一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。     

A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.     

GaN发光二极管表观电容极值分析

利用正向交流(ac)小信号方法对GaN发光二极管的电容-电压特性进行测量,可以观察到GaN发光二极管中的负电容现象。正向偏压越大,测试频率越低,负电容现象越明显。测量到的负电容现象是表象,不存在负电容;提出GaN发光二极管p-n结的结电容在特定的正向电压范围内等效于可变电容。分析可变电容对正向交流小信号响应得到:特定参数的可变电容使结电容电流相位落后于交流小信号电压相位π/2,使得在测量中表现为负电容。发现表观电容-正向电压曲线的极值点与理论模型相吻合,证明了该理论模型的正确性。     

Representation of the space of polyanalytic functions as a direct sum of orthogonal subspaces. Application to rational approximations

Suppose thatD={z:|z|<1}, L ₂ (D) is the space of functions square-integrable over area inD,A _k (D) is the set of allk-analytic functions inD, (A ₁ (D)=A(D) is the set of all analytic functions inD),A _k L ₂ (D)=L ₂ (D)∩A _k (D),A ₁ L ₂ (D)=AL ₂ (D),

求条件极值的一种新方法

利用线性代数的理论方法，对多元函数求条件极值的拉格朗日乘数法加以改进，建立了求条件极值的一种新方法     

含边界在内的一般极值的必要条件与拉格朗日乘数法

讨论包括定义域边界点在内的极值,称为一般极值.对可导的一元和多元函数给出了一般极值点的必要条件,这些必要条件与经典极值的必要条件是相容的.还利用一般极值的必要条件导出了条件极值的拉格朗日乘数法.     

矩形通道内层流对流换热的最优速度场

针对矩形通道内的层流对流换热问题,通过数值求解速度场协同方程,得到了给定黏性耗散条件下通道内的最优速度场为多纵向涡的流动结构,表明多纵向涡流型可在流阻增加不多的情况下使换热显著强化.通过在通道壁面布置不连续双斜肋,在通道内产生了接近于最优速度场的多纵向涡流动,数值计算结果表明,在Re=1000时,与光滑通道相比,不连续...     

Dual extremum principles for geometrically exact finite strain beams

Both necessary and sufficient conditions for the existence of two complementary-dual extremum principles for geometrically exact finite strain (one-dimensional) beam models are investigated by means of two different approaches. One is based on the results published by Gao and Strang, and the other relies on the approach proposed by Noble and Sewell. While the former is limited to beam models restricted to moderate large deformations, the latter is valid for arbitrarily large deformations (and strains). The numerical implementation of the complementary-dual extremum principles can lead to simple true global upper bounds of the error of the approximate solutions.     

Lee极值原理与结构的大挠度塑性动力响应

本文介绍了利用Lee 极值原理确定结构的大挠度塑性动力响应的数值方法,给出了在均布冲击载荷作用下的理想刚塑性门形框架的大挠度进化模态解,指出如果模态形式取得合适,可使进化模态解接近于真实解.这样得到的门形框架的大挠度模态解与文献[8]中的实验结果和文献[9]中的大挠度完全解都符合得很好.     

Extremum of second-order directional derivatives

In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.