On integers of the forms k−2 and k2+1

In this paper we prove that if (r,12)?3, then the set of positive odd integers k such that k^r−2ⁿ has at least two distinct prime factors for all positive integers n contains an infinite arithmetic progression. The same result corresponding to k^r2ⁿ+1 is also true.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa^[6], G. Gundersen^[7] and J.K. Langley^[8], Li Chun-hong^[11].     

Crystallographic report: Bis(norfloxacin)dilead(II) tetranitrate, [Pb2(H‐Norf)2(ONO2)4]

The centrosymmetric binuclear structure of [Pb₂(H‐Norf)₂(ONO₂)₄]shows the geometry around each lead(II) atom to be distorted trigonal bipyramidal with Pb–O distances ranging from 2.357(3) to 2.769(4) Å. Copyright © 2003 John Wiley & Sons, Ltd.     

Below-band-gap waveguiding behaviors of a weakly index-guided GaAs/AlGaAs quantum well laser

We report the reduced waveguiding efficiency for the signals around 1560 nm as the injection current of an GaAs/AlGaAs multiple quantum well laser diode (lasing wavelength at 840 nm) with a ridge-loading waveguide configuration increased. This reduction trend stopped when the injection current reached the threshold condition of the laser diode. The decreased waveguide transmission and the more expanded mode profile indicated the variation of the effective refractive index gradient in the lateral dimension with injection current. This variation was due to the refractive index decrease with increasing carrier density even below band gap. A slab waveguide model was used to simulate the lateral mode profile variation with injection current. The refractive index differences between the guiding layer and claddings in the slab waveguide model provided estimates of refractive index contrasts of the laser diode at a concerned wavelength under various injection conditions.     

副品红共振光散射法测定脱氧核糖核酸

本文基于脱氧核糖核酸 (DNA)对有机染料副品红的共振光散射的增强效应 ,拟定了一种测定DNA的共振光散射法。在pH =0 5～ 1 5范围内 ,有机染料副品红于 35 5nm处的共振光散射强度被DNA强烈增强 ,且增强程度与DNA浓度呈线性关系 ,线性范围为 0 10～ 15 μg·mL- 1 ,检出限可达 36ng·mL- 1 。该方法简便、快速、具有较高的灵敏度和准确度 ,且线性范围较宽。将该方法用于混合样品中DNA的测定 ,结果令人满意。     

四种多变量校准方法在FTIR多组分分析中的性能比较

本文对四种多变量校准方法－－经典最小二乘法（CLS），偏最小二乘法（PLS），卡尔曼滤波法（KFM）以及人工神经网络法（ANN）－－在多组分浓度分析方面的性能进行了比较。选择五种红外谱图严重混叠的大气有机毒物－－1，3－丁二烯，苯，邻二甲苯，氯苯和丙烯醛－－作为分析对象。分别计算各种方法对该5组分体系的平均预测误差MPE和平均相对误差MRE进行比较。结果表明，偏最小二乘法在处理这类问题中是最稳健的方法。     

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.     

A Nonconforming Arbitrary Quadrilateral Finite Element Method for Approximating Maxwell's Equations

The main aim of this paper is to provide convergence analysis of Quasi-Wilson nonconforming finite element to Maxwell's equations under arbitrary quadrilateral meshes.The error estimates are derived,which are the same as those for conforming elements under conventional regular meshes.     

Adaptive regulation for deterministic systems

For the linear deterministic system with unknown orders and coefficients adaptive controls are given so that the closed-loop system is stabilized and the unknown parameters are consistently estimated. Moreover, if the parameter estimation is ignored, then the system input and output can be reduced to zero with an exponential rate.This project is supported by the National Natural Science Foundation of China.In Commemoration of the 15th Anniversary of the Acta Mathematicae Applicatae Sinica.     

Discovery of a new long-lived isomeric state in 125Ce

A new long-lived isomeric state in the near proton dripline nucleus ¹²⁵Ce has been identified with Schottky mass spectrometry at GSI. The excitation energy E ^* = 103(12)keV and the decay time of 193(1)s have been obtained from a single stored fully ionized ^125m Ce⁵⁸⁺ ion. The data implies an E3 transition and a 1/2⁺ assignment for the spin of the isomer.