Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

Experimental Study on Time-Spread/Wavelength-Hop Optical Code Division Multiplexing with Dispersion-Compensating En/Decoder

10Gbit/s time-spread/wavelength-hop optical code generation and decoding are performed by dispersion-compensating fiber Bragg grating (FBG) en/decoder pair. Error-free 10km single mode fiber (SMF) transmission of 10Gbit/s optical code division multiplexing (OCDM) has been experimentally demonstrated.     

Determination of midodrine in human plasma by high-performance liquid chromatography with fluorescence detection.

A simple and sensitive fluorometric high-performance liquid chromatographic method was developed for the determination of midodrine in human plasma. After liquid-liquid extraction from plasma, the drug and 2-phenylglycinol (internal standard) were convened into the corresponding fluorescent derivatives by reaction with 3,4-dihydro-6,7-dimethoxy-4-methyl-3-oxoquinoxaline-2-carbonyl chloride, a fluorescence derivatization reagent for amines. The derivatives were separated within 30 min on a reversed-phase column using isocratic elution with acetonitrile-methanol-water (10:30:60, v/v) and were detected spectrofluorometrically at 485 nm with excitation at 400 nm. The detection limit for midodrine was 0.3 pmol (76 pg) per mL plasma at a signal-to-noise ratio of 3.     

Stereocontrol of diene polymers by topochemical polymerization of substituted benzyl muconates and their crystallization properties

We report the stereocontrol of diene polymers by the topochemical polymerization of alkoxy-substituted benzyl muconates in the solid state. A monomer stacking structure is controlled by the weak intermolecular interactions in the monomer crystals, depending on the structure and position of the alkoxy-substituent. The translational and alternating types of molecular stacking structures in a column provide diisotactic and disyndiotactic polymers, respectively, by the solid-state polymerization under UV and γ-ray irradiation. On the other hand, the meso and racemo structures of the resulting polymers are determined by the molecular symmetry of the used muconate monomers. The various substituted benzyl ester polymers are transformed into the same ethyl ester polymers with the four types of tacticities. The structure and crystallization behavior of the substituted benzyl ester polymers as well as the ethyl ester polymers have been revealed in detail. We clarify the effects of the tacticity on the crystallization property of the stereoregular polymuconates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4952–4965, 2006     

Borderline of hydrogen bonding of silanols

Two new silanols bearing very bulky silyl groups, (i-Pr₃ Si)₃SiOH and (t − BuMe₂Si)₃SiOH were prepared by peracidoxidation of their respective silanes. The X − ray crystallographic analysis revealed that (t − BuMe₂Si)₃ SiOH forms a dimeric structure with hydrogen bonding, while (i − Pr₃ Si)₃ SiOH exists as a monomer in the crystal. The effects of the size of the substituents as well as the reactivity of these silanols are discussed.     

Reactions of hydropolysilanes with alcohols catalysed by tris(triphenylphosphine)chlororhodium

[RhCl(PPh₃)₃] is a very effective catalyst for the cleavage of Si-Si bonds by alcohols.     

Metal-insulator transition in VnO2n−1

Research on phase relationships and structure studies by electron diffraction confirm V_nO_2n?1 (n = 3–9) phases between V₂O₃ and VO₂. Metal-insulator phase transitions have been found in all phases but V₃O₅ and V₇O₁₃. Electrical, magnetic and thermodynamic properties associated with the transitions are reported for sintered samples or for single crystals prepared by a vapor-transport method. The results are collated and reviewed in summarized form.     

Ruthenium-catalyzed formation of aryl(diphenyl)phosphine oxides by reactions of propargylic alcohols with diphenylphosphine oxide

1,1-Diaryl-1-penten-4-yn-3-ols react with diphenylphosphine oxide in the presence of a thiolate-bridged diruthenium complex as a catalyst and give high yields of aryl(diphenyl)phosphine oxide products via an initial substitution followed by a cyclization at the produced allene intermediate. [reaction: see text]     

Novel Host Compounds, 1,1′-Binaphthyl-2,2′-Dihydroxy-5,5′- and 6,6′-Dicarboxylic Acid, which Trap Guest Molecules Tightly in their Inclusion Crystals

The host compounds 1,1’-binaphthyl-2,2′-dihydroxy-5,5′-dicarboxylic acid (1) and 1,1′-binaphthyl-2,2′-dihydroxy-6,6′-dicarboxylic acid (2) have been synthesized, and their inclusion properties have been studied. Inclusion complexes formed by 1 and 2 with volatile guests such as acetone and methanol release the guests only at much higher temperatures than their boiling points. The crystal structures of the inclusion complexes have been determined from single crystal X-ray diffraction data and show different host lattices.