The analysis of a finite element method for the three-species Lotka–Volterra competition-diffusion with Dirichlet boundary conditions

A Galerkin finite element method is developed for the two dimensional/three dimensional nonlinear time-dependent three-species Lotka–Volterra competition-diffusion equations on a bounded domain. The existence and uniqueness of the solution to the numerical formulation are proved. An error estimate for the numerical solution is obtained. Numerical computations are carried out to examine the expected orders of accuracy in the error estimates.     

Variational formulation of the material failure process in solids by embedded discontinuities model

This work presents a variational formulation of the material failure process, idealized as strain or displacement discontinuities, by weak, strong, or discrete embedded discontinuities into a continuum. It is shown that the solution of the proposed variational formulation may be approximated by different types of finite elements with embedded discontinuities. The developed displacement approximation of a finite element split by the discontinuity leads to a symmetric stiffness matrix, which considers not only the continuity of tractions but also the rigid body relative motions of the portions in which the element is split. The variational formulation of a continuum with more than one discontinuity in its interior is developed. It is shown that this formulation may lead to finite elements with embedded discontinuities that can be classified as displacement, force, mixed, and hybrid models. To show the effectiveness of the proposed formulation, the classical example of a bar under tension is solved using one and 2D finite element approximations. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices

Using the variational method, it is shown that the set of all strong peak functions in a closed algebra A of Cb(K) is dense if and only if the set of all strong peak points is a norming subset of A. As a corollary we can induce the denseness of strong peak functions on other certain spaces. In case that a set of uniformly strongly exposed points of a Banach space X is a norming subset of , then the set of all strongly norm attaining elements in is dense. In particular, the set of all points at which the norm of is Fréchet differentiable is a dense Gδ subset. In the last part, using Reisner's graph-theoretic approach, we construct some strongly norm attaining polynomials on a CL-space with an absolute norm. Then we show that for a finite dimensional complex Banach space X with an absolute norm, its polynomial numerical indices are one if and only if X is isometric to . Moreover, we give a characterization of the set of all complex extreme points of the unit ball of a CL-space with an absolute norm.     

The early exercise region for Bermudan options on two underlyings

This paper investigates the early exercise region for Bermudan options on two underlying assets. We present a set of analytical validation results for the early exercise region which can be used as a means of validating pricing techniques. When all strike prices are identical we show the existence of an intersection point such that for any asset price pair below this point early exercise is always optimal. We develop an approximation to this point in the two asset put case. When the strike prices are not all equal, we show that three separate cases exist for the early exercise region. For a Bermudan put on two assets we present these cases and show that there exists a critical point in which the boundaries of the two asset early exercise region bifurcate. Comparisons are drawn between the Bermudan results presented and the corresponding American option results.     

MKdV方程的多辛Fourier拟谱方法

基于谱微分矩阵方法,给出MKdV方程的多辛Fourier拟谱格式及其相应多辛离散守恒律,证明了它等价于通常的Fourier拟谱格式．数值结果表明,格式对于长时间计算具有稳定性与高精度．     

Differentiability of Lipschitz Maps from Metric Measure Spaces to Banach Spaces with the Radon–Nikodym Property

We prove the differentiability of Lipschitz maps X → V, where X denotes a PI space, i.e. a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V denotes a Banach space with the Radon–Nikodym Property (RNP). As a consequence, we obtain a bi-Lipschitz nonembedding theorem for RNP targets. The differentiation theorem depends on a new specification of the differentiable structure for PI spaces involving directional derivatives in the direction of velocity vectors to rectifiable curves. We give two different proofs of this, the second of which relies on a new characterization of the minimal upper gradient. There are strong implications for the infinitesimal structure of PI spaces which will be discussed elsewhere.     

Testing diffusion processes for non-stationarity

Financial data are often assumed to be generated by diffusions. Using recent results of Fan et al. (J Am Stat Assoc, 102:618–631, 2007; J Financ Econometer, 5:321–357, 2007) and a multiple comparisons procedure created by Benjamini and Hochberg (J R Stat Soc Ser B, 59:289–300, 1995), we develop a test for non-stationarity of a one-dimensional diffusion based on the time inhomogeneity of the diffusion function. The procedure uses a single sample path of the diffusion and involves two estimators, one temporal and one spatial. We first apply the test to simulated data generated from a variety of one-dimensional diffusions. We then apply our test to interest rate data and real exchange rate data. The application to real exchange rate data is of particular interest, since a consequence of the law of one price (or the theory of purchasing power parity) is that real exchange rates should be stationary. With the exception of the GBP/USD real exchange rate, we find evidence that interest rates and real exchange rates are generally non-stationary. The software used to implement the estimation and testing procedure is available on demand and we describe its use in the paper.     

Bergman型空间的加权复合算子

Let g1,g2 be normal functions. For all 0 〈 p,q 〈 ∞, the necessary and sufficient conditions for weighted composition operators Tψ,φ ： A^Pg1 → A^Pg2 to be bounded or compact between Bergman type spaces on the unit ball of C^n are given.     

一种有机/金属肖特基二极管的实验研究

提出了一种简单有效的有机/金属肖特基二极管的制备方法:通过简单的真空气相沉积工艺,依次将有机材料PTCDA(C24H8O6)薄膜和金属电极Au蒸镀在透明导电玻璃ITO上.通过在室温条件下对该二极管的电流-电压(I-V)特性的测试发现,其整流系数可达104.根据标准肖特基理论以及实验所得电容-频率(C-f)和电容-电压(C-V)的测试结果,得到该有机肖特基势垒高度在0.2～0.3eV范围内.     

Continuous glucose detection using boronic acid-substituted viologens in fluorescent hydrogels: linker effects and extension to fiber optics

A fluorescent anionic dye and a viologen appended with boronic acids, which serve as glucose receptors, have been synthesized and immobilized into a poly(2-hydroxyethyl methacrylate) hydrogel for use as a continuous glucose monitor. The fluorescence of the dye is modulated by the quenching efficiency of the viologen-based receptor, which in turn is dependent on the glucose concentration. Two monomeric versions of the quencher/receptor unit were prepared and their performance within the hydrogel evaluated. By tethering the quencher/receptor to the hydrogel matrix using a single-point attachment, slightly improved glucose sensing was observed. The hydrogels were tested for their ability to continuously and reversibly detect glucose over the course of several hours. The tests were carried out using a cuvette-based system, as well as a fiber-optic-based configuration. Under physiological conditions (0.1 M phosphate buffer, pH 7.4, 37 degrees C), the fluorescent hydrogels display an excellent dynamic response to glucose concentrations within the biologically significant range (2.5-20 mM).