On the Conservativeness of Some Markov Processes

We give a unified method to obtain the conservativeness of a class of Markov processes associated with lower bounded semi-Dirichlet forms on L ²(X;m), including symmetric diffusion processes, some non-symmetric diffusion processes and jump type Markov processes on X, where X is a locally compact separable metric space and m is a positive Radon measure on X with full topological support. Using the method, we give an example in each section, providing the conservativeness of the processes, that are given by the “increasingness of the volume of some sets(balls)” and “that of the coefficients on the sets” of the Markov processes.     

Axisymmetrical buckling of an initially deformed shallow spherical shell under external pressure

Axisymmetrical snap buckling of a clamped shallow spherical shell with initial deformation and subject to uniform pressure is analysed based on the finite-deformation theory. As a refinement to analyses given in the author's previous papers, a variable term in the deformation pattern is introduced and Galerkin's method is applied to the non-linear simultaneous differential equations, so that upper buckling pressures are obtained as a function of the geometrical parameter α. Non-uniqueness of solution is shown in the region of larger values of α, where the higher order of deformation mode takes place. Stability of a number of possible equilibrium states is checked by use of the second variation of total potential energy to clarify the actual buckling process. The remark- able decrease of buckling pressure is reasonably explained by introducing a small initial deflection, which explains the discrepancy between the classical buckling pressure and experimental results.     

Two-dimensional self-assembled structures of melamine and melem at the aqueous solution-Au(111) interface

Self-assembled structures of melamine and the condensed melamine derivative melem were investigated at aqueous solution-Au(111) interfaces by cyclic voltammetry and in situ scanning tunneling microscopy (STM) observation. The adsorption/desorption behaviors of both molecules on Au(111) surfaces could be controlled by varying the electrochemical potential and solution concentration. In the negative potential region, self-assembled structures of melem and melamine were constructed by double hydrogen bonding systems between nitrogen atoms of triazine rings and amine groups. In addition, melem formed a closely packed structure at potentials of between -0.3 and -0.15 V or in solutions at higher concentrations.     

Engineering the promiscuous racemase activity of an arylmalonate decarboxylase

Variant G74C of arylmalonate decarboxylase (AMDase) from Bordatella bronchoseptica has a unique racemising activity towards profens. By protein engineering, variant G74C/V43A with a 20-fold shift towards promiscuous racemisation was obtained, based on a reduced activity in the decarboxylation reaction and a two-fold increase in the racemisation activity. The mutant showed an extended substrate range, with a 30-fold increase in the reaction rate towards ketoprofen. Molecular dynamics simulations and the substrate profile of the racemase indicate that the steric and polar effects of the substrate structure play a more dominant role on catalysis than mere kinetic α-proton acidity. The observation that the conversion of β,γ-unsaturated carboxylic acids does not lead to a rearrangement to form their α,β isomers indicates a concerted rather than a stepwise mechanism. Interestingly, a substrate bearing a nitro group instead of the carboxylic acid group on the α-carbon atom was also converted by the racemase.     

Halichonines A, B, and C, novel sesquiterpene alkaloids from the marine sponge Halichondria okadai Kadota

Novel sesquiterpene alkaloids, halichonines A (1), B (2), and C (3), were identified from the marine sponge Halichondria okadai Kadota. By spectroscopic analyses and synthesis, their structures were revealed to include a 6,6-bicyclic ring system and two prenylated amine moieties. In addition, 2 induced apoptosis in HL60 human leukemia cells.     

On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities

Journal of Theoretical Probability - We consider symmetric stable-type processes with degenerate/singular Lévy densities via Dirichlet form theory. We give conditions of some global path...     

Synthesis and properties of π‐conjugated dithiafulvene oligomers by addition of a monofunctionalized compound

Dithiafulvene oligomers ( 3 ) were prepared by cycloaddition polymerization of aldothioketenes with their alkynethiol tautomers derived from 1,4‐diethynylbenzene ( 2 ) with the addition of 1‐ethynyl‐4‐methylbenzene ( 1 ) as a monofunctionalized compound. Different feed ratios of 2 / 1 were used to control the molecular weights of 3 . The structures of 3 were confirmed by IR and ¹H NMR spectroscopies in comparison with those of 2‐(4‐tolylidene)‐4‐tolyl‐1,3‐dithiol ( 4 ) as a model compound, which was obtained by the treatment of lithium 2‐tolylethynethiolate with water in Et₂O. The number‐average degree of polymerization (DP) and the number‐average molecular weight were measured by gel permeation chromatographic and ¹H NMR analysis. DP increased with an increasing feed ratio of 2 / 1 . The ultraviolet–visible spectra of 3 in diluted acetonitrile showed that the absorption maxima of 3 increased with an increasing DP of 3 . These redshifts are ascribed to an effective expansion of the π‐conjugation system in 3 . The oligomers exhibited a maximum conjugation length of seven repeating units. The redox properties of 3 were examined by cyclic voltammetry. The oxidation half‐peak potentials (E_p/2) of 3 were slightly cathodically shifted with increasing DP. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 708–715, 2003