The Best Lower Bound for the Permanent of a Correlation Matrix of Rank Two

If 1≤k≤n, then Cor(n,k) denotes the set of all n×n real correlation matrices of rank not exceeding k. Grone and Pierce have shown that if A∈Cor (n, n-1), then per(A)≥n/(n-1). We show that if A∈Cor(n,2), then , and that this inequality is the best possible.     

LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS

In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method （L-BFGS） with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.     

Conceptions of function translation: obstacles, intuitions, and rerouting

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of the parabola y=(x−3)² and its relationship to y=x². The participants’ explanations focused on attending to patterns, locating the zero of the function, and the point-wise calculation of function values. The results confirm that the horizontal shift of the parabola is, at least initially, inconsistent with expectations and counterintuitive to most participants. We articulate possible sources of this perceived inconsistency and describe a pedagogical approach aimed at resolving it.     

Existence of positive solutions of nonlinear fractional differential equations

Existence of positive solutions for the nonlinear fractional differential equation D^su(x)=f(x,u(x)), 0<s<1, has been studied (S. Zhang, J. Math. Anal. Appl. 252 (2000) 804-812), where D^s denotes Riemann-Liouville fractional derivative. In the present work we study existence of positive solutions in case of the nonlinear fractional differential equation:

L(D)u=f(x,u),u(0)=0,0<x<1,     

Global linear convergence of a path-following algorithm for some monotone variational inequality problems

We consider a primal-scaling path-following algorithm for solving a certain class of monotone variational inequality problems. Included in this class are the convex separable programs considered by Monteiro and Adler and the monotone linear complementarity problem. This algorithm can start from any interior solution and attain a global linear rate of convergence with a convergence ratio of 1 ?c/√m, wherem denotes the dimension of the problem andc is a certain constant. One can also introduce a line search strategy to accelerate the convergence of this algorithm.     

带时滞观测线性离散系统的递推滤波

本文讨论带时滞观测线性离散系统的滤波问题,提出利用联合分布函数,得到滤波递推格式.这种方法还适用于一般的带有状态时滞的线性离散系统.     

A unified theory for coherent systems in reliability part III: Two special cases for multinary systems—binary-type coherence and homogeneous coherence

As shown in a companion-paper,¹ binary and multinary coherent systems can be studied with unified arguments, through monotone binary coherent systems. These are binary coherent systems submitted to some monotone constraint and generalize the classic theory of free binary coherent systems. By considering the unified point of view thus obtained, this paper gives what is perhaps the most suggestive representation for multinary coherent systems, since this extends the definition of binary coherent systems in terms of series-parallel (parallel-series) structures. Then, this paper examines the special case of multinary systems that can be studied directly with the classic theory of free binary coherent systems. It thus enlarges and complements, in a shorter unified manner, the particular cases considered in earlier studies.     

Condensations of projective sets onto compacta

For a coanalytic-complete or -complete subspace of a Polish space we prove that there exists a continuous bijection of onto the Hilbert cube . This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen.

Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.

     

平面ISODYNE法及其在复合材料力学中的应用

由J. T. Pindera提出的平面isodyne法是散光法的一种发展。具有非破坏性直接测取受力物体内部应力的特点。不需要大功率的激光器,条纹清晰,无畸变,对于平面应力问题可以得到应力分量的全部信息。在复合材料力学、断裂力学和接触问题等领域有广泛的应用前景。文章闸述了该方法的原理和技术,并应用它得到一受三点弯曲荷载的有裂纹的复合材料梁粘结层的应力分布。     

The MPE/UCB far-infrared imaging Fabry-Perot interferometer (FIFI)

FIFI is an imaging spectrometer with two or three Fabry-Perot interferometers (FPI) in series for airborne astronomical observations in the far-infrared range (=40...200m). It employs 5×5 arrays of photoconducting detectors and offers spectral resolutions as small as 2km/s. Resolution and bandwidth can be set over a wide range to match a variety of astronomical sources. Cryogenic optics minimizes thermal background radiation and provides for in-flight step tunable spatial resolution. At 158 m wavelength the background-limited NEP is 3 × 10^-15W/Hz at 40 km/s resolution and with two FPI's; with three FPI's the expected NEP is 10^-15WHz at 5 km/s resolution.The frequency-chopping mode of the high-resolution Fabry-Perot allows for line detection in extended objects. Absolute internal flux calibration ensures adequate flat fielding of the array elements.