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     

A new method for atmospheric nitrogen dioxide measurements using the combination of a stripping coil and fluorescence detection.

A new stripping coil for the collection of nitrogen dioxide (NO2) has been developed to increase its versatility and efficiency. Nitrogen dioxide measurements based on quantitative collection through a reaction coil into an alkaline solution has been examined. Nitrogen dioxide is collected in a 0.1 N NaOH solution. This collection system has an efficiency of nearly 100%. The absorbed nitrogen dioxide has been measured by fluorescence detection with sub-ppbv detection limits. The excitation wavelength at 360 nm and the produced emission wavelength at 405 nm were suitable for nitrite ion measurements.     

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.     

A comparison of supercritical carbon dioxide and organic solvents for the intercalation of 4-phenylazoaniline into a pillared clay mineral

The intercalation of 4-phenylazoaniline (PAA) in supercritical carbon dioxide (SC-CO(2)) into montmorillonite (TMA-Mnt) pillared with tetramethylammonium ions at 313 K and 15 MPa was investigated. The adsorption rate and equilibrium PAA uptake were compared with those in n-hexane, CCl(4) and benzene solutions at 313 K. The XRD and N(2) adsorption/desorption analyses showed that TMA-Mnt after adsorption of PAA in SC-CO(2) had the same pore structure as after adsorption of PAA in normal solvents. SC-CO(2) was found to be a good medium for PAA adsorption owing to its having a relatively high adsorption rate and the highest adsorptivity at the same PAA concentration. The properties of PAA adsorption on TMA-Mnt could be well elucidated by the difference in solubility parameters between liquid and solid phases.