Optimality of the double exponential formula – functional analysis approach –

Summary. In the light of the functional analysis theory we establish the optimality of the double exponential formula. The argument consists of the following three ingredients: (1) introduction of a number of spaces of functions analytic in a strip region about the real axis, each space being characterized by the decay rate of their elements (functions) in the neighborhood of the infinity; (2) proof of the (near-) optimality of the trapezoidal formula in each space introduced in (1) by showing the (near-) equality between an upper estimate for the error norm of the trapezoidal formula and a lower estimate for the minimum error norm of quadratures; (3) nonexistence theorem for the spaces, the characterizing decay rate of which is more rapid than the double exponential. Received September 15, 1995 / Accepted December 14, 1995     

Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

Gelation with N-lauroyl-L-glutamic-α,γ-dibutylamide for liquid scintillation counting of low specific activities of35S and32P

A gelling agent, N-lauroyl-L-glutamic-,-dibutylamide, was applied for liquid scintillation counting of inorganic³²P and³⁵S. The gel with toluene cocktail is transparent and rigid for a long time. Several grams of ammonium magnesium phosphate or barium sulfate can easily be measured without complicating procedures.     

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.     

Diffusion coefficient of 36Cl in silver chloride

Diffusion coefficient of 36Cl in silver chloride was revealed to be about 1 x 10(-10)-4 x 10(-11) cm2 . s-1 in the range of 400 degrees C-200 degrees C by means of radioactive tracer measurements. Activation energy for diffusion was calculated about 0.13 eV. These results were different from those obtained by Maurer and Compton.     

Oligothiophene-containing coumarin dyes for efficient dye-sensitized solar cells

We have developed oligothiophene-containing coumarin dyes fully functionalized for dye-sensitized nanocrystalline TiO(2) solar cells (DSSCs). DSSCs based on the dyes gave good performance in terms of incident photon-to-current conversion efficiency (IPCE) in the range of 400-800 nm. A solar energy-to-electricity conversion efficiency (eta) of 7.4% was obtained with a DSSC based on 2-cyano-3-[5'-(1,1,6,6-tetramethyl-10-oxo-2,3,5,6-tetrahydro-1H,4H,10H-11-oxa-3a-aza-benzo[de]anthracen-9-yl)-[2,2']bithiophenyl-5-yl]acrylic acid (NKX-2677) under simulated AM 1.5G irradiation (100 mW cm(-2)) with a mask: short-circuit current density (J(sc)) = 13.5 mA cm(-2); open-circuit voltage (V(oc)) = 0.71 V; fill factor (FF) = 0.77. Transient absorption spectroscopy measurements indicated that electron injection from NKX-2677 to the conduction band of TiO(2) is very rapid (<100 fs), which is much faster than the emission lifetime of the dye (1.0 ns), giving a highly efficient electron injection yield of near unity.