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In view of urban water consumption's being affected by many factors and its systemic stability and non-linear characteristic,a non-linear time series forecasting method is studied in this paper based on neural network,and it was used to predict the water consumption for Zhengzhou city to verify its accuracy and rationality.

考虑城市用水量受众多因素影响，具有系统稳定性和非线性的特点，探讨了基于神经网络的城市用水量预测的非线性时间序列递推预测方法，并利用该方法对郑州市城市用水量进行了时间序列模拟，实例证明了该方法的正确性和科学性。

Leaf blades linear to linear-lanceolate; ligule a ciliate membrane.

叶片线形到线状披针形；叶舌一层纤毛的膜。

Computer graphics simple linear and circular painting of a simple realization of the two paintings linear method, a method Circle.

计算机图形学的简单的画直线和圆的简单实现，两种画直线的方法，一种画圆的方法。

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。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。