Generating Function for GL<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-Invariant Differential Operators in the Skew Capelli Identity

Let Alt _n be the vector space of all alternating n × n complex matrices, on which the complex general linear group GL _n acts by \({x \mapsto gxg^t}\). The aim of this paper is to show that Pfaffian of a certain matrix whose entries are multiplication operators or derivations acting on polynomials on Alt _n provides a generating function for the GL _n -invariant differential operators that play an essential role in the skew Capelli identity, with coefficients the Hermite polynomials.     

Theoretical analysis of oxygen reduction reaction and H2O2 formation and the impact of CF3SO3H coverage on Pt (111)

Theoretical analysis of ORR on Pt (111) was carried out with the combined technique of DFT calculation and the UBI-QEP method in order to understand the overall ORR pathways, behavior of H₂O₂ formation, and the impact of trifluoromethane sulfonic acid (CF₃SO₃H and TfOH) coverage, the alternative material of Nafion^®, on the reactivity on the Pt surface. The ORR scheme consisting of elementary reactions was then modeled to determine the dominant path and the limiting step based on their activation energies. The results showed that the dominant ORR path included the H₂O₂ formation step and OOH formation step was limiting. When TfOH covered the Pt surface, it was revealed that the adsorption energy of an O₂ molecule on Pt (111) was decreased due to the lower Fermi level and the d-band center, resulting in decreasing the activation energy of the limiting step. TfOH, however, could suppress the O₂ adsorption on the Pt surface. In addition, with the TfOH coverage, it was indicated that the limiting step of ORR was shifted to H₂O-production step which was after the H₂O₂ production, resulting in the enhancement of the H₂O₂ formation.     

Structure and excitation relaxation dynamics of dimethylanthracene dimer in a gamma-cyclodextrin nanocavity in aqueous solution

Dimethylanthracene (DMA), which exhibits almost no self-association in bulk organic solvents, forms a dimer and emits excimer-like fluorescence in a gamma-cyclodextrin nanocavity in a dilute aqueous solution. The 1Bb and 1La electronic transitions of the DMA dimer split by 2230 and 344 cm(-1), respectively, in a fluorescence excitation spectrum obtained with the excimer-like emission. From these energy splits, the structure of dimer in relation to a dielectric constant inside gamma-CD was discussed on the basis of atom-atom Lennard-Jones potential calculations including Coulombic interactions. Excitation relaxations of DMA in the presence of alpha-, beta-, and gamma-CDs in aqueous solutions were investigated by time-resolved fluorescence. The results suggest that both the hydrated and anhydrated species exist in the alpha- and gamma-CD complexes, while only the anhydrated species exists in the beta-CD complex.     

Synthesis of macrosphelides with a thiazole side chain: new antitumor candidates having apoptosis-inducing property

Hybrid compounds of macrosphelides and epothilones, both of which are natural macrolides having a 16-membered skeleton, were designed and synthesized using a ring-closing metathesis (RCM) strategy. Some of these hybrids were found to exhibit notable apoptosis-inducing activity against human lymphoma cells with higher potency than parent natural macrosphelides, and to be a promising lead compound for development of a new antitumor agent.     

One-dimensional chiral self-assembly of pyrene derivatives based on dendritic oligopeptides

Supramolecular chiral columnar liquid crystals have been formed through one-dimensional self-assembly of pyrene-containing oligopeptides. Supramolecular chirality is further tuned by cooperation of intermolecular hydrogen bonding and electron donor-acceptor interactions. [reaction: see text]     

Unified characterizations for modifications ofR 0 andR 1 topological spaces

Cammaroto and Noiri [14] introduced a separation axiom calledm-R ₀ in anm-space (X, m). In this paper, we introduce the notion ofm-R ₁ spaces and offer many characterizations ofm-R ₀ (resp.m-R ₁) spaces which enable us to obtain unified characterizations of separation axiomsR ₀, semi-R ₀, pre-R ₀,α-R ₀,δ-semiR ₀, (δ, p)-R ₀ (resp.R ₁, semi-R ₁, pre-R ₁,α-R ₁,δ-semiR ₁, (δ, p)-R ₁).     

Molecular and functional diversity of vascular endothelial growth factors

Summary Members of the vascular endothelial growth factor (VEGF) family are crucial regulators of neovascularization and are classified as cystine knot growth factors that specifically bind cellular receptor tyrosine kinases VEGFR-1, VEGFR-2, and VEGFR-3 with high but variable affinity and selectivity. The VEGF family has recently been expanded and currently comprises seven members: VEGF-A, VEGF-B, placenta growth factor (PlGF), VEGF-C, VEGF-D, viral VEGF (also known as VEGF-E), and snake venom VEGF (also known as VEGF-F). Although all members are structurally homologous, there is molecular diversity among the subtypes, and several isoforms, such as VEGF-A, VEGF-B, and PlGF, are generated by alternative exon splicing. These splicing isoforms exhibit differing properties, particularly in binding to co-receptor neuropilins and heparin. VEGF family proteins play multiple physiological roles, such as angiogenesis and lymphangiogenesis, while exogenous members (viral and snake venom VEGFs) display activities that are unique in physiology and function. This review will highlight the molecular and functional diversity of VEGF family proteins.     

Stationary solutions to the Falk system on shape memory alloys

We study the Falk model system describing martensitic phase transitions in shape memory alloys. Its physically closed stationary state is formulated as a nonlinear eigenvalue problem with a non‐local term. Then, some results on existence, stability, and bifurcation of the solution are proven. In particular, we prove the existence of dynamically stable nontrivial stationary solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis and Some Properties of Low Melting Ferroelectric Liquid Crystals of Benzylidene Anilines

A series of chiral benzylidene-aniline compounds, 4-alkoxybenzylidene 4′-(2-methylbutyloxycarbonyl)anilines, have been synthesized and their mesomorphic properties are examined. They showed a monotropic chiral smectic C phase in conjunction with enantiotropic smectic A phase, and their chiral smectic C—smectic A phase transition temperatures are around room temperatures. Their spontaneous polarization values are moderately higher than those of DOBAMBC “4-decyloxybenzylidene 4′-amino-(2-methylbutyl)cinnamate”.