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     

Reaction of C3 and C4 ketoses with alkenals and alkenones in water

Treatment of 1,3-dihydroxyacetone and acrolein with aqueous KOH gave a tetrahydrofuran derivative, 1,4-dihydroxy-3,7-dioxabicyclo[3.3.0]octane, in 80% yield. Similarly, 6-alkyl substituted 1,4-dihydroxy-3,7-dioxabicyclo[3.3.0]octanes were obtained by reaction of 1,3-dihydroxyacetone with various α,β-unsaturated aldehydes. In the cases of long chain alkenals, the reaction was effectively accelerated in the presence of organic co-solvent. On the other hand, the corresponding tricyclic products were synthesized by reaction of 1,3-dihydroxyacetone with cyclic enones, such as 2-cyclopentenone and 2-cyclohexenone. This method was successfully applied to the reaction of a tetrulose in the absence of any protecting groups.     

Electronic and geometric properties of alkali-C60 molecules

First-principle electronic structure calculations are carried out for M_xC ₆₀ ^q , where M = Li, Na, K and ( x , q ) = (1, 0),(1,±1),(2, 0),(3, - 1),(6, 0),(6, - 1),(12, 0) using the local density functional. The electric dipole moment for MC₆₀ agrees with the experimental results. The calculated Mulliken charge indicates that the bonding of the alkali atom with C₆₀ is mostly ionic except for lithium. The alkali atom prefers to make many bonds with the carbon atoms rather than a single bond with the neighbor carbon atom. The calculated adsorption energy suggest that the metal-metal bonding of sodiums and potassiums on C₆₀ arises for more than the six valence electrons in the alkali atoms. The lithium-lithium bond is, on the other hand, not appeared for x ? 12. The difference in the most stable geometry between lithiums and the other alkali atoms on C₆₀ comes from the covalent character of the lithium-carbon bond.     

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.     

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.