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.     

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.     

Second-order nonlinear optical properties from poled silicate channel-waveguide

Thin film waveguides of germanosilicate glass are fabricated byrf-sputtering. Second-order nonlinearity ofd ₃₃=3.2 pm/V is obtained from electrically poled film, and the lifetime of the nonlinearity is found to be310 years. The poled channel-waveguide is prepared and the Cerenkov-type phase-matched frequency doubling is successfully observed.     

TMS triflate-catalyzed cleavage of prenyl (3-methylbut-2-enyl) ester

[reaction: see text] Prenyl (3-methylbut-2-enyl) ester is catalytically cleaved by TMS triflate affording carboxylic acid and isoprene in high yield under mild conditions with high chemoselectivity without causing epimerization of the neighboring chiral center.