Tannakian categories, linear differential algebraic groups, and parameterized linear differential equations

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the category of representations of a linear algebraic group.Comment: 26 pages; corrected misprints; simplified Definition 2; more references adde

Measurement of surface roughness slope

Instrument, consisting of isolator, differentiator, absolute value circuit, and integrator, uses output signal from surface texture analyzer profile-amplifier to calculate surface roughness slope. Calculations provide accurate, instantaneous value of the slope. Instrument is inexpensive and applicable to any commerical surface texture analyzer

Generalized Thermalization in an Integrable Lattice System

After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (~10^10 eigenstates) validate our approach.Comment: 8 pages, 9 figures, as publishe

Chaos and Thermalization in the one-dimensional Bose-Hubbard model in the classical-field approximation

In this thesis, we present a comprehensive study of chaos and thermalization of the one-dimensional Bose-Hubbard Model (BHM) within the classical field approximation. Two quantitative measures are compared: the ensemble-averaged Finite-time Maximal Lyapunov exponent, a measures of chaos and the normalized spectral entropy, a measure of the distance between the numerical time-averaged momentum distribution and the one predicted by thermodynamics. A threshold for chaos is found, which depends on two parameters, the nonlinearity and the total energy-per-particle. Below the threshold, the dynamics are regular, while far above the threshold, complete thermalization is observed, as measured by the normalized spectral entropy. We study individual resonances in the Bose-Hubbard model to determine the criterion for chaos. The criterion based on Chirikov's method of overlapping resonances diverges in the thermodynamic limit, in contrast to the criterion parameters inferred from numerical calculations, signifying the failure of the standard Chirikov's approach. The Ablowitz-Ladik lattice is one of several integrable models that are close to the BHM. We outline the method of Inverse Scattering Transform and generate the integrals of motion of the Ablowitz-Ladik lattice. Furthermore, we discuss the possible role of these quantities in the relaxation dynamics of the BHM.Comment: PhD Thesis. 143 pages. Minor edits

Chapter~1. Alkylation chemistry of the camphor imine of tert-butyl glycinate and its derivatives. Chapter~2. Synthesis and reactions of a new carbon(2) symmetric ketone.

Factors which influence the diastereoselectivity in the alkylation of the (R)-camphor imine of tert-butyl glycinate (24) were investigated in order to further refine the alkylation model. It was demonstrated that when alkylating 24 with various benzyl bromides or allyl bromide that the diastereoselectivity was dependent on the $\pi$-electron density of the alkylating agent, the metal cation of the enolate and the cosolvent used. Inferior selectivities (de\u27s $$ 95%) were obtained when using HMPA as the cosolvent, Li or Na as the metal cation and alkylating agents with electron rich $\pi$-systems. Further study included the preparation of several camphor derivatives (ketopinic acid, methyl ketopinate, 3-hydroxycamphor, 1-hydroxymethyl camphor) which were utilized as chiral auxiliaries in the alkylation of their corresponding imines of tert-butyl glycinate. These investigations lead to the discovery of two new and unexpected reactions of the camphor skeleton. Finally, a new C\sb2 symmetric ketone, cis,anti,cis-tricyclo (6.3.0.0\sp{3,7}\rbrackundecan-2-one (91) was prepared in 91% ee. Initial efforts to use this ketone as a chiral auxiliary in the alkylation of chiral imines of tert-butyl glycinate failed since condensation of 91 with several amines was not possible. This lead to an investigation into the utility of cis,anti,cis-tricyclo (6.3.0.0\sp{3,7}\rbrackundecan-2-ol (92) as a chiral auxiliary. Source: Dissertation Abstracts International, Volume: 53-12, Section: B, page: 6300. Thesis (Ph.D.)--University of Windsor (Canada), 1992

Tannakian approach to linear differential algebraic groups

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.Comment: 31 pages; corrected misprint

In-vivo magnetic resonance imaging of hyperpolarized silicon particles

Silicon-based micro and nanoparticles have gained popularity in a wide range of biomedical applications due to their biocompatibility and biodegradability in-vivo, as well as a flexible surface chemistry, which allows drug loading, functionalization and targeting. Here we report direct in-vivo imaging of hyperpolarized 29Si nuclei in silicon microparticles by MRI. Natural physical properties of silicon provide surface electronic states for dynamic nuclear polarization (DNP), extremely long depolarization times, insensitivity to the in-vivo environment or particle tumbling, and surfaces favorable for functionalization. Potential applications to gastrointestinal, intravascular, and tumor perfusion imaging at sub-picomolar concentrations are presented. These results demonstrate a new background-free imaging modality applicable to a range of inexpensive, readily available, and biocompatible Si particles.Comment: Supplemental Material include

Investigation of additives for improvement of adhesive and elastomer performance Final report

Improvement additives for adhesive and elastomer performanc

Make it so! Jean-Luc Picard, Bart Simpson and the design of e-public services

In this paper, we report on a project applying participatory design methods to include people who have experience of social exclusion (in one form or another) in designing possible technologies for e-(local)-government services. The work was part of a project for the Office of the Deputy Prime Minister in the UK, and was concerned with ‘access tokens’ that can provide personal identification for individuals accessing public services, based on technologies such as multi-functional smartcards, flash memory sticks, mobile phone SIMs or similar devices. In particular we report on our experience using the ‘pastiche scenarios’ technique recently developed by Mark Blythe. Our findings indicate that the technique can be effective and engaging in helping people to create realistic scenarios of future technology use and highlight some possible pitfalls to consider when using this technique.</p

Trade Policy Aspects of Industrial Policy in the U.S.

trade policy and industrial strategy--United State