Mathematics Commons^™

Discrete-Time Control With Non-Constant Discount Factor, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau

Mathematics Faculty Research Publications

This paper deals with discrete-time Markov decision processes (MDPs) with Borel state and action spaces, and total expected discounted cost optimality criterion. We assume that the discount factor is not constant: it may depend on the state and action; moreover, it can even take the extreme values zero or one. We propose sufficient conditions on the data of the model ensuring the existence of optimal control policies and allowing the characterization of the optimal value function as a solution to the dynamic programming equation. As a particular case of these MDPs with varying discount factor, we study MDPs with stopping, …

The Wedge Family Of The Cohomology Of The C-Motivic Steenrod Algebra, Hieu Trung Thai

Wayne State University Dissertations

Computing the stable homotopy groups of the sphere spectrum is one of the most important problems of stable homotopy theory. Focusing on the 2-complete stable homotopy groups instead of the integral homotopy groups, the Adams spectral sequence appears to be one of the most effective tools to compute the homotopy groups. The spectral sequence has been studied by J. F. Adams, M. Mahowald, M. Tangora, J. P. May and others.

In 1999, Morel and Voevodsky introduced motivic homotopy theory. One of its consequences is the realization that almost any object studied in classical algebraic topology could be given a motivic …

Variational Analysis In Second-Order Cone Programming And Applications, Hang Thi Van Nguyen

Wayne State University Dissertations

This dissertation conducts a second-order variational analysis for an important class on nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone. These second-order cone programs (SOCPs) are mathematically challenging due to the nonpolyhedrality of the underlying second-order cone while being important for various applications. The two main devices in our study are second epi-derivative and graphical derivative of the normal cone mapping which are proved to accumulate vital second-order information of functions/constraint systems under investigation. Our main contribution is threefold:

- proving the twice epi-differentiability of the indicator function of the second-order cone and of the augmented Lagrangian associated with …

Study Of Grain Growth In Single-Phase Polycrystals, Pawan Vedanti

Wayne State University Dissertations

Materials with random microstructure are characterized by additional thermodynamic parameters, entropy and temperature of microstructure. It has been argued that there is one more law of thermodynamics: entropy of microstructure decays in isolated systems. This assertion has been checked experimentally for the process of grain growth which showed that entropy of grain structure decays indeed as expected. The equation of state for microstructure entropy has also been studied. In general, entropy of grain microstructure is expected to be a function of grain structure energy and the average grain size. Our experiments suggest that in fact, the equation of state degenerates …

Making Real-World Connections In High School Mathematics: The Effectiveness Of A Professional Development Program In Changing Teachers’ Knowledge, Beliefs, And Practices, Thad Ludlam Wilhelm

Wayne State University Dissertations

The study aimed to assess the impact of a professional development workshop at changing secondary mathematics teachers’ knowledge, beliefs, and practices related to real-world applications of algebra. It also addressed gaps in the research literature related to teacher knowledge of how algebra is used by professionals in non-academic settings and their beliefs about the relevance of algebra to their students’ lives. The observational study employed mixed methods. Principal components analysis was conducted on responses to an online questionnaire. Pre-test vs. post-test comparisons were made for workshop participants. Treatment vs. control comparisons were also made using a nationally representative random sample …

Stochastic Approximation And Applications To Networked Systems, Thu Thi Le Nguyen

Wayne State University Dissertations

This dissertation focuses on a class of SA algorithms with applications to networked systems and is based on the published works that have been done jointly during my Ph.D. training. The networked systems are fundamentally characterized by interaction among control, communications, and computing, with applications in a vast array of emerging technologies such as smart grids, intelligent transportation systems, social networks, smart city, to name just a few. Networked systems encounter many environment uncertainties that are inherently stochastic. Besides the aforementioned advantages, the framework of SA can also accommodate multiple random processes and diversified system dynamics, even random and distributed …