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数学 & 物理 & 化学 & 力学 : 学术学位

A SUSY SO(10) GUT model with lopsided structure.

The standard model (SM) of elementary particles has been established for more than 30 years and tested by a large number of experiments. However, because of the naturalness problem of the electroweak symmetry breaking scale and a large number of unexplained parameters in SM, physicists have been loo

Division algebras over generalized local fields.

We call F a generalized local field (abbreviated GLF) if F is Henselian and , the residue field of F, is finite. In this thesis, we prove several results on finite-dimensional division algebras over GLF's. The aim of the firs

Spectroscopy of mass-selected metal clusters in argon matrices.

The chemistry of metal clusters is a fascinating and expanding area of research. During the last three decades, the study of metal clusters and in particular transition metal clusters has been the subject of numerous experimental and theoretical investigations. The desire to understand the frontier

Studies toward the enantioselective total synthesis of pectenotoxin 2.

Studies toward the enantioselective total synthesis of the marine natural toxin pectenotoxin 2 are described. A successful approach to a fully functionalized precursor to the C(29)--C(40) FIG sector began with the establishment of a proper stereochemical relationship between the hydroxyl and methyl

Diophantine equations and the generalized Riemann hypothesis.

Questions about the existence of integer solutions to Diophantine equations have interested mathematicians since antiquity. In the 1970s, the work of Davis, Matiyasevic and Robinson showed that no universal algorithm may exist which can test, all arbitrary Diophantine equation for integer solutions.

Characterization of HMX phases using Raman microscopy.

The study and characterization of high power explosives has become an important research field due to the constant use of these kinds of materials by terrorists. In order to develop an efficient explosive detection system, the explosives must be fully characterized. One of the techniques being explo

Luminescent polymers via alkyne metathesis.

Part I begins with an investigation of the alkyne metathesis process, particularly with regards to the catalyst's tolerance to different functional groups. The findings are taken into account as the same simple catalyst system is used to form novel macrocycles (chapter 2) and novel alkyne-bridged co

Wide band gap semiconductor optical waveguide.

This dissertation involves the design, fabrication and characterization of wide band gap semiconductor optical waveguide devices. Prism coupling was used as the primary characterization method to obtain design parameters of the refractive index and propagation loss of the wide band gap semiconductor

Optimal switching with applications to energy tolling agreements.

We consider the problem of optimal switching with finite horizon. This special case of stochastic impulse control naturally arises during analysis of operational flexibility of exotic energy derivatives. The current practice for such problems relies on Markov decision processes that have poor dimens

Thin films and surface interactions.

The focus of this work is the employment of thin films on surfaces to create novel optical, mechanical, or chemical properties. In the case of novel optical properties, the successful production of a thin solid film of potassium niobate is described as well as the usefulness of nonlinear optical app

Lie algebras and their universal envelopes.

The main results of this thesis can be divided into two parts. In the first part, we consider the isomorphism problem for enveloping algebras. Let L be a Lie algebra with universal enveloping algebra U( L). Given another Lie algebra H with the property that U(L) ≅ U( H) as algebras, the isomor

Learning from molecules: Coherent feedback control in liquid phase.

Coherent control of light and matter is a major tool in current atomic physics and physical chemistry research. Technological advances in ultrafast laser pulse shaping allow control over the dynamics of molecular systems on sub-picosecond timescales. This thesis demonstrates feedback control over a