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     

The Nonexistence of Procedures with Bounded Performance Characteristics in Certain Parametric Inference Problems

This paper gives a condition which implies the nonexistence of parametric statistical procedures with bounded risk or error performance characteristics. Many examples for which such a condition is satisfied are considered.     

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.     

Aurilide, a cytotoxic depsipeptide from the sea hare Dolabella auricularia: isolation, structure determination, synthesis, and biological activity

The bioassay-guided fractionation of the cytotoxic constituents of the Japanese sea hare Dollabella auricularia led to the isolation of aurilide (1), a 26-membered cyclodepsipeptide. The gross structure of 1 was established by spectroscopic analysis including 2D NMR techniques. The absolute stereostructure was determined by chiral HPLC analysis of acid hydrolysates of 1 and by the enantioselective synthesis of a degradation product arising from a dihydroxylated fatty acid portion. The enantioselective synthesis of 1 was achieved in 12% overall yield (16 steps) and confirmed the absolute stereostructure of 1. The cytotoxicity of 1 was evaluated using a synthetic sample, which was found to exhibit potent cytotoxicity against HeLa S₃ cells with an IC₅₀ of 0.011 μg/mL. Further biological and pharmacological studies of 1 have been carried out by using synthetic 1.     

The core structure of ukonan A, a phagocytosis-activating polysaccharide from the rhizome of Curcuma longa, and immunological activities of degradation products.

The controlled Smith degradation of ukonan A, a phagocytosis-activating polysaccharide isolated from the rhizome of Curcuma longa L., was performed. The reticuloendothelial system-potentiating, anti-complementary and alkaline phosphatase-inducing activities of ukonan A and its degradation products were investigated. Methylation analyses of both the primary and the secondary Smith degradation products indicated that the core structural features of ukonan A include a backbone chain mainly composed of beta-1,3-linked D-galactose, beta-1,4-linked D-xylose and alpha-1,2-linked L-rhamnose residues. All of the galactose units in the backbone carry side chains composed of alpha-L-arabino-beta-D-galactosyl or beta-D-galactosyl residues at position 6. Ukonan A has a remarkable effect on each of the three kinds of immunological activities. Periodate oxidation caused pronounced decrease or disappearance of the activities, but the controlled Smith degradation product having the core structure of polysaccharide showed considerable restoration of these activities.     

A study of GABA and its analogues using the molecular orbital method

GABA is a major neurotransmitter in the central nervous system. Data on GABA and its analogues calculated by using the ab initio and the MNDO method were compared with data obtained experimentally. The structures of GABA analogues calculated by the ab initio method agree well with the experimental data. This finding suggests the high reliability of this method. However, the structures of GABA analogues calculated by the MNDO method reflect only some aspects of the experimental data. Therefore the MNDO method should be used only for carefully selected chemical compounds.

The amino group in GABA and its analogues was proved to be the major active site. The electrostatic potential around the amino group in these compounds seems to be related to their biological activity. The difference in the electrostatic potential between the receptor binding molecules and the neuronal uptake molecules suggests that the structure of post-synaptic receptors might differ from that of uptake receptors. This finding suggests that there are at least two GABA-A receptors. GABA molecules seem to have a high potential for binding to the two receptors because they are highly flexible and can readily change their conformation. These results indicate a high reliability of the data calculated by the molecular orbital method and suggest that this method provides us with useful information that cannot be obtained experimentally.