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Full-Text Articles in Physical Sciences and Mathematics
The Kalman Filter On Time Scales, Nicholas J. Wintz
The Kalman Filter On Time Scales, Nicholas J. Wintz
Doctoral Dissertations
"In this work, we study concepts in optimal control for dynamic equations on time scales, which unfies the discrete and continuous cases. After a brief introduction of dynamic equations on time scales, we will examine controllability and observability for linear systems. Then we construct and solve the linear quadratic regulator for arbitrary time scales. Here, we seek to find an optimal control that minimizes a given cost function associated with a linear system. We will find such an input under two different settings; when the final state is fixed and when it is free. Later, we extend these results to …
Holomorphic Extensions In Toric Varieties, Malgorzata Aneta Marciniak
Holomorphic Extensions In Toric Varieties, Malgorzata Aneta Marciniak
Doctoral Dissertations
"The dissertation describes the Hartogs and the Hartogs-Bochner extension phenomena in smooth toric varieties and their connection with the first cohomology group with compact support and sheaf coefficients. The affirmative and negative results are proved for toric surfaces and for line bundles over toric varieties using topological, analytic, and algebraic methods"--Abstract, page iii.