A posteriori error analysis for nonconforming approximations of an anisotropic elliptic problem

We develop in this article an a posteriori error estimator for the P₁‐nonconforming finite element approximation, for a diffusion‐reaction equation. We adopt the error in a constitutive law approach in two and three dimensional space, for not necessary piecewise constant data of problems. The efficiency and the reliability of our estimators are proved, neither Helmholtz decomposition of the error nor saturation assumption. The constants are explicitly given, which prove the robustness of these estimators. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 950–976, 2015     

Positive numerical splitting method for the Hull and White 2D Black–Scholes equation

We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015     

复微分方程组的代数解

本文研究了一类复微分方程组的代数解的存在问题.利用最大模原理和Nevanlinna值分布理论,得到了一个结论,推广和改进了一些文献的结果,例子表明结论精确.     

Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.     

Surface tensor estimation from linear sections

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n‐dimensional Euclidean space. The estimators are based on one‐dimensional linear sections. In a design based setting we suggest three types of estimators. These are based on isotropic uniform random lines, vertical sections, and non‐isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting.     

相机位姿估计的加速正交迭代算法

面对需要实时计算的相机位姿估计问题,针对经典的广泛应用的正交迭代算法,提出了一种加速正交迭代算法。其关键思想是将每一次迭代过程规整化,从而提炼出每一次迭代的重复计算,若将此重复计算在迭代开始前提前计算,则可以大幅度的减少迭代过程中的计算量,使得每一次迭代的计算复杂度从O(n)降低为O(1)。因此,可以在更短的时间内迭代更多的次数,从而获得更高的精度。进行了对比实验,结果显示本加速算法计算精度更高,速度更快。并通过实验提出了选择稳健n点透视(RPn P)计算初值,再使用加速正交迭代算法进行迭代运算的方法,在控制点不多的情况下,是一种精度接近最大似然估计,计算速度最快的算法。     

Al_2O_3薄层修饰SiN_x绝缘层的IGZO-TFTs器件的性能研究

采用原子层沉积工艺(ALD)生长均匀致密的三氧化二铝(Al2O3)薄层对氮化硅(Si Nx)绝缘层进行修饰,研究了铟镓锌氧薄膜晶体管(IGZO-TFTs)器件的性能。当Al2O3修饰层厚度为4 nm时,绝缘层-有源层界面的最大缺陷态密度相比于未修饰器件降低了17.2%,器件性能得到显著改善。场效应迁移率由1.19 cm2/(V·s)提高到7.11 cm2/(V·s),阈值电压由39.70 V降低到25.37 V,1 h正向偏压应力下的阈值电压漂移量由2.19 V减小到1.41 V。     

Numerical study on magneto-convection of cold water in an open cavity with variable fluid properties

The aim of the present study is to understand the problem of buoyancy and thermocapillary induced convection of cold water near its density maximum in an open cavity with temperature dependent properties in the presence of uniform external magnetic field. The governing equations are solved by the finite volume method. The results are discussed for various values of reference temperature parameter, density inversion parameter, Rayleigh, Hartmann and Marangoni numbers. It is observed that the temperature of maximum density leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. Convection heat transfer is enhanced by thermocapillary force when buoyancy force is weakened.     

Discrete maximum principles for FE solutions of nonstationary diffusion‐reaction problems with mixed boundary conditions

In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion‐reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

OPTIMAL HARVEST FEEDBACK RULE ACCOUNTING FOR THE FISHING‐UP EFFECT AND SIZE‐DEPENDENT PRICING

Abstract Fishing leads to truncation of a population's age and size structure. However, large‐sized fish are usually more valuable per unit weight than small ones. Nevertheless, these size‐related factors have mostly been ignored in bioeconomic modeling. Here, we present a simple extension to the Gordon–Schaefer model that accounts for variations in mean individual catch weight, and derive the feedback rule for optimal harvest in this setting. As the Gordon–Schaefer model has no population structure, size effects have to be accounted for indirectly. Here we assume a simple negative relationship between fishing effort and mean individual weight, and a positive relationship between mean catch weight and price. The aim is to emulate alterations of size structure in fish populations due to fishing and the influence of size on price per weight unit and eventually, net revenues. This demonstrates, on a general level, how such size‐dependent effects change the patterns of optimal harvest paths and sustainable revenue in single fish stocks. The model shows clear shifts toward lower levels of optimal effort and yield compared to classical models without size effects. This suggests that ignoring body size could lead to misleading assumptions and policies, potentially causing rent dissipation and suboptimal utilization of renewable resources.