Status of heavy element research using a gas-filled recoil separator at RIKEN

A gas-filled type of recoil separator for heavy element research was installed at an experimental hall of RIKEN Linear Accelerator facility to realize getting higher intensity of primary beam and long beam time. Performance of the separator was studied using target recoils and various nuclear reactions. The results show the high performance of the separator for heave element research. As an application of the GARIS, production and identification of an isotope of the 110th element ²⁷¹[110] have been performed using the ²⁰⁸Pb(⁶⁴Ni,1n)²⁷¹[110] reaction. Three decay chains coincide well both in decay times and energies with the ones reported by the group of SHIP experiment at GSI, Germany. Our results provide a confirmation of the synthesis of an isotope ²⁷¹[110] of element 110.     

Improved detectability with a polymer-based trapping device in rapid HPLC analysis for ultra-low levels of bisphenol A (BPA) in environmental samples.

A new high-performance liquid chromatography (HPLC) method has been developed to detect ultra-low concentrations of bisphenol-A (BPA) (below 1 ng/L (ppt)) using column switching electrochemical detection (ECD). The results were superior to those obtained from manual pretreatment procedure with membrane stationary phase. BPA is inherently ubiquitous in the environment, including tools and solvents used for its analysis; to obtain meaningful results, therefore, the concentration of the overall BPA contamination must be below the detection limit for BPA using the analytical system. Therefore, purified water for preparing the standard BPA solution must be filtered with a hydrophobic membrane to suppress BPA background levels of contamination. In addition, we investigated methods for effectively preserving environmental water containing BPA. The addition of a small amount of ethylenediaminetetraacetic acid (EDTA) provided good recovery even after overnight storage. By employing these precautionary measures and procedures to reduce BPA contamination from the analytical procedure, we could accurately determine l(-10) ppt of BPA in environmental water samples using a column switching HPLC system.     

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.     

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.     

Influence of nuclear reactor accident at Chernobyl' on the environmental radioactivity in Toyama

The environmental radioactivity caused by the reactor accident at Chernobyl' was investigated from May 7 to May 31 of 1986 in Toyama. Measurement of radioactivities in airborne particles, rain water, drinking water, milk, and mugwort are carried out by gamma-ray spectrometry (pure Ge detector; ORTEC GMX-23195). Ten different nuclides (103Ru, 106Ru, 131I, 132Te-I, 134Cs, 136Cs, 137Cs, 140Ba-La) are identified from samples of airborne particles. In the air samples, a maximum radioactivity concentration of each nuclide is observed on 13th May 1986. The time of the reactor shut-down and the flux of thermal neutron at the reactor were calculated from 131I/132I and 137Cs/134Cs ratio. The exposure dose in Toyama by this accident is given as follows: internal exposure; [thyroid] adult-59 microSv, child-140 microSv, baby-130 microSv, [total body] adult-0.2 microSv, child, baby-0.4 microSv, external exposure; 7 microSv, effective dose equivalent; adult-9 microSv, child-12 Sv, baby-11 microSv.