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.     

Exiguolide, a new macrolide from the marine sponge Geodia exigua

A new 20-membered macrolide designated exiguolide has been isolated from the marine sponge Geodia exigua, and its structure determined by interpretation of spectroscopic data. Exiguolide specifically inhibited fertilization of sea urchin (Hemicentrotus pulcherrimus) gametes but not embryogenesis of the fertilized egg.     

Effect of Ru crystal orientation on the adhesion characteristics of Cu for ultra-large scale integration interconnects

The adhesion of Cu on Ru substrates with different crystal orientations was evaluated. The crystal orientation of sputter deposited Ru could be changed from (1 0 0) to (0 0 1) by annealing at 650 °C for 20 min. The adhesion of Cu was evaluated by the degree of Cu agglomeration on Ru. Cu films on annealed Ru films with the (0 0 1) crystal orientation showed 28% lower RMS values and 50% lower Ru surface coverage than Cu as-deposited on Ru having the (1 0 0) crystal orientation after annealing at 550 °C for 30 min, which suggest that Cu wettability on the Ru(0 0 1) was better than that on the Ru(1 0 0) plane. The low lattice misfit of 4% between Cu(1 1 1) and Ru(0 0 1) may be the reason for this good adhesion property.     

Magneto-Optical Measurement of Organic Conductor Using Rotational Cavity System

We have developed a new magneto-optical measurement system using a rotational cavity system equipped with a millimeter vector network analyzer and a 14 T solenoid type super conducting magnet. The measurement can be performed in the transmission configuration down to 1.6 K. The results of the precise angular dependence measurement of quasi-one-dimensional organic conductor (DMET)₂I₃ using the new system are shown, and its Fermi surface will be discussed in connection with the previous reports.     

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.     

Noncommutative algebras related with Schubert calculus on Coxeter groups

For any finite Coxeter system (W,S) we construct a certain noncommutative algebra, the so-called bracket algebra, together with a family of commuting elements, the so-called Dunkl elements. The Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra of the Coxeter group W. We prove this conjecture for classical Coxeter groups and I₂(m). We define a “quantization” and a multiparameter deformation of our construction and show that for Lie groups of classical type and G₂, the algebra generated by Dunkl’s elements in the quantized bracket algebra is canonically isomorphic to the small quantum cohomology ring of the corresponding flag variety, as described by B. Kim. For crystallographic Coxeter systems we define the so-called quantum Bruhat representation of the corresponding bracket algebra. We study in more detail the structure of the relations in B_n-, D_n- and G₂-bracket algebras, and as an application, discover a Pieri-type formula in the B_n-bracket algebra. As a corollary, we obtain a Pieri-type formula for multiplication of an arbitrary B_n-Schubert class by some special ones. Our Pieri-type formula is a generalization of Pieri’s formulas obtained by A. Lascoux and M.-P. Schützenberger for flag varieties of type A. We also introduce a super-version of the bracket algebra together with a family of pairwise anticommutative elements, the so-called flat connections with constant coefficients, which describes “a noncommutative differential geometry on a finite Coxeter group” in the sense of S. Majid.     

Constructive and Destructive Two-Pulse Excitation Investigated with a White-Light Michelson Interferometer

Linear propagation of two pulses through methanol solution of aluminum phthalocyanine chloride is investigated using a modified white-light Michelson interferometer. The observed coherence time of the white light is 6 fs, and the separation between the two-excitation pulses is set to about 10 fs. The excitation is dependent on the phase-relation between the two pulses. We have observed an enhancement of the excitation when the two pulses are in-phase and strong suppression of the excitation when the two pulses are out of phase by π.