Randomly generating portfolio-selection covariance matrices with specified distributional characteristics

In portfolio selection, there is often the need for procedures to generate “realistic” covariance matrices for security returns, for example to test and benchmark optimization algorithms. For application in portfolio optimization, such a procedure should allow the entries in the matrices to have distributional characteristics which we would consider “realistic” for security returns. Deriving motivation from the fact that a covariance matrix can be viewed as stemming from a matrix of factor loadings, a procedure is developed for the random generation of covariance matrices (a) whose off-diagonal (covariance) entries possess a pre-specified expected value and standard deviation and (b) whose main diagonal (variance) entries possess a likely different pre-specified expected value and standard deviation. The paper concludes with a discussion about the futility one would likely encounter if one simply tried to invent a valid covariance matrix in the absence of a procedure such as in this paper.     

脉冲时滞微分方程的周期性和稳定性研究

利用Gaines和Mawhin的重合度理论,给出了一个周期环境下具有分布时滞的脉冲微分方程的正周期解的存在性的判定。与此同时,通过引入分片连续Lyapunov函数的方法,建立了脉冲效应下时滞微分方程的零解稳定性的充分条件。     

Two-dimensional computational simulation of eccentric annular cementing displacements

We consider a two-dimensional Hele–Shaw type model fordisplacement flows occurring in the primary cementing of anoil well. The fluids are visco-plastic and may get stuck inthe annulus if a critical pressure gradient is not exceeded.The model consists of solving a nonlinear elliptic variationalinequality equation for the stream function, coupled to an equationfor interface advection, or alternatively a concentration equationfor the mass fraction of each fluid. The key difficulty is toaccurately compute yielded and unyielded zones of the wellborefluids, which we accomplish by use of an augmented Lagrangianmethod to solve the stream function equation. We validate theaccuracy of our method against analytical solutions for stablesteady-state displacements. We study the convergence of theinterface to the steady state, showing that the apparent meta-stabilityis illusory. We then explore the effects of increasing eccentricity,showing that although the interface may remain stable it becomesunsteady. Initially fully mobile flows are found, but as theeccentricity increases further the narrow side fluids fail tomove in the far field. The narrow side interface can progressslowly through the static fluids by a burrowing motion, butfor still larger eccentricities even the interface becomes staticand a narrow-side mud channel forms.     

部分相干离焦散斑照相的统计理论

运用散斑统计理论，探讨了部分相干离焦散斑照相的统计规律，指出了影响条纹质量的各种因素，并给出了实验验证。     

Positivity of certain sums over Jacobi kernel polynomials

We present a computer-assisted proof of positivity of sums over kernel polynomials for ultraspherical Jacobi polynomials.     

Blood flow dynamics and fluid–structure interaction in patient‐specific bifurcating cerebral aneurysms

Hemodynamics plays an important role in the progression and rupture of cerebral aneurysms. The current work describes the blood flow dynamics and fluid–structure interaction in seven patient‐specific models of bifurcating cerebral aneurysms located in the anterior and posterior circulation regions of the circle of Willis. The models were obtained from 3D rotational angiography image data, and blood flow dynamics and fluid–structure interaction were studied under physiologically representative waveform of inflow. The arterial wall was assumed to be elastic, isotropic and homogeneous. The flow was assumed to be laminar, non‐Newtonian and incompressible. In one case, the effects of different model suppositions and boundary conditions were reported in detail. The fully coupled fluid and structure models were solved with the finite elements package ADINA. The vortex structure, pressure, wall shear stress (WSS), effective stress and displacement of the aneurysm wall showed large variations, depending on the morphology of the artery, aneurysm size and position. The time‐averaged WSS, effective stress and displacement at the aneurysm fundus vary between 0.17 and 4.86 Pa, 4.35 and 170.2 kPa and 0.16 and 0.74 mm, respectively, for the seven patient‐specific models of bifurcating cerebral aneurysms. Copyright © 2008 John Wiley & Sons, Ltd.     

一类Hammerstein积分方程的正分歧点

本文考虑有序Banach空间中形如x(t)=∫_Gk(t,s)[λAx(s) f(s,x(s),λ)]ds的Hammerstein型积分方程,给出了此类方程存在正分歧点的某些充分条件。     

光栅位移激光多普勒遥测技术的研究

研究了利用运动光栅的多普勒效应进行切向位移的遥测技术。提出了测量光路，采用声光调制器作为分光和频移器件并用于鉴向，实现了５０ｍ的远距离光栅位移遥测。达到测量分辨率０．８μｍ，光栅位移４０ｍｍ，最大累积误差优于３４μｍ。并用理论分析和实验，证明了远距离目标的焦深及其计算方法，导出了计算公式。     

Uniqueness of positive solutions for quasilinear boundary value problems

Sufficient conditions for the uniqueness of positive solutions of boundary value problems for quasilinear differential equations of the type

(|u′|^m−2u′)′ + f(t,u,u′)=0, m 2

are established. These problems arise, for example, in the study of the m-Laplace equation in annular regions.