Matrix inequalities from a two variables functional

Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea and technical tool is a two variables log-convex norm functional (Theorem 1.2).Comment: Final version, to appear in International J. Math: Two corollaries on Schur products have been added at the end of Section

Pinchings and Positive linear maps

We employ the pinching theorem, ensuring that some operators A admit any sequence of contractions as an operator diagonal of A, to deduce/improve two recent theorems of Kennedy-Skoufranis and Loreaux-Weiss for conditional expectations onto a masa in the algebra of operators on a Hilbert space. We also get a few results for sums in a unitary orbit

Selective Oxidative Homo- and Cross-Coupling of Phenols

The efforts described in this dissertation initially focus on the asymmetric coupling of phenols. We have developed Schiff base vanadium catalyst for the oxidative coupling of phenols with high reactivity and enantioselectivity. To the best of our knowledge, this example constitutes the first highly selective asymmetric coupling of phenols. Several substrates were coupled with our vanadium catalyst with good enantioselectivity (72-89% ee). The first simple catalystic system that uses atom-economical oxygen as the terminal oxidant to accomplish selective ortho−ortho, ortho−para, or para−para homo-couplings of phenols was developed. Chromium salen catalysts have been discovered and verified as uniquely effective in the cross-coupling of different phenols with high chemo- and regio-selectivity. A broad scope of phenol substrates was found for these reaction conditions giving cross-coupling products with good yield (up to 88%). In order to understand the mechanism of cross-coupling reaction, spectroscopic methods, additive experiments, SAR studies, and kinetic experiments were performed and a mechanism was postulated. Finally, we established an efficient route for the total synthesis of honokiol by utilizing a novel disconnection that transits new structures. This five step (six chemical reactions) synthesis was initiated by oxidative cross-coupling of inexpensive commercial phenols with high yield (91%). Following retro Friedel-Crafts alkylation, a protection reaction proceeded smoothly with excellent yield (89% for three steps). The remaining steps of radical bromination, Kumada coupling and demethylation were each optimized. The total yield over five steps was 34% and gram-scale reactions were conducted for each step

On a decomposition lemma for positive semi-definite block-matrices

This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices

The origin of working memory deficits in Parkinson's disease

Title from PDF of title page (University of Missouri--Columbia, viewed on February 27, 2013).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Dissertation advisor: Steven A. HackleyIncludes bibliographical references.Vita.Ph. D. University of Missouri--Columbia 2012."December 2012"Two experiments were conducted to examine the mechanisms underlying deficits of visual working memory in Parkinson's disease (PD). One study combined behavioral methods with event-related potentials (ERPs), the other, behavioral methods with structural and functional magnetic resonance images (MRIs). In both experiments, participants viewed an array of colored rectangles, some of which were task-irrelevant. Then, after a brief delay, they reported whether the orientation of any relevant figures had changed. By comparing trials with and without task-irrelevant items, it was shown that poor attentional filtering contributes to poor memory, both in people with and in those without PD. Measures of basal ganglia activation prior to the retention interval were generally consistent with claims that this structure serves as a “gate-keeper” to working memory. Structural analyses identified three regions for which disease-specific atrophy was negatively correlated with capacity—the right intraparietal sulcus (IPS) and the left and right pre-supplementary motor area (pre-SMA). Thus, converging evidence from behavior, electrophysiology, and MRI indicate that lowered capacity and poor attentional filtering both underlie deficits of working memory in people with Parkinson's disease.Includes bibliographical reference