Regularity of Harmonic Functions in Cheeger-Type Sobolev Spaces

We give a geometric approach to the study of the regularity of harmonic functions in Cheeger-type Sobolev spaces, and prove the Hölder continuity of such functions. In the proof, we give a definition of an upper curvature bound of the unit sphere of a Banach space, which seems to be of independent interest.     

Products, cones, and suspensions of spaces with the measure contraction property

This article concerns several geometric properties of metricmeasure spaces satisfying the measure contraction property (MCP),which can be considered as a generalized notion of lower Riccicurvature bounds. We prove that the MCP of spaces descends totheir products and Euclidean cones. We also show that a positivelycurved space in terms of the MCP with a maximal diameter canbe represented as the spherical suspension of some topologicalmeasure space.     

Accelerated glycosylation under frozen conditions

O-Glycosylations using thiomethyl glycosides as donors were compared under both frozen and unfrozen conditions. In the presence of MeOTf as a promoter, enormous rate acceleration was observed when the glycosylation was conducted in p-xylene below its freezing point.     

Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations

We study here instability problems of standing waves for the nonlinear Klein–Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave's frequency or the wave's speed of propagation and on the nonlinearity.     

Electrochiroptical systems based on biphenyl-2,2′-diyl-type dicationic dyes: strong chiroptical signals through the transmission of point chirality to axial chirality

Huge CD amplitude (A = +538) was attained by diastereomeric preference (50% de) for the title dication with two bis[4-(R)-sec-butoxyphenyl]methylium units in benzene at 23 °C. Intramolecular π-π stacking is the origin for effective transmission of point chirality to axial chirality to attain the chiroptical enhancement of 400-times. Thanks to the strong CD signaling, chiroptical changes upon electrolysis could be readily detected, thus realizing a new class of electrochiroptical response systems. Chiroptical properties could also be modified by solvent polarity.     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

Formation of non-racemic E- and Z-olefins based on discrimination of enantiotopic carbonyl groups in α-diketones by a chiral phosphonate reagent

A chiral HWE reagent reacted with an alternative carbonyl group of meso-α-diketones of bicyclo[2.2.1] system to give non-racemic (Z)- and (E)-olefins, respectively.     

Combinatorial synthesis of MUC1 glycopeptides: polymer blotting facilitates chemical and enzymatic synthesis of highly complicated mucin glycopeptides

The chemoselective polymer blotting method allows for rapid and efficient synthesis of glycopeptides based on a "catch and release" strategy between solid-phase and water-soluble polymer supports. We have developed a heterobifunctional linker sensitive to glutamic acid specific protease (BLase). The general procedure consists of five steps, namely (i) the solid-phase synthesis of glycopeptide containing BLase sensitive linker, (ii) subsequent deprotections and the release of the glycopeptide from the resin, (iii) chemoselective blotting of the glycopeptide intermediates in the presence of water-soluble polymers with oxylamino functional groups, (iv) sugar elongations using glycosyltransferases, and (v) the release of target glycopeptides from the polymer platform by selective BLase promoted hydrolysis. The combined use of the solid-phase chemical syntheses of peptides and the enzymatic syntheses of carbohydrates on water-soluble polymers would greatly contribute to the production of complicated glycopeptide libraries, thereby enhancing applicative research. We report here a high-throughput synthetic system for the various types of MUC1 glycopeptides exhibiting a variety of sugar moieties. It is our belief that this concept will become part of the entrenched repertoire for the synthesis of biologically important glycopeptides on the basis of glycosyltransferase reactions in automated and combinatorial syntheses.