Kinetic study of the crosslinking reaction of 1,2‐polybutadiene with dicumyl peroxide in the absence and presence of vinyl acetate

The crosslinking reaction of 1,2-polybutadiene (1,2-PB) with dicumyl peroxide (DCPO) in dioxane was kinetically studied by means of Fourier transform near-infrared spectroscopy (FTNIR). The crosslinking reaction was followed in situ by the monitoring of the disappearance of the pendant vinyl group of 1,2-PB with FTNIR. The initial disappearance rate (R₀) of the vinyl group was expressed by R₀ = k[DCPO]^0.8[vinyl group]^−0.2 (120 °C). The overall activation energy of the reaction was estimated to be 38.3 kcal/mol. The unusual rate equation was explained in terms of the polymerization of the pendant vinyl group as an allyl monomer involving degradative chain transfer to the monomer. The reaction mixture involved electron spin resonance (ESR)-observable polymer radicals, of which the concentration rapidly increased with time owing to a progress of crosslinking after an induction period of 200 min. The crosslinking reaction of 1,2-PB with DCPO was also examined in the presence of vinyl acetate (VAc), which was regarded as a copolymerization of the vinyl group with VAc. The vinyl group of 1,2-PB was found to show a reactivity much higher than 1-octene and 3-methyl-1-hexene as model compounds in the copolymerization with VAc. This unexpectedly high reactivity of the vinyl group suggested that an intramolecular polymerization process proceeds between the pendant vinyl groups located on the same polymer chain, possibly leading to the formation of block-like polymer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4437–4447, 2004     

Visible-light-sensitive photocatalytic reaction on chromium-containing mesoporous silica: selective partial oxidation of propane with molecular oxygen

The photocatalytic reactivities of chromium-containing mesoporous silica molecular sieves (Cr-HMS) under visible light irradiation have been investigated. Cr-HMS involves tetrahedral chromium oxide (Cr-oxide) moieties which are highly dispersed and incorporated in the framework of molecular sieve with two terminal Cr=O groups. In the presence of propane with molecular oxygen, a partial oxidation proceeded under visible light irradiation to produce acetone and acrolein, with high selectivity, while a complete oxidation proceeded under UV light irradiation mainly to produce CO₂. The charge-transfer excited state of the tetrahedral Cr-oxide moieties plays a significant role in the photocatalytic reactions.     

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     

On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed.     

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.     

Determination of cyclosporin A in the serum of kidney transplant patients by rapid-flow fractionation and normal-phase high-performance liquid chromatography

High-performance liquid chromatography was used to determine cyclosporin A (CsA) concentrations in the serum of kidney transplant patients by rapid-flow fractionation (RFF) followed by silica gel normal-phase high-performance liquid chromatography (HPLC). The extraction of CsA from serum was achieved by RFF using a short diatomaceous earth column eluted with diethyl ether-n-hexane (50:50, v/v). The recovery was more than 80% at concentrations of 50-150 micrograms/l. The concentration of this compound was determined by HPLC using a conventional silica gel column with 3.3 M ammonia solution-ethanol-n-hexane (0.31:10.69:89, v/v) as eluent. Concentration calibration was made on the basis of the peak-height ratio of CsA to CsD as the internal standard. The coefficient of variation of this assay was less than 6.5% and the results were used for the therapeutic drug monitoring of CsA administered to kidney transplant patients. Measurements of the CsA concentrations in 160 serum specimens were also made by conventional radioimmunoassay (RIA) using commercial kits. The data obtained by RIA were on average 2.5 times those obtained by HPLC. Higher values in RIA were observed characteristically with patients with severe disfunction resulting from CsA hepatotoxicity. From the results, it appeared that HPLC rather than RIA provides more precise and reliable values for the concentration of this drug.     

Effect of Hydrolysis Conditions on the Direct Formation of Nanoparticles of Ceria–Zirconia Solid Solutions from Acidic Aqueous Solutions

The effect of the cation concentration, hydrolysis temperature, and composition in the CeO₂–ZrO₂ system on the direct precipitation of ceria–zirconia solid solutions and the structure of the precipitates from acidic aqueous solutions of (NH₄)₂Ce(NO₃)₆ and ZrOCl₂ by hydrolysis under hydrothermal conditions were investigated. Nanometer-sized (8–10 nm) ceria–zirconia solid solution particles in a composition range of 0 to 60 mol% ZrO₂ were directly precipitated from the solutions with total metal cation concentration less than 0.2 mol/dm³ by simultaneous thermal hydrolysis at 150–240°C. The crystalline phase of the precipitates gradually changed from cubic and/or tetragonal to monoclinic with increasing the cation concentration of the solution from 0.2 to 0.8 mol/dm³ at the starting composition of 50 mol% ZrO₂ under hydrolysis condition of 150°C for 48 h, which was attributed to decrease in the supply of hydrolyzed Ce component caused by decrease in the hydrolysis ratio of (NH₄)₂Ce(NO₃)₆. Ceria–zirconia solid solutions containing large amount of ZrO₂ maintained high specific surface area and small-sized crystallite after heat-treatment at 900–1000°C for 1 h.     

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.     

Primal-dual proximal point algorithm for linearly constrained convex programming problems

A primal-dual version of the proximal point algorithm is developed for linearly constrained convex programming problems. The algorithm is an iterative method to find a saddle point of the Lagrangian of the problem. At each iteration of the algorithm, we compute an approximate saddle point of the Lagrangian function augmented by quadratic proximal terms of both primal and dual variables. Specifically, we first minimize the function with respect to the primal variables and then approximately maximize the resulting function of the dual variables. The merit of this approach exists in the fact that the latter function is differentiable and the maximization of this function is subject to no constraints. We discuss convergence properties of the algorithm and report some numerical results for network flow problems with separable quadratic costs.