CA2 (Continuum Analysis, 2- dimensional) is a computer program developed by the author. CA2 can solve a variety of complex geotechnical problems using explicit finite difference method. In this paper, an introduction will be given to the theoretical and numerical basis of the program and the capability of the code will be shown by solving a few interesting nonlinear and transient problems. Fina...

Using a “3 by 3 matrix trick” we previously showed that multiplication in a C*-algebra A, an algebraic structure, is determined by the geometry of the C*-algebra of the 3 by 3 matrices with entries from A, M3(A). As an application of this algebra-geometry duality we now construct an order theoretic based duality theory for all groups which are either locally compact abelian or finite. This cons...

In the present study, stress analysis and explicit solution of rectangular plate with arbitrarily located circular hole, subjected to linear normal stresses on two opposite edges, has been investigated. Airy function and hoop stresses occurring at the edge of the circular have been computed. In this method 2D dimension elasticity and Airy stress function was used. The present method for explici...

ACKNOWLEDGEMENTS I would like to truly thank all of my committee members for their encouragement and guidance in the preparation of this thesis. I especially want to express my gratitude to Dr. Kevin Clarno for his insight and assistance. My advisor, Dr. Cassiano de Oliveira, has been immensely helpful with his continuous encouragement and unique perspectives. Perhaps most of all, I want to tha...

Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation, and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise...

In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtaine...

Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this paper we study the problems of intersection, complementation and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise t...

‎‎we exhibit an explicit construction for the second cohomology group‎ ‎$h^2(l‎, ‎a)$ for a lie ring $l$ and a trivial $l$-module $a$‎. ‎we show how the elements of $h^2(l‎, ‎a)$ correspond one-to-one to the‎ ‎equivalence classes of central extensions of $l$ by $a$‎, ‎where $a$‎ ‎now is considered as an abelian lie ring‎. ‎for a finite lie‎ ‎ring $l$ we also show that $h^2(l‎, ‎c^*) cong m(l)$‎...