On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

In this paper we focus on the problem of identifying the index sets P(x):=i|x_i>0, N(x):={i|F_i(x)>0 and C(x):=i|x_i=F_i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.Mathematics Subject Classification (2000): 90C33, 65K10     

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.     

Determination of metal-binding proteins in soft tissues of rock oyster by neutron activation analysis and particle induced X-ray emission

In this work, we determined the levels of trace metals in protein fractions isolated from rock oysters by neutron activation analysis (NAA) and particle induced X-ray emission (PIXE). Proteins were extracted from mantles and hepatopancreases of rock oysters and fractionated by size-exclusion high performance liquid chromatography (HPLC). The protein fractions from mantles and hepatopancreases are found to be abundant in Fe, Cu, Zn, Mn, Pb, and Ag. HPLC profiles of Fe, Cu, Zn, and Ag indicate that those elements are bound to proteins extracted from mantles and hepatopancreases.     

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.     

Adsorption Isotherm of Water Vapor and Its Large Hysteresis on Highly Ordered Mesoporous Silica

The first and second adsorption–desorption isotherms of water vapor on a new mesoporous material derived from kanemite have been measured. The isotherms show unusual type V isotherms and large hysteresis. The type V isotherms, which have never been observed for the other adsorbates, suggest that the mesoporous material has a hydrophobic surface, although the hydrophobicity decreased after treatment with water vapor because of rehydration of the surface. The significantly large hysteresis could be explained by the difference in contact angle between adsorption and desorption.     

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).