Distributivity and stationary reflections

In this paper, we present some relations between generalized distributivity of quotient algebras and Mahlo operations, and show that the distributivity implies some variants of stationary relections.

     

On global solutions to the initial–boundary value problem for the nonlinear Schrödinger equations in exterior domains

We consider the initial–boundary value problem for the nonlinear Schr‐dinger equations in an exterior domain. Global existence theorem of smooth solutions is established by using a–priori decay estimates of solutions which are obtained by the pseudoconformal indentity     

Inlet throttling effect on the boiling two-phase flow stability in a natural circulation loop with a chimney

 Experiments have been conducted to investigate an effect of inlet restriction on the thermal-hydraulic stability. A Test facility used in this study was designed and constructed to have non-dimensional values that are nearly equal to those of natural circulation BWR. Experimental results showed that driving force of the natural circulation at the stability boundary was described as a function of heat flux and inlet subcooling independent of inlet restriction. In order to extend experimental database regarding thermal-hydraulic stability to different inlet restriction, numerical analysis was carried out based on the homogeneous flow model. Stability maps in reference to the core inlet subcooling and heat flux were presented for various inlet restrictions using the above-mentioned function. Instability region during the inlet subcooling shifted to the higher inlet subcooling with increasing inlet restriction and became larger with increasing heat flux. Received on 17 January 2000     

Repetitive spectral subtraction method for the spectrophotometric determination of rare earth elements

Summary A new multiwavelength data-analysis method for the determination of multicomponent mixtures, the repetitive spectral subtraction method (RSSM), is proposed. In RSSM, spectral data are obtained at evenly spaced wavelengths in the range of interest, and the analysis of the spectrum is performed as repetitive determination-subtraction cycle. In the determination step, the series of data in the narrow wavelength range is used, which is specified as to include the most characteristic or the largest peak for each component. Assuming a linear background, the target component, which can be a small group of components, is simultaneously determined together with co-existing components. In the next subtraction step, the calculated contribution of the component is subtracted from the spectral data in the whole measured wavelength range, and the component is assigned as determined and is excluded from the following analysis. This determination-subtraction cycle is repeated until all the components are determined.With RSSM, a mixture of many components can be precisely determined by the use of most information contained in the spectrum. The accuracy of determination can be improved by automatic estimation of the background and the gradual decrease of interferences. In order to demonstrate the usefulness of RSSM, the 8 rare earth elements (Pr, Nd, Sm, Eu, Dy, Ho, Er, Tm) in the model mixtures were determined by spectrophotometry, and the results were compared with those of the usual correction factor method and the derivative method. Furthermore, the 8 rare earth elements were determined in ores, monazite and xenotime.

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Spektralphotometrische Bestimmung von Seltenen Erden mit Hilfe eines Verfahrens der wiederholten Subtraktion

     

A microsensor for adenosine-5′-triphosphate pH-sensitive field effect transistors

The sensor for adenosine-5′-triphosphate (ATP) is based on H⁺-ATPase immobilized via a polyvinylbutyral resin on a pH-sensitive field effect transistor. A linear relationship was obtained between the initial rate of change of the differential gate output voltage and the logarithm of the ATP concentration over the range 0.2–1.0 mM ATP. The optimum pH was 9.0 at 40°C but pH 7.0 was preferred for routine measurements. Only slight responses were obtained for 1 mM glucose, creatinine or urea. The ATP-sensing system exhibited a response to 1 mM ATP for at least 18 days.     

Discussion of substantially identical gel points among multiallyl monomers based on characterization of resultant network polymer precursors consisting of oligomeric primary polymer chains

No difference in the actual gel points was substantially observed among three isomeric diallyl phthalates such as diallyl phthalate (DAP), diallyl isophthalate, and diallyl terephthalate (DAT); this interesting gelation behavior was discussed further in terms of the correlation between gelation and the difference in cyclization modes, and also, the difference in reactivity between the uncyclized and cyclized radicals for cross‐linking. In the present work, we tried to extend the preceding discussion to the polymerization of triallyl trimellitate (TAT) because the molecular structure of TAT is presumed to essentially involve the characteristics of three isomeric diallyl phthalates and, therefore, the enhanced gelation was expected in TAT polymerization. However, no enhancement of gelation was observed. For a full understanding of the gelation in multiallyl cross‐linking polymerization, we explored further the polymerizations of DAP, DAT, and TAT, especially focusing on the characterization of resultant network polymer precursors (NPPs) using SEC‐MALLS‐viscometry providing the correlation of [η] versus M_w of fractionated samples. Notably, the structure of NPP consisting of oligomeric primary polymer chains generated from specific allyl polymerization would become core‐shell type dendritic with the progress of polymerization. The correlation between delayed gelation and decreased reactivity of dendritic NPP for intermolecular cross‐linking is discussed. Conclusively, the reactivity for intermolecular cross‐linking between NPPs decreased with the progress of polymerization leading to a delayed gelation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2871–2881, 2009     

Permeability control in electro‐sensitive microcapsules with immobilized ferroelectric liquid crystalline segments

Nylon‐polystyrene microcapsules with immobilized ferroelectric liquid crystalline segments were prepared, and permeability control of an encapsulated core material was investigated under an external electric field. A ferroelectric liquid crystal monomer possessing both mesogenicity and chirality responded effectively to the external electrical field. Permeation of the material (oxprenolol) contained in the inner aqueous core of the microcapsules was enhanced under a weak electric field (2 V). Furthermore, the permeability of oxprenolol did not depend on the external electric field in the absence of the ferroelectric liquid crystal segments. To clarify the controlled‐release mechanism of the core material, the light transmittance of the polymer membranes was quantitatively evaluated under an external electric field using a handmade polarized light transmittance apparatus. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1749–1757, 2008     

NMR spectroscopic characterization of inclusion complexes comprising cyclodextrins and gallated catechins in aqueous solution: cavity size dependency

The structure of inclusion complexes of γ‐cyclodextrin (γ‐CD), (–)‐gallocatechin gallate (GCg), and (–)‐epigallocatechin gallate (EGCg) in D₂O was investigated using several NMR techniques. GCg formed a 1:1 inclusion complex with γ‐CD in which the A and C rings of GCg were inserted deep at the head of the A ring into the γ‐CD cavity from the wide secondary hydroxyl group side. In the 1:1 inclusion complex with GCg and γ‐CD, the GCg moiety maintained a conformation in which the B and B′ rings of GCg took both pseudoequatorial positions with respect to the C ring. The structure of the inclusion complex of GCg and γ‐CD obtained from NMR experiments supported well that determined from PM6 semiempirical SCF MO calculations. However, ¹H NMR experiments suggested that EGCg did not form any inclusion complex with γ‐CD in D₂O. The marked difference between GCg and EGCg in inclusion behavior toward γ‐CD may be explained in terms of the stabilization energy calculated with the PM6 method. Copyright © 2008 John Wiley & Sons, Ltd.     

A generating function for sums of multiple zeta values and its applications

A generating function for specified sums of multiple zeta values is defined and a differential equation that characterizes this function is given. As applications, some relations for multiple zeta values over the field of rational numbers are discussed.