L2(q) and the rank two lie groups : their construction, geometry, and character formulas

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.Includes bibliographical references (leaves 111-113).by Mark R. Sepanski.Ph.D

Finite elements software and applications

The contents of this thesis are a detailed study of the software for the finite element method. In the text, the finite element method is introduced from both the engineering and mathematical points of view. The computer implementation of the method is explained with samples of mainframe, mini- and micro-computer implementations. A solution is presented for the problem of limited stack size for both mini- and micro-computers which possess stack architecture. Several finite element programs are presented. Special purpose programs to solve problems in structural analysis and groundwater flow are discussed. However, an efficient easy-to-use finite element program for general two-dimensional problems is presented. Several problems in groundwater flow are considered that include steady, unsteady flows in different types of aquifers. Different cases of sinks and sources in the flow domain are also considered. The performance of finite element methods is studied for the chosen problems by comparing the numerical solutions of test problems with analytical solutions (if they exist) or with solutions obtained by other numerical methods. The polynomial refinement of the finite elements is studied for the presented problems in order to offer some evidence as to which finite element simulation is best to use under a variety of circumstances

Workshop on Squeezed States and Uncertainty Relations

The proceedings from the workshop are presented, and the focus was on the application of squeezed states. There are many who say that the potential for industrial applications is enormous, as the history of the conventional laser suggests. All those who worked so hard to produce squeezed states of light are continuing their efforts to construct more efficient squeezed-state lasers. Quite naturally, they are looking for new experiments using these lasers. The physical basis of squeezed states is the uncertainty relation in Fock space, which is also the basis for the creation and annihilation of particles in quantum field theory. Indeed, squeezed states provide a unique opportunity for field theoreticians to develop a measurement theory for quantum field theory