Fibre raman amplifier properties for applications to long-distance optical communications

This paper reviews recent theoretical and experimental studies on optical amplification by stimulated Raman scattering (Raman amplification) in single-mode optical fibres, and discusses its possible applications to long-distance optical communications. The fibre Raman amplifier can be used as an in-line optical amplifier in both repeaterless and non-regenerative all-optical repeater configurations. In the former application, signal transmission of over 400 km has been predicted theoretically, although high-power pump sources are considered to be required. In the latter configuration, in which optical fibre losses are compensated for by Raman gains, it has been shown that extremely long-distance transmission over more than 1000 km is feasible in terms of signal-to-noise ratio, where the distance achievable is mainly limited by the accumulation of Raman noise. Recent experimental demonstrations including bit-error rate measurements on the Raman amplified signal, and laser-diode pumped amplification, etc., are also reviewed. The results confirm the effectiveness of fibre Raman amplifiers in future long-haul systems.     

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.     

Fabrication and transport properties of multiwall carbon nanotube crossroads

A multiwall carbon nanotube crossroads has been fabricated by a manipulation technique using a glass microcapillary, and the low temperature transport properties investigated. The two-terminal conductance of an individual tube shows Tomonaga–Luttinger liquid behavior G∝T^α at high temperature and dI/dV ∝V ^α at low temperature. However, no evidence of such a power-law behavior is obtained in the four-terminal conductance at the junction, where the conductance shows an almost metallic behavior ‘corrected’ by weak localization. Weak localization would essentially appear in electron states at the junctions of MWNTs.     

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.     

Local structure analysis of smoky and colorless topaz using single crystal Al NMR

The angular dependence of the ²⁷Al NMR spectrum was measured for single crystals of smoky and colorless topaz, Al₂SiO₄(F,OH)₂. Smoky topaz was obtained by irradiating high energy neutrons to colorless topaz. The quadrupole coupling constant e²Qq/h and the asymmetry parameter η were obtained from the analysis of the angular dependences of quadrupole splitting of the ²⁷Al NMR spectrum. The local structures around the aluminum atoms in smoky and colorless topaz were discussed from the magnitude and the direction of the electric field gradient. The directions of principal axes of the EFG tensor of ²⁷Al were close to the directions of Al-O and Al-F bonds. The difference in the bond lengths between Al(1)-F(1) and Al(1)-F(2) was found to affect the x and y components of the EFG tensor.     

Analysis of Spectral Reflectance Using Normalization Method from Endoscopic Spectroscopy System

Objective assessment of gastrointestinal mucosal color is extremely important in the endoscopic diagnosis of digestive tract disease. In this paper, we propose a method to clarify the spectral characteristics of gastric and colon cancer. A large number of spectral reflectance data of mucous membrane are measured by the endoscopic spectroscopy system (ESS) in the National Cancer Center Hospital East, Kashiwa, Japan and the Department of Internal Medicine, Self-Defense Force Center Hospital, Tokyo, Japan. We assume that early cancer appears primarily in the spectral data of short wavelength, because it is usually present in a superficial cell where short wavelength light is scattered more strongly than long wavelength light. To identify the features in the short wavelength components, the spectral reflectance was divided by the reflectance of a long wavelength. We investigated the possibility of distinguishing early cancer from normal spectral data through statistical analysis, employing the projection axis as the mean difference between them. Early cancer and normal spectral data were projected on the projection axis, and the Student’s T-test was applied to evaluate the mean of the distribution between these data.