Formation of Supramolecular Nanostructures through in Situ Self-Assembly and Post-Assembly Modification of a Biocatalytically Constructed Dipeptide Hydrazide**

Aqueous self-assembly of short peptides has attracted growing attention for the construction of supramolecular materials for various bioapplications. Herein, we describe how the thermolysin-assisted biocatalytic construction of a dipeptide hydrazide from an N-protected amino acid and an amino acid hydrazide leads to the formation of thermally stable supramolecular hydrogels. In addition, we demonstrate the post-assembly modification of the supramolecular architectures constructed in situ tethering hydrazide groups as a chemical handle by means of fluorescence imaging.     

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.     

Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.     

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     

Exact coexistence surfaces containing double critical points for a three-component solution on the Bethe,honeycomb, and square lattices

A model is considered in which the bonds of a lattice are covered by rodlike molecules. Neighboring molecular ends interact with orientation-dependent interactions. The model exhibits closed -loop phase diagrams and double critical points. Exact coexistence surfaces are calculated for the model on the Bethe, honeycomb, and square lattices. The nature of the doubling of the critical exponent near a double critical point is calculated. The behavior of the critical line in the neighborhood of a double critical point is calculated exactly.     

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.