Polarisation characteristics of a 12 fibre coupler under femtosecond pulsed and continuous wave illumination

We report on the experimental investigation carried out in the polarisation characteristics of femtosecond pulsed and continuous wave beams propagating through a 1×2 fibre coupler. It is demonstrated that the polarisation states of pulsed and continuous wave illumination over the broad wavelength range can be preserved in a conventional fused fibre coupler. Furthermore, the fibre coupler acts as a low-pass spectral filter in the visible wavelength range with a splitting ratio between 99.6/0.4 and 99.7/0.3. The result is of importance for fibre-optic second harmonic generation microscopy which requires the polarisation preservation to extract molecular organization of a sample.     

Tensor-product monotonicity preservation

This paper studies systems of tensor-product functions for which the functions they span are monotonic in any direction when their control nets are monotonic in that direction. It is shown that Bernstein polynomials and B-splines have this property but that totally positive systems in general, such as certain trigonometric and rational bases, do not. This revised version was published online in August 2006 with corrections to the Cover Date.     

层次分析中广义最小偏差法的性质

广义最小偏差法（GLDM）是层次分析中一种重要的排序方法．本文讨论了广义最小偏差法的性质和灵敏度分析问题．     

低速二维流动的粒子仿真研究

本文运用信息保存法对低速二维的流动现象进行模拟，考察了低速条件下的有限平板绕流以及微槽道气体流动问题。研究表明：在对低速流动的模拟过程中，运用IP法在能够获得较好的结果的同时，具有比DSMC方法更高的计算效率。     

A new property of Bernstein-Kantorovi? operators

In the present paper, we prove that the Bernstein-Kantorovič operators have the ability of preserving translation property in both C and L^p norms. Supported (in part) by the NSFC(10471130,10371024) of PRC and the Natural Science Foundation (Y604003) of Zhejiang Province.     

B-SERIES METHODS CANNOT BE VOLUME-PRESERVING

Volume preservation is one of the qualitative characteristics common to many dynamical systems. However, it has been proved by Kang and Shang that e.g. Runge–Kutta (RK) methods can not preserve volume for all linear source-free ODEs (let alone nonlinear ODEs). On the other hand, certain so-called Exponential Runge–Kutta (ERK) methods do preserve volume for all linear source-free ODEs. Do such ERK methods perhaps also preserve volume for all nonlinear ODEs? Here we prove that the answer to this question is negative; B-series methods (which include RK, ERK and several more classes of methods) cannot preserve volume for all source-free ODEs. The proof is presented via the theory of K-loops, which is an extension of the theory of classical rooted trees.     

THE RATE OF DISCOUNT AND THE PRESERVATION OF NATURAL ENVIRONMENTS

This paper examines the relationship between the rate of discount and the the optimal level of permanently preserved natural environments. A lower rate of discount increases the demand for both preserved environments and capital accumulation. The greater demand for capital indirectly increases the demand for the productive resource inputs found within the natural environments thereby reducing the level of preservation. This indirect effect outweighs the direct effect of the rate of discount on the level of preservation if the elasticity of output with respect to capital is greater that the elasticity of output with respect to the resource input. In general, the asymptotic values of the output elasticities depend upon the rate of discount and so there can be a nonmonotonic relationship between the rate of discount and the optimal level of permanently preserved natural environments.     

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

It is shown that, depending upon the orientation of the end tangents t₀,t₁ relative to the end point displacement vector p=p₁–p₀, the problem of G¹ Hermite interpolation by PH cubic segments may admit zero, one, or two distinct solutions. For cases where two interpolants exist, the bending energy may be used to select among them. In cases where no solution exists, we determine the minimal adjustment of one end tangent that permits a spatial PH cubic Hermite interpolant. The problem of assigning tangents to a sequence of points p₀,...,p_n in R³, compatible with a G¹ piecewise-PH-cubic spline interpolating those points, is also briefly addressed. The performance of these methods, in terms of overall smoothness and shape-preservation properties of the resulting curves, is illustrated by a selection of computed examples.     

AHP中增加一组元素的严格保序性条件

给出了左主特征向量法（LEM）下增加一组元素严格保序的充要条件,通过研究在右主特征向量法（REM）,左主特征向量法（LEM）,几何平均特征向量法（GMEM）下增加一组元素严格保序的条件之间的关系,从而给出GMEM下增加一组元素严格保序的充分条件。     

The preservation of Sahlqvist equations in completions of Boolean algebras with operators

Monk [1970] extended the notion of the completion of a Boolean algebra to Boolean algebras with operators. Under the assumption that the operators of such an algebra are completely additive, he showed that the completion of always exists and is unique up to isomorphisms over . Moreover, strictly positive equations are preserved under completions a strictly positive equation that holds in must hold in the completion of . In this paper we extend Monk’s preservation theorem by proving that certain kinds of Sahlqvist equations (as well as some other types of equations and implications) are preserved under completions. An example is given that shows that arbitrary Sahlqvist equations need not be preserved. Received May 3, 1998; accepted in final form October 7, 1998.