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.     

Direct determination of benzamides in serum by column-switching high-performance liquid chromatography.

A column-switching high-performance liquid chromatographic method with fluorescence detection was developed for the simultaneous determination of four benzamide-type anti-psychotic drugs: sulpiride, tiapride, sultopride and metoclopramide in human serum. In this method, a TSKgel Super-ODS column was used as an analytical column, and a TSKgel G 2000SW was prepared as a pretreatment column. Under the optimized analytical conditions, four benzamide-type anti-psychotic drugs were eluted within 18 min. The detection limits (S/N = 3) for sulpiride, tiapride, sultopride and metoclopramide are 1 ng/ml, 4 ng/ml, 2 ng/ml and 0.5 ng/ml, respectively. Finally, the method was applied to the determination of sulpiride in human serum samples obtained after a single oral dose of sulpiride.     

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.     

Second order evolution equations with time-dependent subdifferentials

We study an abstract second order nonlinear evolution equation in a real Hilbert space. We consider time-dependent convex functions and their subdifferentials operating on the first derivative of the unknown function. Introducing appropriate assumptions on the convex functions and other data, we prove the existence and uniqueness of a strong solution, and give some applications of the abstract theorem to hyperbolic variational inequalities with time-dependent constraints.      

Laser spectroscopy of trapped 7Be and 10Be at a prototype slow RI-beam facility of RIKEN

A next-generation slow radioactive nuclear ion beam facility (SLOWRI) which provides slow, high-purity and small emittance ion beams of all elements is being build as one of the principal facilities at the RIKEN RI-beam factory (RIBF). High energy radioactive ion beams from the projectile fragment separator BigRIPS are thermalized in a large gas catcher cell. The thermalized ions in the gas cell are guided and extracted to a vacuum environment by a combination of dc electric fields and inhomogeneous rf fields (rf carpet ion guide). From there the slow ion beam is delivered via a mass separator and a switchyard to various devices: such as an ion trap, a collinear fast beam apparatus, and a multi-reflection time of flight mass spectrometer. In the R&D works at the present RIKEN facility, an overall efficiency of 5% for a 100A MeV ⁸Li ion beam from the present projectile fragment separator RIPS was achieved and the dependence of the efficiency on the ion beam intensity was investigated. Recently our first spectroscopy experiment at the prototype SLOWI was performed on Be isotopes. Energetic ions of ¹⁰Be and ⁷Be from the RIPS were trapped and laser cooled in a linear rf trap and the specific mass shifts of these isotopes were measured for the first time.