Kaehler structures on

Let be a compact connected semi-simple Lie group, let , and let be an Iwasawa decomposition. To a given -invariant Kaehler structure on , there corresponds a pre-quantum line bundle on . Following a suggestion of A.S. Schwarz, in a joint paper with V. Guillemin, we studied its holomorphic sections as a -representation space. We defined a -invariant -structure on , and let denote the space of square-integrable holomorphic sections. Then is a unitary -representation space, but not all unitary irreducible -representations occur as subrepresentations of . This paper serves as a continuation of that work, by generalizing the space considered. Let be a Borel subgroup containing , with commutator subgroup . Instead of working with , we consider , for all parabolic subgroups containing . We carry out a similar construction, and recover in the unitary irreducible -representations previously missing. As a result, we use these holomorphic sections to construct a model for : a unitary -representation in which every irreducible -representation occurs with multiplicity one.

     

Global existence and blow-up for a system of heat equations with non-linear boundary conditions

In this paper, we consider non-negative solutions of We prove that if pq ? 1 every solution remains bounded, while all solutions blow up in a finite time if pq > 1. We also show that if p,q > 1, then blow-up can only occur on the boundary.     

Temperature programmed decomposition (TPDE) of [Mo(CO)(6)] on metal oxide supports: a novel tool to elucidate surface acidity and surface-mediated reactions

A novel technique, the temperature programmed decomposition (TPDE) of [Mo(CO)(6)], has been developed to examine surface acid/base properties. In particular, the nucleophility of different surface hydroxyl groups can be quantified with this method, and it is found that the activation energy for decarbonylation of the carbonyl complex correlates well with the field strength of the metal cations in the support. Activation energies are derived from the CO peak maxima in the TPDE spectra by means of the Redhead equation. TPDE is also used to probe surface-mediated reactions of metal carbonyls. The technique enables identification of intermediates formed during the thermal decomposition process. Comparison with simulated TPDE spectra provides evidence for cluster formation during decarbonylation. By quantifying the amounts of CO and H(2) generated during the TPDE reaction, the surface concentration of the adsorbed species and the oxidation state of the central atom can be deduced at any given temperature.     

Nonparameterized MO calculations of ligand-bridged M2(CO)8-(U2-X)2-type dimers containing metal---metal interactions: Evidence for dictation of stereochemistry by one-electron and two-electron metal---metal σ-type bonds

Nonparameterized MO calculations performed on the (edge-bridged)-bioctahedral metal dimers of the Dessy-characterized [Cr₂(CO)₈(μ₂-PR₂)₂]^(n-2) series and of the [Mn₂(CO)₈(μ₂-PR₂)₂]ⁿ series (n = 0, +1, +2) have revealed that the corresponding dimeric pairs with n = 0, +1, and +2 have two, one, and no electrons, respectively, in the antibonding 2b_3u MO corresponding to a “net” no-electron metal---metal bond, a “net” one-electron metal---metal bond, and a two electron metal---metal bond. Of prime significance is that this 2b_3u MO, which is the LUMO in both electron-pair (metal---metal)-bonded dimers (n = +2) and the HOMO in the corresponding dimers to which one or two electrons have been added, is found to be largely composed of in-plane antibonding σ-type dimetal orbital character rather than either out-of-plane π-type dimetal antibonding orbital character or bridging-ligand orbital character. These MO results are also shown to be completely compatible with the available spectral and X-ray data.     

Molecular epidemiological investigation of Ascaris genotypes in China based on single-strand conformation polymorphism analysis of ribosomal DNA

Using a single-strand conformation polymorphism-based approach, we investigated nucleotide variation in part of the first internal transcribed spacer (pITS-1) of nuclear ribosomal DNA within and among a large number of Ascaris individuals from humans and pigs from six endemic regions in China, and examined the frequency of the different genotypes of Ascaris in relation to host species and geographical origin. Five different SSCP genotypes (G1-G5) were recorded for human Ascaris (n = 486), of which three (genotypes G1-G3) were detected for pig Ascaris (n = 329). Of the five Ascaris genotypes detected, genotype G1 predominantly infected humans (approximately 63-74%) whereas genotype G3 infected mainly pigs (approximately 79-86%), indicating that each of these genotypes has a particular host affiliation. In contrast, the frequencies of the other three genotypes was substantially lower for each of the two host species. The findings also suggested that the rate of cross infection of Ascaris between humans and pigs is relatively low and that gene flow between the predominant genotypes is limited, consistent with previous proposals for endemic regions in other countries. While the nature and extent of nucleotide variation in the pITS-1 (and the proposal of host affiliated Ascaris populations) may relate to "introgression" or "lineage sorting and retention of ancentral polymorphism", other explanations are possible. Evidence of multiple pITS-1 sequence types in some Ascaris individuals representing particular genotypes (e.g., G2 and G5) may suggest hybridization between human- and pig-affiliated Ascaris. This aspect and the species status of Ascaris (from each host species) warrant future experimental testing, employing the pig/Ascaris model and the present electrophoretic approach.*     

Optimal Control of Cancer Chemotherapy with Delays and State Constraints

Journal of Optimization Theory and Applications - A mathematical model of cancer chemotherapy is considered as an optimal control problem with the objective of either minimizing a weighted sum of...     

Revisit to the formation mechanism of exfoliated montmorillonite/PMMA nanocomposite latex through soap‐free emulsion polymerization

Soap‐free emulsion polymerization of methyl methacrylate (MMA) in the aqueous suspension of montmorillonite (MMT) was able to fabricate the exfoliated MMT/PMMA nanocomposite latex. Because neither MMA nor substantial quantity of potassium persulfide (KPS) initiator could be individually absorbed into the interlayer region of MMT, the polymerizing ionic radicals in water phase were considered as a major component to diffuse into the gallery of MMT. They have been observed to organize into disk‐like micelles in the interlayer regions to exfoliate MMT. The diffusion of the polymerizing ionic radicals was further supported by using sodium dodecyl sulfate (SDS) surfactant as a model compound to diffuse into the gallery of MMT. The exfoliation of MMT was almost completed before micellization stage was over. After exfoliation, the disk‐like micelles became a polymerization loci for monomers. Because the disk‐like micelles in numbers were substantially over the commonly formed spherical micelles in the typical soap‐free emulsion polymerization, the conversion rate of MMA to MMT/PMMA nanocomposite latex was faster. Based on the above experimental observation, a justified exfoliation mechanism of MMT was proposed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 459–466, 2009