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     

Anisotropic friction model of DNA electrophoresis in polymer solutions: Comparison with direct observations

The electrophoresis of DNA chains in uncrosslinked polymer solutions with a Brownian dynamics simulation with an anisotropic friction tensor was analyzed. According to the degree of anisotropy, three types of migration behavior are obtained: fluctuation without or with periodicity between U‐shaped and compact conformations, or migration with linear conformation. We found good agreement between our simulation results and the direct observations of DNA by fluorescence microscopy. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1316–1322, 2003     

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.     

Cross-metathesis of vinyl aromatic heterocycles with 1-octene in the presence of a Schrock catalyst

Metathesis of 2-vinyl aromatic heterocycles such as furan, thiophene, pyrrole and pyridine in the presence of a molybdenum-based Schrock catalyst has been investigated from a synthetic point of view. The self-metathesis of 2-vinyl aromatic heterocycles was not successful. However, in cross-metathesis of thiophene, furan and styrene with 1-octene, the cross-metathesis product, heterodimer, was readily obtained selectively, together with only small amounts of the two corresponding self-metathesis products. The origin of the surprisingly high selectivity of heterodimer formation was elucidated through metallacyclobutane intermediate mechanism, observations of carbenes by in situ ¹H NMR, and reaction products.     

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.     

Novel method to control release of lipophilic drugs with high potency from silicone

Silicone has been utilized as a carrier material for sustained release system of lipophilic drugs. Extensive studies revealed that drug release rate is influenced by factors such as physicochemical properties of the drug and additives.(1-5)) When a lipophilic drug is highly potent at low concentrations, the drug release rate should be strictly controlled so as to avoid side effects. In this study, using vitamin D(3) (VD(3)) as an example of such drugs, we investigated novel method to suppress initial burst and to modify drug release rate from silicone matrix. As a result, it was found that (a). addition of human serum albumin (HSA) suppressed initial burst and enhanced release rate in the later stage, resulting constant release of VD(3), (b). covering a matrix formulation with a membrane of low diffusivity (core-rod formulation) suppressed initial burst and released drug in a constant rate, and (3) using materials for which the drug has high affinity as dissolution solvent (reservoir formulation), the drug release rate was reduced.