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     

High-throughput characterization of local conductivity of Nd0.9Ca0.1Ba2Cu3O7−δ thin film by the low-temperature scanning microwave microscope

We developed a scanning microwave microscope (SμM) designed for high-throughput electric-property screening as well as for rapid construction of electronic phase diagrams at low temperatures. As a sensor probe, we used a high-Qλ/4 coaxial cavity resonator to which a thin needle with ball-tip end was attached. The sensor module was mounted on the low-temperature XYZ stage, which allowed us to map out the change of resonance frequency and quality factor due to the local tip-sample interaction at low temperatures. From the measurements of combinatorial thin films, such as Ti_1−xCo_xO_2−δ and Nd_0.9Ca_0.1Ba₂Cu₃O_7−δ (NCBCO), it was demonstrated that this SμM system has enough performance for the high-throughput characterization of sample conductance under variable temperature conditions.     

Synthesis of Bioactive and Porous Organic-Inorganic Hybrids for Biomedical Applications

Bioactivity has been exhibited by a limited range of ceramics since the invention of Bioglass®. Recently, some bioactive polymeric organic-inorganic hybrids were introduced, including not only organically modified silicates (Ormosils) synthesized from polydimethylsiloxane (PDMS) and tetraethoxysilane but also those with gelatin and 3-glycidoxypropyl-tremethoxysilane. Preparation of the bulk and porous hybrids and their polymeric structures analyzed by Si NMR spectroscopy were presented. In vitro bioactivity or apatite deposition in a simulated body fluid of the Kokubo recipe were also described for those hybrids. Freeze-drying techniques introduced porosity (up to 90%) and pores extending in a preferred direction.     

Investigation of the drying conditions for amidosulfuric acid.

The drying conditions for primary standards of volumetric analysis have a significant effect on the titration results due to changes in the purity, stability and homogeneity. Amidosulfuric acid, a strong acid used as a reference material for volumetric analysis in Japan, was dried in a vacuum desiccator or heated at different temperatures, and then measured by Karl-Fischer titration, thermogravimetry/mass spectroscopy (TG-MS), ion chromatography and coulometric titration. The optimum drying conditions were at 50 degrees C for 24 h with crushing.     

Inhibitory effects of 3-O-acyl-(+)-catechins on Epstein-Barr virus activation

In the course of an exploratory investigation of antitumor-promoting catechins, 3-O-acyl-(+)-catechins of varying carbon lengths from C(4) to C(18) were assessed for inhibitory effects on the activation of the Epstein-Barr virus early antigen. Like 3-O-acyl-(-)-epigallocatechins, the (+)-catechin derivatives showed promising effects with the C-3 acyl chain of C(8)-C(11) carbon atoms.     

Synthesis,crystal structure and charge transport characteristics of stable peri-tetracene analogues

peri-Acenes have shown great potential for use as functional materials because of their open-shell singlet biradical character. However, only a limited number of peri-acene derivatives larger than peri-tetracene have been synthesized to date, presumably owing to the low stability of the target compounds in addition to the complicated synthesis scheme. Here, a very simple synthesis route for the tetrabenzo[a,f,j,o]perylene (TBP) structure enables the development of highly stable peri-tetracene analogues. Despite a high degree of singlet biradical character, the compounds with four substituents at the zigzag edge show a remarkable stability in solution under ambient conditions, which is better than that of acene derivatives with a closed-shell electronic configuration. The crystal structures of the TBP derivatives were obtained for the first time; these are valuable to understand the relationship between the structure and biradical character of peri-acenes. The application of peri-acenes in electronic devices should also be investigated. Therefore, the semiconducting properties of the TBP derivative were investigated by fabricating the field-effect transistors.

Highly stable peri-tetracene analogues with a high degree of singlet biradical character were synthesized in a very simple route, and their crystal structures and semiconducting properties were investigated.     

Total Synthesis of Natural PI-091, a New Platelet Aggregation Inhibitor of Microbial Origin

The total synthesis of a new platelet aggregation-inhibiting gamma-lactam PI-091 (1) gave a 1:1 diastereomeric mixture at the gamma-ketal carbon. The high-yielding aldol reaction of an appropriately protected 1,3,4-trihydroxy-4-methyldecan-2-one 42, prepared from D-glucose, with the kinetically generated enolate of 3-methyl-2-butanone provided 43. The resulting diastereomeric mixture of the aldol adduct 43 was converted to a 2,4-alkylated furan 45 via an intramolecular ketalization followed by dehydration. The addition of a singlet oxygen to the alpha-trimethylsilylated furan 48derived from 45 under photochemical conditions efficiently provided an alpha,gamma-dialkylated gamma-hydroxy gamma-lactone 47. The transformation of methyl ketal 52 prepared from 47 into gamma-hydroxy gamma-lactam 53 was achieved by exposure to liquid ammonia in MeOH. The total synthesis of 1 was achieved from 52 through the Dess-Martin periodinane oxidation of the secondary hydroxy group in the side chain. The present total synthesis revealed that the stereogenic carbon center in the side chain in natural 1 is S.     

Optical microscopy and in situ Raman scattering of single crystalline ethylene hydrate and binary methane-ethylene hydrate at high pressures

Visual observations through a microscope and in situ Raman measurements have been made for single crystalline ethylene hydrate (EH) and binary methane-ethylene hydrate (MEH) at pressures up to 3.7 GPa and room temperature. Both hydrates showed pressure-induced phase transitions at 1.6, 2.0, and 3.0 GPa for EH and at 1.7, 2.1, and 3.3 GPa for MEH. The cubic sI phase of EH and MEH remains stable up to 1.6 and 1.7 GPa, respectively, which are more widely ranging values than the values for the methane hydrate sI phase. In this sI phase of binary MEH, the cage occupancies by methane and ethylene molecules are investigated from Raman spectra. Above P = 3.0 GPa for EH and 3.3 GPa for MEH, they decomposed by associating with the formation of the polyethylene.     

Dynamic covalent approach to [2]- and [3]roxtanes by utilizing a reversible thiol-disulfide interchange reaction

A dynamic covalent approach to disulfide-containing [2]- and [3]rotaxanes is described. Symmetrical dumbbell-shaped compounds with two secondary ammonium centers and a central located disulfide bond were synthesized as components of rotaxanes. The rotaxanes were synthesized from the dumbbell-shaped compounds and dibenzo-[24]crown-8 (DB24C8) with catalysis by benzenethiol. The yields of isolated rotaxanes reached about 90 % under optimized conditions. A kinetic study on the reaction forming [2]rotaxane 2 a and [3]rotaxane 3 a suggested a plausible reaction mechanism comprising several steps, including 1) initiation, 2) [2]rotaxane formation, and 3) [3]rotaxane formation. The whole reaction was found to be reversible in the presence of thiols, and thermodynamic control over product distribution was thus possible by varying the temperature, solvent, initial ratio of substrates, and concentration. The steric bulk of the end-capping groups had almost no influence on rotaxane yields, but the structure of the thiol was crucial for reaction rates. Amines and phosphines were also effective as catalysts. The structural characterization of the rotaxanes included an X-ray crystallographic study on [3]rotaxane 3 a.     

Stereoselective synthesis of cis- and trans-2,3-disubstituted eight-membered medium-ring ethers based on Ireland-Claisen rearrangement of 3-alkoxy-2-propenyl glycolate esters and ring-closing olefin metathesis

A simple stereoselective synthesis of cis- and trans-2,3-disubstituted medium-sized cyclic ethers has been developed based on geometry-selective synthesis of 3-alkoxy-2-propenyl glycolate esters, Ireland-Claisen rearrangement of the glycolate esters, and ring-closing olefin metathesis.