查询词典 piecewise linear function

Special solutions for the ring circular domain with crack surfaces acted on uniform compressive force, linear compressive force and linear shearing force are deduced in polar coordinate employed the eigenfunction expansion technique in the Hamiltonian system of elastic mechanics. Combined with the general solution for the above problems, the analytical solutions for crack tip fields with surfaces acted on the above three kinds of loads are obtained. These solutions offer theoretical basis to construct analytical elements for plastic analysis of crack.

从弹性力学哈密顿体系理论出发，利用平面弹性力学极坐标系下的本征向量展开求解，推导了环形圆形域裂纹边作用有均布压力、线性压力和均布剪切力情况下的特解，从而得到了裂纹表面作用有以上三种荷载情况下的裂纹尖端场的解析解，为进一步构造进行弹塑性裂纹分析的奇异解析元奠定了理论基础。

In addition, the voltage-current characteristic of linear resistive components is the general solution of Clairaut equation, and the voltage-current characteristic of non- linear components is the singular solution of Clairaut equation.

论文摘要：本文讨论了任意伏安特性电阻元件满足的基本微分方程以及非线性电路的功率匹配问题的几个定理，指出任意伏安特性电阻元件均满足非线性一阶的clairaut方程，并且，线性电阻元件的伏安特性是clairaut 方程通解，而非线性电阻元件的伏安特性是clairaut 方程的奇解。

The result indicated that 237 combinations amplified a total of 13 079 AFLP fragments with an average of 55 fragments, the average of 1.30 markers per 1 000 AFLP fragments were found to be linked to clubroot resistant gene; the amplified polymorphic fragments were 3 167 between the two parents, account for 24 percent of polymorphic frequency; the number of amplified fragments and the number of polymorphic fragments was in positive linear correlation; GC content of AFLP primer combinations significantly affects the number of amplified fragments and the number of polymorphic fragments, indicating negative linear correlation between them.

结果表明：平均每个组合检测到55条带，共扩增13079条带，平均每1000条带检测到1.30个根肿病抗性基因连锁标记；多态性带数为3167条，双亲间多态性频率约为0.24；扩增带数与多态性带数呈线性正相关，引物组合中的不同GC含量与扩增带数和多态性带数存在显著性差异，并表现出线性负相关。

This paper researches linear maps preserving orthogonality,obtains the linear maps preserving othrogonality,it is either a rank -declining or rank -keeping map or a map with nilpotent element in its codomain.

利用分块成向量的方法证明了MnMn(F为域F上所有n×n矩阵构成的乘法半群上的n×n拟正交矩阵组至多含有n个矩阵，利用方程组的解的理论证明了Mn中与给定矩阵A构成两两拟正交矩阵组的矩阵个数不超过n-Rank+1，从而得到Mn上保持拟正交性的线性映射φ要么是降秩的或者保秩的映射，要么φ的值域中含有幂零元。

If for every k-list assignment L, there exists a linear edge L-coloring, then G is called linear k-list colorable.

图G的列表线性荫度是使得G是线性边k-列表可着色的最小正整数，记为lla。

Fast algorithm of minimal norm least square solution for Cauchy linear system;2. For the m×n Cauchy-type matrix with full column rank,the fast algorithm of the minimal norm least square solution to the linear system Cx=b was obtained by construction of a special block matrix and study of the triangular decomposition.

对于秩为n的m×n阶Cauchy型矩阵C，通过构造特殊分块矩阵并研究其三角分解，进而得到了线性方程组C x=b的极小范数最小二乘解的快速算法，所需运算量为O+O(n2)，而通常构造法方程组的方法所需运算量为O(m n2)+O(n3)，用正交化法虽然避免了构造法方程组，但所需的运算量更大些。

The definitions of intrinsical linear nonholonomic constrain and intrinsical nonlinear nonholonomic constrain are put forward in this paper. The nonholonomic systems are divided into intrinsical linear nonholonomic system and intrinsical nonlinear nonholonomic system.The rational spectrums of all kinds of virtual displacement definitions and commutativity of d,?

本文研究了非完整动力学中使不定性问题确定化的交换关系和将非线性问题线性化的虚位移定义，首次证明并给出了在非完系统中各种虚位移定义与交换关系的合理适用范围，指出完整动力学与本质线性非完整动力学在研究方法上具有相同性。

In order to eliminate the influence caused by the nonminimum phase characteristic of a common Boost DC／DC converter, Viswanathan K has proposed a novel tristate Boost DC／DC converter. For enhancing performance, the statespace averaging model of this converter was first presented in this paper. Due to the nonlinear nature in this model, an inputoutput feedback linearization technique was adopted, and a complete controllable linear system was obtained. Then a statefeedback control strategy was designed based on this linear system. Simulation results show that the proposed control strategy can assure constant output voltage in a wide range, so as to realize the stability of the system during large fluctuation of power supply and load disturbance. Good dynamic performance can also be achieved.

针对 Viswanathan K为消除普通BOOST DC／DC变换器的非最小相位特性而提出的三态Boost DC／DC变换器，为进一步提高这种电路拓扑的性能，在建立了变换器状态空间平均模型的基础上，针对其多变量、非线性特点，采用输入输出线性化将其转化为一个完全可控的线性系统，在此基础上应用现有成熟的线性控制策略进行了控制系统的设计，并且采用MATLAB进行仿真验证，结果表明：这种非线性控制策略可以确保输出电压在大范围内恒定可调，且即使存在大范围扰动(输入电压和负载变化均较大)的情况下，系统也可以确保稳定性和良好的动态性能。

The linear manifold-learning algorithms represented by PCA, with their substantial mathematical foundation and simple implementation, but they are not able to show complex nonlinear manifold structure with their linear essence, which gives rise to nonlinear manifold-learning algorithms such as Isomap, SIE etc.

以PCA为代表的线性流形学习算法有较强的数学基础，实现简单，但是其线性本质并不能揭示复杂的非线性流形结构；于是又出现了以Isomap、SIE等为代表的非线性流形学习算法。

Thereby, these facts indicate that the SDE not only have better statistic properties but also have uniformly smaller mean square errors than ANOVAE in an available group of linear mixed models. The other significative following work is to generalize the idea of SDE to multivariate linear mixed model and obtain the SDE of variance component matrices which uniformly dominate the ANOVAE either.

对于含有一个随机效应的混合模型，目前文献中都仅讨论了方差分量的谱分解估计和ANOVA估计等价的充要条件，本文首次给出了方差分量的谱分解估计在均方误差意义下严格的优于ANOVA估计的理论结果，并推广到广义谱分解估计，从而说明谱分解估计不仅较ANOVA估计有更好的统计性质，而且在一类常用的模型下有更小的风险损失。

What was it that made you want to change sider ?

是什么使你临阵倒戈？

I don't know what he wants, but let's play along with him.

我不知道他要干什么，可我