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.     

Applying a Mode Selector to Improve the Pulse-Compression Performance of Asymmetric-Coupled-Waveguide-Based Dispersion Compensators

An InGaAsP slab-type asymmetric-coupled-waveguide-based dispersion compensator with a mode selector has been designed and fabricated. The mode selector is necessary to select either a symmetric [with a positive group-velocity dispersion (GVD)] or antisymmetric (with a negative GVD) supermode. These supermodes exist simultaneously in the dispersion-compensation region of the device. Pulse-compression experiments were used to test the dispersion compensator, evaluating the function of the mode selector. A theoretical study of the experimental results shows that the mode selector obtains a very strong selectivity (nearly 100%) for the antisymmetric supermode.     

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.     

Application of total reflection X-ray fluorescence spectrometry to small glass fragments.

Total reflection X-ray fluorescence spectrometry (TXRF) has been applied for trace elemental analysis of small glass fragments. A small glass sample (a fragment with weight less than 0.5 mg) was decomposed by 100 microg of HF/HNO3 acid; the material was condensed to 10 microl and was dried on a Si wafer. Since the size of the dried residue on the Si wafer was less than 1 cm in diameter, an incident X-ray beam with about 1 cm in width could effectively excite elemental components in such a small glass fragment. The precision of the present technique was checked by analyzing the glass fragments (<0.5 mg) from NIST SRM612; the relative standard deviations (RSD) of less than 8.1% were achieved for elemental ratios that were normalized by Sr. Fragments (<0.5 mg) obtained from 23 figured sheet glasses were used as samples for estimating the utility of this technique to forensic discrimination. Comparison of five elemental ratios of Ti/Sr, Mn/Sr, Zn/Sr, Rb/Sr, and Pb/Sr calculated from X-ray fluorescence spectra was effective in distinguishing glass fragments that could not be differentiated by their refractive indexes (RI).     

A fast atom bombardment mass spectrometric analysis of crown ether complexes [1]

Analyses of crown ether complexes of alkali metal ions and characterization of the complexes formed inm-nitrobenzyl alcohol have been carried out by fast atom bombardment (FAB) mass spectrometry. By using m-nitrobenzyl alcohol as a matrix for measurements, the stoichiometry of the complexes was assessed on the basis of the observed FAB peaks. In addition, the formation of crown ether-alkali metal complexes at a 2 : 1 molar ratio was enhanced by increasing the ionic radius of the metal ion in agreement with previous observations. On these grounds, FAB mass spectrometry may provide a rapid means for investigation of the complexation behavior of crown ethers and the stoichiometry of the complexes.     

Average heat transfer rates measured and numerically analyzed for combined convection of air in an inclined cylindrical enclosure due to both magnetic and gravitational fields

The average heat transfer rates were measured for natural convection of air in a shallow cylindrical enclosure heated from below and cooled from above in a bore space of an inclined super-conducting magnet. Depending on the location of the enclosure in the bore space, the angle of inclination and the strength of magnetic field, the net acceleration force could be arbitrarily varied and in this report, two locations where mostly axial magnetizing force prevails were selected. The average heat transfer rates varied with the angle of inclination due to the change in the total net acceleration of gravitational and magnetizing forces. Numerical computations were also carried out for the similar system under the combined magnetizing and gravitational forces and the computed average Nusselt numbers agreed mostly with the measured results. Detailed flow modes were graphically presented for the computed cases.     

Synthesis and chiroptical properties of optically active poly(ethynylcarbazole) derivatives: Substituent effect on the helix formation

Novel chiral acetylene monomers containing carbazole, 2‐ethynyl‐9‐[(S)‐2‐methylbutoxycarbonyl]carbazole ( 1 ), 3‐ethynyl‐9‐[(S)‐2‐methylbutoxycarbonyl]carbazole ( 2 ), 2‐ethynyl‐9‐[(S)‐2‐methylbutyl]carbazole ( 3 ), and 2‐ethynyl‐9‐[(S)‐4‐methylhexyl]carbazole ( 4 ) were synthesized and polymerized with [(nbd)RhCl]₂? Et₃N. The corresponding polyacetylenes with number‐average molecular weights ranging from 68,700 to 310,000 were obtained in good yields. Poly( 1 ) exhibited a large specific rotation and an intense Cotton effect in toluene, indicating that it formed a helix with predominantly one‐handed screw sense, while the other three polymers showed no evidence for taking a helical structure. Poly( 1 ) largely decreased the CD intensity upon heating from ?10 to 60 °C. Poly( 1 ) showed a Cotton effect in film state in a manner similar to solution state. No chiral amplification was observed in the copolymerization of 1 with achiral 2‐ethynyl‐9‐tert‐butoxycarbonylcarbazole ( 5 ). © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4450–4458, 2007     

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.     

Synthesis and properties of poly(phenylacetylenes) having two polar groups or one cyclic polar group on the phenyl ring

Phenylacetylene (PA) derivatives having two polar groups (ester, 2a – d ; amide, 4) or one cyclic polar group (imide, 5a – c ) were polymerized using (nbd)Rh⁺[(η⁶‐C₆H₅)B^?(C₆H₅)₃] catalyst to afford high molecular weight polymers (～1 × 10⁶ – 4 × 10⁶). The hydrolysis of ester‐containing poly(PA), poly( 2a) , provided poly(3,4‐dicarboxyPA) [poly ( 3 )], which could not be obtained directly by the polymerization of the corresponding monomer. The solubility properties of the present polymers were different from those of poly(PA) having no polar group; that is, poly( 2a )–poly( 2d ) dissolved in ethyl acetate and poly( 4 ) dissolved in N,N‐dimethylformamide, while poly(PA) was insoluble in such solvents. Ester‐group‐containing polymers [poly( 2a )–poly( 2d )] afforded free‐standing membranes by casting from THF solutions. The membrane of poly( 2a ) showed high carbon dioxide permselectivity against nitrogen (PCO₂/PN₂ = 62). © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5943–5953, 2006     

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.