Long Time Behavior of the Volume of the Wiener Sausage on Dirichlet Spaces

Potential Analysis - In the present paper, we consider long time behaviors of the volume of the Wiener sausage on Dirichlet spaces. We focus on the volume of the Wiener sausage for diffusion...     

Reconstruction of a penetrable obstacle by complex spherical waves

We consider an inverse acoustic scattering problem for identifying a non-convex penetrable obstacle in three dimensions in a homogeneous medium. We apply the complex geometrical optics solutions with logarithmic phase, which is called complex spherical waves, to reconstruction problem. The reconstruction schemes will be demonstrated in the last section.     

Unification of Laughlin and Moore-Read states in SUSY quantum Hall effect

Based on the recently proposed SUSY quantum Hall effect, we show that Laughlin and Moore-Read states are related by a hidden SUSY transformation. Regarding the SUSY Laughlin wavefunction as a master wavefunction, Laughlin and Moore-Read states appear as two extreme limits of component wavefunctions. Realizations of topological excitations on Laughlin and Moore-Read states are also discussed in the SUSY formalism. We develop a stereographically projected formulation of the SUSY quantum Hall effect. With appropriate interpretation of Grassmann odd coordinates, we illustrate striking analogies between SUSY quantum Hall effect and superfluidity.     

Developments of nano-polycrystalline diamond anvil cells for neutron diffraction experiments

ABSTRACT

A new high pressure cell for neutron diffraction experiments using nano-polycrystalline anvils is presented. The cell design, off-line pressure generation tests and a gas-loading procedure for this cell are described. The performance is illustrated by powder neutron diffraction patterns of ice VII to ～82?GPa. We also demonstrate the feasibility of single crystal neutron diffraction experiments of Fe₃O₄ at ambient conditions using this cell and discuss the current limitation and future developments.     

Redox reaction characteristics of ferritin-immobilized onto poly(l-lysine)-modified indium oxide electrodes

Ferritin-immobilized poly(l-lysine)-modified electrodes showed well-defined redox waves representing ferritin. Cathodic and anodic peak currents obtained from cyclic voltammograms were proportional to potential sweep rates. From charge flow values during oxidation or reduction reactions calculated by peak areas in cyclic voltammograms, and the surface coverage of ferritin, reacted iron atoms per ferritin molecule were calculated. Obtained numbers of reacted iron atoms were significantly smaller than expected values from iron atoms at ferrihydrite core surfaces of ferritin, which would be caused by the rate-determining ion flow through ion channels of ferritin to compensate for charges in the ferritin cavity. Anodic and cathodic peak potentials in cyclic voltammograms were significantly dependent on cationic species in the solution, though voltammetric shapes and peak currents were independent of cations. From the obtained results that structural changes in ferritin were not detected by fluorescent spectra, it is thought that the cationic dependence on ferritin redox peak potentials is caused by ferritin cores.     

Tuning the chiral cavity of macrocyclic receptor for chiral recognition and discrimination

The size and shape of the chiral cavity of a macrocyclic receptor were tuned by the alteration of the binaphthyl moiety to improve the chiral recognition/discrimination ability. For example, host 3 with the 3,5-bis(trifluoromethyl)phenyl group at the 3,3'-positions showed improved enantioselectivity for small molecules such as 2-chloropropionic acid and methyl lactate as evaluated by the binding constants. This host 3 also had an excellent ability as an NMR chiral solvating agent.     

Switchable C- and N-bound isomers of transition-metal cyanocarbanions: synthesis and interconversions of cyclopentadienyl ruthenium complexes of phenylsulfonylacetonitrile anions

The synthesis, structure, and dynamic behavior of bistable C- and N-bound isomers of transition-metal cyanocarbanions are described. A series of C-bound cyclopentadienyl (Cp) ruthenium phosphane complexes, [Ru{CH(CN)SO2Ph}(Cp)L1L2] (3), and their N-bound isomers, [Ru+(Cp)(NCCH(-)SO2Ph)L1L2] (4), were prepared by treating [RuCl(Cp)(PR3)2] with the sodium salt of phenylsulfonylacetonitrile and performing ligand-exchange reactions with the resulting compounds. Structural characterization by X-ray diffraction indicates that the cyanocarbanion moiety of 3 has an alpha-metalated structure, whereas that of 4 has a zwitterionic, end-on structure. Heating these complexes in aprotic solvents gives rise to irreversible linkage isomerization between C- and N-bound isomers, in which the relative thermal stabilities vary greatly depending on the steric and electronic nature of the ligands. Mechanistic studies of N-to-C isomerization revealed that the reaction proceeds irreversibly in a unimolecular manner without the formation of coordinatively unsaturated species. A metal-sliding process, which occurs over the -C-C triple chemical bond N pi-conjugated surface of the cyanocarbanion moiety, was suggested by results from kinetic studies and density functional theory (DFT) calculations. C-to-N isomerizations proceed by the above-mentioned intramolecular process, with a temperature-dependent contribution from the formation and cleavage of mu2-C,N coordination dimers [{Ru{CH(CN)SO2Ph}(Cp)(PPh3)}2] (15 and 16).     

Clintoniosides A – C,New Polyhydroxylated Spirostanol Glycosides from the Rhizomes of Clintonia udensis

Phytochemical analyses were carried out on the rhizomes of Clintonia udensis (Liliaceae) with particular attention paid to the steroidal glycoside constituents, resulting in the isolation of three new polyhydroxylated spirostanol glycosides, named clintonioside A ( 1 ), B ( 2 ), and C ( 3 ). On the basis of their spectroscopic data, including 2D‐NMR spectroscopy, in combination with acetylation and hydrolytic cleavage, the structures of 1 – 3 were determined to be (1β,3β,23S,24S,25R)‐1,23,24‐trihydroxyspirost‐5‐en‐3‐yl O‐β‐D ‐glucopyranosyl‐(1→4)‐O‐[α‐L ‐rhamnopyranosyl‐(1→2)]‐β‐D ‐glucopyranoside ( 1 ), (1β,3β,23S,24S)‐3,21,23,24‐tetrahydroxyspirosta‐5,25(27)‐dien‐1‐yl O‐α‐L ‐rhamnopyranosyl‐(1→2)‐O‐[β‐D ‐xylopyranosyl‐(1→3)]‐β‐D ‐glucopyranoside ( 2 ), and (1β,3β,23S,24S)‐21‐(acetyloxy)‐24‐[(6‐deoxy‐β‐D ‐gulopyranosyl)oxy]‐3,23‐dihydroxyspirosta‐5,25(27)‐dien‐1‐yl O‐α‐L ‐rhamnopyranosyl‐(1→2)‐O‐[β‐D ‐xylopyranosyl‐(1→3)]‐β‐D ‐glucopyranoside ( 3 ).     

A Bulky Thiyl‐Radical Catalyst for the [3+2] Cyclization of N‐Tosyl Vinylaziridines and Alkenes

Thiyl‐radical‐catalyzed cyclization reactions of N‐tosyl vinylaziridines and alkenes were developed as a new synthetic method for the generation of substituted pyrrolidines. The key to making this process accessible to a broad range of substrates is the use of a sterically demanding thiyl radical, which prevents the undesired degradation of the catalyst.     

Global existence of small solutions for the fourth-order nonlinear Schrödinger equation

We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation

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where \(n=1,2\). We prove global existence of small solutions under the growth condition of \(f\left( u\right) \) satisfying \(\left| \partial _{u}^{j}f\left( u\right) \right| \le C\left| u\right| ^{p-j},\) where \(p>1+\frac{4}{n},0\le j\le 3\).