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     

Studies on the antitumor-promoting activity of naturally occurring substances. II. Inhibition of tumor-promoter-enhanced phospholipid metabolism by umbelliferous materials

Ninety-five extracts prepared from 14 kinds of Umbelliferous materials were studied to determine their effects on tumor-promoter-induced phenomena in vitro. Of the materials, 5 Chinese crude drugs, two Bai-Hua Qian-Hu classified as Q-I and Q-II types, the root of Peucedanum praeruptorum Dunn., Zi-Hua Qian-Hu, the root of P. decursivum Maxim., Tang-Bai-Zhi, the root of Angelica dahurica Benth, et Hook. var. pai-chi Kimura, Hata et Yen., Dang-Gui, the root of A. acutiloba Kitagawa and 2 Umbelliferous plants, ashita-ba. A. keiskei Koidz., and ama-nyuu, A. edulis Miyabe, showed potent inhibitory effects on 12-O-tetradecanoylphorbol-13-acetate (TPA)-stimulated 32Pi incorporation into phospholipids of cultured cells. From the active fraction of the crude drug "Tang-Bai-Zhi," imperation (1), isoimperatoin (2), oxypeucedanin (3), pabulenol (4), neobyakangelicol (5) and byakangelicin (6) were identified as active or inactive principles. Compound 4 had not previously been isolated from Tang-Bai-Zhi, A. dahurica var. pai-chi. We also discuss the structure-activity relationship among the above 6 kinds of linear-type furanocoumarins, together with 3 kinds of antitumor-promoter coumarins having the same skeleton, psoralen (7), bergapten (8) and xanthotoxin (9), obtained from "ashita-ba" (eaten as a vegetable in Japan). Among the compounds in the present experiment, compounds 1 and 2 showed potent inhibitory activity at the concentration of 50 micrograms/ml and 3-9 were found to have less or no activity.     

Diastereoselective addition of organolithiums to 1,3-oxazolidines complexed with aluminum tris(2,6-diphenylphenoxide) (ATPH)

1,3-Oxazolidines were easily obtained by condensation of N-substituted (R)-phenylglycinol with aldehydes. Addition of organolithium reagents to 1,3-oxazolidines by complexation with the bulky Lewis acid aluminum tris(2,6-diphenylphenoxide) (ATPH) readily produced the corresponding chiral amines with good yield and high diastereoselectivity. The configuration of the new stereogenic center was shown to be opposite to that of adducts obtained for the same 1,3-oxazolidines using Grignard reagents. The best diastereoselectivity was achieved using N-isopropyl-1,3-oxazolidines. The mechanism of addition was deduced by determining the stereochemistry of the iminium-aluminum complex by NOE experiments.     

Three new quassinoids,ailantinol E,F, and G,from Ailanthus altissima

Three new quassinoids, ailantinol E (1), ailantinol F (2), and ailantinol G (3), and related compounds were isolated from Ailanthus altissima grown in Taiwan. Their structures were elucidated from spectral evidence. Each new quassinoid was evaluated for its antitumor promoting effects against Epstein-Barr virus early antigen activation introduced by 12-O-tetradecanoylphorbol-13-acetate in Raji cells. The new quassinoids were found to show potent activity without showing any cytotoxicity. The screening for inhibitors against nitric oxide donor action was also conducted using the new quassinoids and some standard samples.     

Magnetic microcapsules for targeted delivery of anticancer drugs

To achieve targeted distribution of anticancer drugs with sustained activity, ferromagnetic ethylcellulose microcapsules containing an anticancer drug, mitomycin C (FM-MMC-mc), were prepared by a method based on phase separation principles. Two prototypes of FM-MMC-mc were made: one with the drug as the core and zinc ferrite on its capsular surface (outer type); the other with both the drug and zinc ferrite as the core (inner type). Both preparations provided a sustained-release property and a sensitive response to conventional magnetic force, although certain differences in the release rate of drug, magnetic responsiveness, and particle size were found between the two dosage forms. Animal studies showed that the magnetic microcapsules could be magnetically controlled in the artery and urinary bladder. VX2 tumors in the rabbit hind limb and urinary bladder were successfully treated with magnetic control of FM-MMC-mc. Pharmacokinetic study revealed that the targeting of the microcapsules markedly enhanced the drug absorption into the surrounding tissues for a prolonged period of time. The results indicate the feasibility and effectiveness of the magnetic microcapsules as a targeted drug delivery system.     

Self-organized glycoclusters along DNA: effect of the spatial arrangement of galactoside residues on cooperative lectin recognition

We describe herein the relationship between the spatial arrangement of self-organized galactose clusters and lectin recognition. beta-Galactose-modified deoxyuridine phosphoramidite was synthesized and applied to solid-phase synthesis to provide 18-, 20-, and 22-mers of site-specifically galactosylated oligodeoxynucleotides (Gal-ODNs). These Gal-ODNs were self-organized through hybridization with the corresponding 18-, 20-, and 22-mers of half-sliding complementary ODNs (hsc-ODNs) to give periodic galactoside clusters. The self-organization of ODNs was confirmed by size exclusion chromatography and gel electrophoresis. The binding of the Gal-clusters to the FITC-labeled RCA(120) lectin was analyzed by monitoring the change in fluorescence intensity. The assembly of 20-mer Gal-ODN with the 20-mer hsc-ODN was strongly and cooperatively recognized by the lectin. The 18-mer assembly was bound more weakly and less cooperatively, and the 22-mer assembly was minimally bound to the lectin. RCA(120) lectin recognized not only the density of galactoside residues, but also the spatial arrangement. The size of the Gal cluster was estimated from the association constant of Gal-ODN with hsc-ODN. The relationship between lectin-recognition and Gal-cluster size is also discussed.     

Influence of nano-structure on electrolytic properties in CeO2 based system

Doped ceria (CeO₂) compounds are fluorite type oxides that show oxygen ionic conductivity higher than yttria stabilized zirconia, in oxidizing atmosphere. In order to improve the conductivity, the effective index was suggested to maximize the oxygen ionic conductivity in doped CeO₂ based oxides. In addition, the true microstructure of doped CeO₂ was observed at atomic scale for conclusion of conduction mechanism. Doped CeO₂ had small domains (10-50 nm) with ordered structure in a grain. It is found that the electrolytic properties strongly depended on the nano-structural feature at atomic scale in doped CeO₂ electrolyte. This revised version was published online in August 2006 with corrections to the Cover Date.     

Novel synthesis and properties of 7,9-dimethylcyclohepta[b]pyrimido[5,4-d]furan-8(7H),10(9H)-dionylium tetrafluoroborate: autorecycling oxidation of some alcohols under photo-irradiation

Three-step reactions starting from 2-chlorotropone with barbituric acid afforded novel 7,9-dimethylcyclohepta[b]pyrimido[5,4-d]furan-8(7H),10(9H)-dionylium tetrafluoroborate (9·BF₄⁻), which is the isoelectronic compound of the 5-ethyl-3-methyllumiflavinium ion. The stability of cation 9 is expressed by the pK_R+ value, which was determined spectrophotometrically, as ca. 6.0. The electrochemical reduction of 9 exhibited low reduction potential at −0.58 (V vs Ag/AgNO₃), upon cyclic voltammetry (CV). In a search for the reactivity, reactions of 9·BF₄⁻ with some nucleophiles, hydroxide, hydride, amines, thiols, and methanol, were carried out to exhibit that the introduction of nucleophiles is dependent on the nucleophile itself. The photo-induced oxidation reactions of some alcohols catalyzed by 9·BF₄⁻ under aerobic conditions were carried out to give the corresponding carbonyl compounds in more than 100% yield [based on compound 9·BF₄⁻], suggesting the oxidizing function of 9·BF₄⁻ toward alcohols in the autorecycling process. The UV-vis and fluorescence spectra of 9 were studied to suggest the electron transfer from alcohols to the excited 9.     

Statistical properties of aggregation with injection

We study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For one-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are continuously injected. The steady-state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension. The response of the system to a perturbation (i.e., relaxation) is characterized by either a power law decay (t ^– ,1) or a compressed exponential decay [exp(–t ),>1].