to write down the solution of theheat *** allows us to derive an explicit representation of the observed temperature interms of the initial *** use this representation and some ideas from the theory ofalmost periodic functions to show that the Fourier coefficients of the initial distribution can berecovered from the observation.

关键词： Observability heat equation inverse problems

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SPLINES AND CONTROL THEORY: PAST,PRESENT AND FUTURE

SPLINES AND CONTROL THEORY: PAST,PRESENT AND FUTURE

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第二十四届中国控制会议

作者： clyde martin MAGNUS EGERSTEDT Department of Mathematics and Statistics Texas Tech Universjty P.O.Box 41042 Lubbock Texas USA Magnus Egerstedt Electrical and Computer Engineering Georgia Institute of Technology. 432 TSRB Atlanta GA 30332

＜正＞ 1. THE PAST Spline functions are those functions that have a certain degree of differentiability at a set of times, called the nodes, and are infinitely differentiable every where else. Mathematical splines wer...

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