Stable all-optical formation of Bose–Einstein condensate using pointing-stabilized optical trapping beams

By stabilizing the beam pointing of optical trapping beams, we have succeeded in stable formation of Bose–Einstein condensate (BEC) of ⁸⁷Rb with all-optical method. The thermal effect of acousto-optic modulator (AOM) is usually one of the most serious problems to induce beam-pointing instability, especially for high power CO₂ laser. By passing the beam through AOM twice, we have improved the beam pointing from about 4.8 mrad to less than 0.4 mrad, which has been experimentally confirmed to be small enough to stably form BEC at the crossed region of CO₂ lasers as well as to perform experiments using an optical lattice which might have been affected by beam-pointing instability. PACS 32.80.Pj; 42.79.Jq; 03.75.Mn     

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 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.     

Intake of different chemical species of dietary arsenic by the japanese,and their blood and urinary arsenic levels

We calculated the intake of each chemical species of dietary arsenic by typical Japanese, and determined urinary and blood levels of each chemical species of arsenic. The mean total arsenic intake by 35 volunteers was 195±235 (15.8-1039) μg As day^?1, composed of 76% trimethylated arsenic (TMA), 17.3% inorganic arsenic (As_i), 5.8% dimethylated arsenic (DMA), and 0.8% monomethylated arsenic (MA): the intake of TMA was the largest of all the measured species. Intake of As_i characteristically and invariably occurred in each meal. Of the intake of As_i, 45-75% was methylated in vivo to form MA and DMA, and excreted in these forms into urine. The mean measured urinary total arsenic level in 56 healthy volunteers was 129±92.0 μg As dm^?3, composed of 64.6% TMA, 26.7% DMA, 6.7% As_i and 2.2% MA. The mean blood total arsenic level in the 56 volunteers was 0.73±0.57 μg dl^?1, composed of 73% TMA, 14% DMA and 9.6% As_i. The urinary TMA levels proved to be significantly correlated with the whole-blood TMA levels (r = 0.376; P<0.01).     

Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement

The present paper gives a more complete treatment of the scattering from a two-dimensional random surface than previous works. Reciprocal theorems for the stochastic wave field and the incoherent scattering distribution (bistatic cross section) are derived and the presence of backscattering enhancement in the case of a slightly random Neumann surface is demonstrated. A physical interpretation of the backscattering enhancement associated with the presence of anomalous scattering on a slightly random Neumann surface is given. Some numerical calculations are performed to show the incoherent scattering distribution and the backscattering enhancement.