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数学 & 物理 & 化学 & 力学 : 学术学位

Theory of random networks and their applications.

This work is a generalization of the classical Erdos-Renyi (ER) random graph and recently emerging theory of "power-law" random networks. Particularly, we are interested in providing the theory of power-law random graphs with a rigorous probabilistic interpretation. We propose a generalized random g

Total synthesis of (+)-discodermolide.

An enantioselective total synthesis of the marine natural product (+)-discodermolide has been accomplished utilizing a highly convergent and stereocontrolled strategy. The C1-C24 fragment was constructed via a palladium-mediated sp2-sp3 cross-coupling reaction between the C1-C14 vinyl iodide and the

Mutually nearly orthogonal Latin squares and their applications.

This work includes both statistical and combinatorial results for mutually nearly orthogonal Latin squares (MNOLS) of order v = 2 m. MNOLS are closely related to mutually orthogonal Latin squares (MOLS); MNOLS modifies the orthogonality condition of MOLS slightly.; Experiments are considered for mai

Tessellations of moduli spaces and the mosaic operad.

The moduli space Mn0 C of Riemann spheres with n punctures has an extensive history. We study the real points Mn0 R of this space, the set of fixed points of Mn0 C under complex conjugation. It is known that Mn0 R is naturally tessellated by open copies of the Stasheff associahedron Kn

Topics in partial differential equations and the calculus of variations.

In this thesis, we study separately the topics in two aspects of the modern analysis: Partial Differential Equations and the Calculus of Variations.; In Part I, we study the differential equation {dollar}P(D)u=f{dollar} on the whole space and the exterior of an infinite cylinder in the case when f h

A combined near-field scanning microwave microscope and transport measurement system for characterizing dissipation in conducting and high-temperature superconducting films at variable temperatures.

Identifying defects and non-superconducting regions in high-temperature superconductors (HTS) is of great importance because they limit the material's capability to carry higher current densities and serve as nucleation spots for "hot spots" that can evolve over time and drive a HTS from superconduc


This dissertation concentrates on three aspects of accelerated depreciation for public utilities: Valuation of a regulated firm, risk and rate of return for electric utilities, and pricing behaviour of electric utilities. First chapter analyzes the literature extensively about accelerated depreciati

A new approach to ultrashort laser pulse amplification.

Ultrashort laser pulse amplification by a counterpropagating pumping beam, through Raman backscattering in plasma, has been demonstrated. The amplification and spectral characteristics of the amplified pulse agree with the linear theory of Raman amplification. This research is part of an investigati

Vibrational energy relaxation in liquids.

Vibrational energy relaxation (VER) and vibrational cooling (VC) of polyatomic liquids are studied with the ultrafast Infrared-Raman (IR-Raman) technique. In the IR-Raman technique, a type of two-dimensional vibrational spectroscopy, a vibrational transition is pumped with a mid- infrared pulse and

Perversions and whips: Static and dynamic problems of elastic filaments.

Two problems of elastic filaments are considered, one a problem of determining the static shape of a filament with intrinsic curvature tinder constant force, and one a problem of determining the dynamical behavior of a planar rod. In the first problem, examining the phenomenon of perversion, methods