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Full-Text Articles in Physical Sciences and Mathematics
Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev
Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev
Masters Theses & Specialist Projects
The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we …
Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix
Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix
Masters Theses & Specialist Projects
This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set.
The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies …