The existence of equilibria in certain games,separation for families of convex functions and a theorem of Borsuk-Ulam type

The existence of a Nash equilibrium in the undiscounted repeated two-person game of incomplete information on one side is established. The proof depends on a new topological result resembling in some respect the Borsuk-Ulam theorem.     

Design of a widely tunable laser with a chirped ladder filter

We theoretically investigated a digitally tunable laser with a chirped ladder filter and a ring resonator to obtain a wide wavelength tuning range covering the whole C- or L- band. The clear relation between the tuning range and laser structure, especially the ladder filter, is described analytically. The introduction of a chirped structure into a ladder filter is effective in achieving both wide tunability and a stable lasing mode. A numerical simulation based on multimode rate equations shows that a tuning range of over 40 nm and a mode suppression ratio over 40 dB can be achieved by introducing a chirped ladder filter.     

Novel synthesis of macrocycles with 1,1′-binaphthalene-2,2′-diol using intramolecular oxidative coupling

A new series of BINOL-based macrocycles with two phenolic protons have been synthesized via oxidative coupling reaction using CuCl(OH)-TMEDA.     

Laser spectroscopic investigation of salicylic acids hydrogen bonded with water in supersonic jets: Microsolvation effects for excited state proton dislocation

Geometric structures and excited-state proton dislocation of size-selected salicylic acid clusters (salicylic acid and 5-methoxysalicylic acid) with water were studied by using laser spectroscopic techniques. Fluorescence excitation, dispersed fluorescence, and infrared (IR) spectra of those clusters in supersonic jets were examined for both the electronic ground (S0) and first excited (S1) states. The geometric structures of the clusters were determined on the basis of the IR spectra of the OH stretch region with the help of quantum chemical calculations. The hydroxyl group of the water moiety in the clusters forms a ring involving the carboxylic group of the salicylic acid moiety. The IR spectra in S0 show that the intramolecular hydrogen bond in the salicylic acid moiety is still held upon cluster formation, but the phenolic OH stretch band intensity is remarkably weaken in the clusters. The IR spectra in the S1 state and dispersed fluorescence spectra indicated that the intramolecular excited state proton dislocation is hardly affected by the microsolvation with water, in contrast with the strong suppression of the dislocation in the self-solvation.     

A practical asymmetric synthesis of trans-4,5-benzhydrindan-1-ones as a precursor of A-nor B-aromatic steroidal compounds

The enantio-controlled synthesis of trans-4,5-benzhydrindan-1-ones was achieved by means of a stereoselective [4+2] cycloaddition of o-quinodimethanes generated by a thermal cleavage of benzocyclobutene derivatives as a key step. The chiral substrates of the thermal reaction were synthesized by a diastereoselective Grignard addition to the chiral O-isopropylideneglyceroketones connected to a benzocyclobutene ring, which were simply prepared from D-mannitol as a chiral source. This approach can provide a new efficient access to A-nor B-aromatic steroidal compounds.     

Crystal structures of n-alkanes with branches of different size in the middle

We synthesized four branched n-alkane samples C35-C1, C35-C4, C35-C6, and C35-C4Ph with the same number of carbons as the main chain, n = 35, to which the methyl, butyl, hexyl, and butyl phenyl groups were respectively attached at the middle, and also the corresponding linear homologue of C35, and studied their crystalline structures from DSC, IR, and Raman spectroscopy, X-ray diffraction measurement, and computer simulation. Solid-solid phase transitions characteristic of linear alkane C35 are not observed for any branched alkanes, and their melting temperatures Tm are lowered to 325.2, 318.5, 314.3, and 314.1K, respectively. Main chains of branched alkane molecules are not folded, irrespective of length and chemical structure of branches, but are extended to take the planar zigzag form in the solid state. The branches of C35-C4 and C35-C6 are also aligned inside the crystal in the extended form. Data analyses on solution-grown crystallized samples reveal that, with increasing the branch length, their crystal structures transform from polymorphic forms of the orthorhombic (P2(1)2(1)2(1)) and the triclinic (P) for C35-C1 and C35-C4 to the unique triclinic form for C35-C6 and C35-C4Ph, so as to minimize extra surface energy invoked by introduction of long branches.     

Asymmetric cyclization of 2-alkenylphenols. A comparative study on the use of palladium(II) and titanium(IV) complexes

The oxidative cyclization of 2-(3-pentenyl)phenol catalyzed by [(η³-pinene)PdOAc]₂ gives optically active (+)-2-vinylchroman (25% e.e.), while (−)-2-(1-hydroxyethyl)chroman (56% e.e.) is formed as a single diastereomer upon treatment with t-BuOOH in the presence of Ti(OⁱPr)₄ and -(+)-diethyl tartrate. 2-(2-Butenyl)phenol also undergoes the Ti-promoted asymmetric cyclization to give (2S,1′R)-(−)-2-(1-hydroxyethyl)-2,3-dihydrobenzofuran (29% e.e.).     

Three novel diepoxy tetrahydrochromones from agarwood artificially produced by intentional wounding

Three novel diepoxy tetrahydrochromones, oxidoagarochromones A (1), B (2), and C (3), were isolated from agarwood artificially produced by intentional wounding of Aquilaria crassna. Inductive production of these compounds was also confirmed at the early stage of wounding in A. sinensis and A. crassna. These diepoxy tetrahydrochromones would play an important role in understanding the biosynthesis of chromone derivatives in agarwood.