RSOS Models and Jantzen–Seitz Representations of Hecke Algebras at Roots of Unity

A special family of partitions occurs in two apparently unrelated contexts: the evaluation of one-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras H_m. We provide an explanation of this coincidence by showing how the irreducible H_m-modules which remain irreducible under restriction to H_{m_1} (Jantzen–Seitz modules) can be determined from the decomposition of a tensor product of representations sl_n.     

Validation of a method for predicting the precision, limit of detection and range of quantitation in competitive ELISA.

The mathematical model for predicting the precision, limit of detection (LOD) and range of quantitation (ROQ) in a competitive enzyme-linked immunosorbent assay (ELISA) proposed by Hayashi et al. (Anal. Chem., 2004, 76, 1295) was validated. The model describes the relative standard deviation (RSD) of concentration estimates by the RSDs of pipetting volumes of analyte, enzyme-conjugated antigen, antibody and substrate solutions, and the standard deviation (SD) of inherent absorbances between the wells in an ELISA plate. For 6 kinds of direct competitive ELISA kits, the LOD and ROQ predicted by the model agreed well with those obtained by experiments with real samples. It was also confirmed that the model is applicable to the prediction of uncertainty that depends on the pipetting error of the viscous antiserum solution. The model was demonstrated to be useful for estimating the LOD and ROQ of competitive ELISA.     

Preparation and condensation reactions of a new light-fluorous Mukaiyama reagent: reliable purification with fluorous solid phase extraction for esters and amides

A modified light-fluorous Mukaiyama reagent bearing a C₈F₁₇ tag was prepared and examined in ester and amide forming condensation reactions. Following the reactions, the desired product was effectively separated from the fluorous pyridone by-product using a simple fluorous solid phase extraction.     

Non-existence of phase transition of oriented percolation on Sierpinski carpet lattices

 A percolation problem on Sierpinski carpet lattices is considered. It is obtained that the critical probability of oriented percolation is equal to 1. In contrast it was already shown that the critical probability p _c of percolation is strictly less than 1 in Kumagai [9]. This result shows a difference between fractal-like lattice and ℤ ^d lattice. Received: 15 May 2002 / Revised version: 11 October 2002 / Published online: 21 February 2003 Mathematics Subject Classification (2000): Primary: 60K35, 82B43; Secondary: 82B26     

Dielectric behavior of polyethyleneoxide (polyox)

Ohne Zusammenfassung     

Synthetic studies toward maytansinoids (2) a new strategy based on asymmetric induction by heteroconjugate addition of methyllithium onto pyranosyl hetero-olefins

The functionalized pyranosyl hetero-olefins $\text{4a}$, $\text{13}$ and $\text{15}$ received a remarkable diastereoselective addition of methyllithium to form $\text{threo}$ adducts, one of which was introduced into a possible synthetic intermediate as $\text{3}$ for maytansine ($\text{1}$) along Scheme I.     

Gelation in free-radical terpolymerization of poly(allyl methacrylate) crosslinked polymer nanosphere with allyl benzoate and vinyl benzoate

Microgel-like poly(allyl methacrylate) (PAMA nanosphere) was prepared by the emulsion polymerization of AMA as the reactive crosslinked polymer nanosphere with abundant pendant allyl groups. The terpolymerization of PAMA nanosphere with allyl benzoate (ABz) and vinyl benzoate (VBz) was conducted in bulk using benzoyl peroxide as initiator at 80 °C. The gelation depended on the feed ABz/VBz molar ratio since the molecular weights of resulting poly(ABz-co-VBz)s that act as the bridges increased with an increase in the mole fraction of VBz in the feed monomer. Beyond the gel point, the sol was rapidly incorporated into the gel and the increasing tendency of the gel fraction became steeper from 70 to 95 mol% of VBz as a reflection of increased chain length of bridge between PAMA nanospheres. Moreover, the swelling ratio became lower with increasing the mole percentage of VBz in the feed monomer. These results would support the preferential incorporation of PAMA nanosphere into the gel and the longer bridge can capture more nanospheres to give a much shrunken gel.     

Parallel synthesis of tandem Ugi/Diels-Alder reaction products on a soluble polymer support directed toward split-pool realization of a small molecule library

A series of parallel reactions were carried out for the tandem Ugi/Diels-Alder reaction on our MPEG-O-CH₂- platform. Ninety-six out of a 100 entries were successful to give complex heterotricycles. The stereoselectivity was found not to be influenced by the building blocks used for amine and carboxylic acid components. An unexpected side pathway was found but was suppressed by employing appropriate reaction conditions. The reaction was also performed on solid phase, by which a larger library is potentially realized by employing the split-pool method.     

The preparation and the nucleophilic reaction of 3,3-di(1-azolyl)-2-alken-1-ones,precursor of acetylketene derivatives

2-Alken-1-ones, 3,3-di-(1-azolyl)-2-alken-1-ones and related compounds were prepared by two methods. These compounds were found to be the useful precursors for acylketene derivatives such as ketene dithioacetals and diaminals by treatment with various nucleophiles.