A globally convergent Newton method for solving strongly monotone variational inequalities

Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method.     

An optimal design of collateralized mortgage obligation with PAC-companion structure using dynamic cash reserve

This paper presents a model for optimally designing a collateralized mortgage obligation (CMO) with a planned amortization class (PAC)-companion structure using dynamic cash reserve. In this structure, the mortgage pool’s cash flow is allocated by rule to the two bond classes such that PAC bondholders receive substantial prepayment protection, that protection being provided by the companion bondholders. The structure we propose provides greater protection to the PAC bondholders than current structures during periods of rising interest rates when this class of bondholders faces greater extension risk. We do so by allowing a portion of the cash flow from the collateral to be reserved to meet the PAC’s scheduled cash flow in subsequent periods. The greater protection is provided by the companion bondholders exposure to interest loss. To tackle this problem, we transform the problem of designing the optimal PAC-companion structure into a standard stochastic linear programming problem which can be solved efficiently. Moreover, we present an extended model by considering the quality of the companion bond and by relaxing the PAC bondholder shortfall constraint. Based on numerical experiments through Monte Carlo simulation, we show the utility of the proposed model.     

Separation of fulvic acid from soil extracts based on ion-pair formation with a cationic surfactant.

A novel method for separating fulvic acid (FA) from soil extracts is proposed. The FA, defined as the acid-soluble fraction of an alkaline extract of soil, was separated based on the precipitation of an ion-pair with a cationic surfactant, such as domiphen bromide. The precipitate was dissolved in aqueous HCl to produce H+ -type FA and a surfactant chloride (SUR-Cl). SUR-Cl, in the aqueous solution, was removed by extraction with CHCl3. After the aqueous phase was passed through a cation-exchanger (H+ -type), H+ -type FA (FA-SUR) was obtained as a powder by lyophylization. The chemical characteristics of FA-SUR were compared with an FA sample separated according to the method of the International Humic Substances Society using a DAX-8 resin (FA-DAX). The oxygen content, O/C atomic ratio and total acidity of the FA-SUR were significantly larger than the corresponding values for FA-DAX. The solid-state CPMS 13C NMR spectra indicated that the higher oxygen content of the FA-SUR could be due to alcoholic hydroxyl groups and polysaccharides as well as carboxylic groups. These results show that FA-SUR is more polar and hydrophilic than FA-DAX.     

Rapid determination method of radiocesium in sea water by cesium-selective resin

A rapid and precise method of determining radiocesium corresponding to 5 mrem/y, the Japan AEC's guideline, was proposed. The development and practical performance of cesium-selective resin and the determination method was described in this paper. The resin was prepared by the formation of ammonium molybdophosphate in the structure of Amberlite XAD-7 resin. It took only 3 hours to carry out all the procedures the authors proposed. This value represents 1/10∼1/2 of the time of conventional method. The concentration of¹³⁷Cs and¹³⁴Cs in sea water was determined to be 0.13∼0.16 pCi/1 and less than 7.1·10⁻² pCi/1, respectively.     

Chiral β-dimethylaminoalkylphosphines. Highly efficient ligands for a nickel complex catalyzed asymmetric grignard cross-coupling reaction

Chiral β-dimethylaminoalkylphosphines were prepared starting with amino acids, (S)-alanine, (S)-phenylalanine, (R)-phenylglycine, (S)-valine, and (R)-tert-leucine. The chiral phosphines were found to be highly efficient ligands for a nickel catalyzed asymmetric Grignard cross-coupling reaction (38～94% optical yield).     

Photon activation analysis of trace metals in the livers and spleens of pigs

Nondestructive photon activation analysis with 30 MeV bremsstrahlung was applied to determine trace element concentrations in the livers and spleens of five pigs. Samples were freeze-dried, pulverized and fractionated into four groups corresponding mesh size; smaller than 60 mesh, 60–100 mesh, 100–200 mesh and larger than 200 mesh. Up to 9 elements in each fraction were analyzed. The concentrations of Br, Fe, Mg, Mn, Mo, Na, Rb and Zn in each liver fractions were almost constant, as were concentrations of Mg and Rb in spleens.     

Capacity and quantum mechanical tunneling

We connect the notion of capacity of sets in the theory of symmetric Markov process and Dirichlet forms with the notion of tunneling through the boundary of sets in quantum mechanics. In particular we show that for diffusion processes the notion appropriate to a boundary without tunneling is more refined than simply capacity zero. We also discuss several examples in ^d .     

Effect of pH on adsolubilization of single and binary organic solutes into a cationic hydrocarbon surfactant adsorbed layer on silica

The adsolubilization behaviors of 2-naphthol, biphenyl, and their binary solutes in the hexadecyltrimethyl ammonium bromide (HTAB) adsorbed layer formed on silica have been studied with solution pH. Two feed concentrations of HTAB are employed: 1.5 and 3.0 mmol dm(-3). At the feed concentration of 1.5 mmol dm(-3) HTAB, most of HTAB are adsorbed on the silica as a monolayer, while a bilayer formation occurs at the feed concentration of 3.0 mmol dm(-3). It is found that the adsolubilized amounts of respective single solutes increase with increasing solution pH except acidic region for biphenyl under a constant feed concentration of 2-naphthol (0.4 mmol dm(-3)) and biphenyl (0.047 mmol dm(-3)). The adsolubilization of binary solutes depends on the feed concentration of HTAB; at the low HTAB feed concentration, competitive adsolubilization between 2-naphthol and biphenyl occurs above pH 4.5, while at the high HTAB feed concentration the adsolubilization of biphenyl is enhanced by the incorporation of 2-naphthol over a whole pH region. These behaviors in the adsolubilization are discussed from the surfactant structure of HTAB adsorbed as well as the admicellar partitioning coefficients.     

Application of 28Mg to the kinetic study of Mg uptake by rice plants

The time course of Mg uptake and release using intact rice plants and ²⁸Mg as a tracer is presented. Since there is no conventional Mg tracer available, ²⁸Mg was produced via ²⁷Al(α, 3p)²⁸Mg reaction using a cyclotron. Using the purified ²⁸Mg tracer, it was found that the uptake amount of ²⁸Mg by the rice plants increased linearly during 30 min of application. After ²⁸Mg treatment for 90 min, the roots were sequentially washed with iced solution for 120 min. Within about 10 min, almost all of the ²⁸Mg, that was thought to be weakly bound to the apoplast, was washed away.