线性的

In the final part of this paper,the experiments show that this algorithm has good results for normal linear systems and ill-conditioned ones.

文末算例实验表明，本文算法对于良态线性系统、病态线性系统均有较好的求解效果。

After linearization of various geophysical inverse problems, all kinds of inversion algorithms are reduced to solve ill-conditioned linear systems.

地球物理反问题线性化处理之后，各种反演算法归结为对病态线性方程组的求解。

A new reduced-order robust filtering method for linear system is derived based on linear matrix inequation methods.

作为大系统鲁棒滤波研究，本文利用线性矩阵不等式得到了一个新的线性系统降阶鲁棒滤波算法。

We make use of a normal element and circular permutations to construct polynomials over the intermediate extension field between F_q and F_ denoted by F_ where s divides t. The polynomials we constructed are F_q-linearly independent and return elements in F_q when they are evaluated at elements of the extension fields.

结合Reed-Solomon码的构造特点，我们将Chaoping Xing与San Ling所构造的线性码的方法推广到有限域的任意次扩张上，首先利用正规元和循环排列来构造系数属于F_q和F_q的任意次扩域F_之间的中间域的具有特殊性质的多项式，中间域记为F_，其中s为t的真因子，由正规元的选择可以保证所构造多项式的F_q-线性无关性，并且这些多项式在扩域F_中取值都属于F_q，从而构造出一类q元线性码。

Summary: The concept of matrix and its determinant computing, matrix determinant, matrix sub-block with the elementary transformation, invertible matrix, rank of matrix; vector and its computation, the linear relationship between vector, vector group of rank; linear equations of the nature and structure of linear equations; matrix eigenvalue and eigenvector, similar to matrix and matrix diagonalization conditions, the standard quadratic form with the normal forms, quadratic and symmetric matrix There are qualitative.

内容提要：行列式矩阵的概念及其运算，方阵的行列式，矩阵的分块与初等变换，可逆矩阵，矩阵的秩；向量及其运算，向量间的线性关系，向量组的秩；线性方程组的性质与结构，线性方程组的求解；矩阵的特征值与特征向量，相似矩阵与矩阵可对角化条件，二次型的标准形与规范形，二次型和对称阵的有定性。

Based on the generalized Fisher linear discriminant criterion, this problem is solved by combining projection transform, isomorphic mapping and compressed transform.

该文基于广义的Fisher线性判别准则，将投影变换、同构变换和压缩变换相结合，解决了这个问题，完善了小样本情况下线性鉴别分析理论。

Namely, the first, the beginning, end and length of growing season of every type of vegetation is estimated with threshold method and moving average method, and the beginning end and length of growing season of vegetation from 1982 to 1999 is fitted linearly, finally, linear trend of the beginning end and length of growing season of vegetation is analyzed. The second, phenological phase in different years and zones is estimated based on greatest changes of slope method and EOF analysis method, and the result monitored by the two methods is compared, as a result, trend of growing season change from 1982 to 1999 in different latitude zones is better acquired. The third, phenological phase of vegetation in different spatial location from 1982 to 1999 is fitted based on curve. Then, spatial difference rules of growing season of every year and average of multi-year is discussed in article. In the end, lag correlation and linear regress are used to study relation between phenological phase of different types of vegetation, different latitude zones, different spatial places and climate changes.

利用阈值法和滑动平均法逐年估测了每种植被类型的生长季的开始、结束日期及长度；对18年中植被生长季的开始、结束时间和长度进行一次线性拟合，分析了植被生长季的开始、结束日期和长度的线性变化趋势；基于最大变化斜率法和EOF分析法估计了不同年份、不同区域内植被生长季的开始、结束时间及其长度，并对这两种方法的监测结果作了比较，从而得到了较好的不同纬度区域1982～1999年植被生长季的变化趋势；基于曲线拟合了1982～1999年的不同空间位置的植被物候期，然后讨论了每年和多年平均的植被生长季的空间分异规律；最后利用时滞相关分析和线性回归研究了不同类型植被的物候期与气候变化的相互关系，不同纬度带的植被物候期与气候变化的相互关系，植被物候期与气候变化空间相互关系。

In this paper,we give the error expressions of piecewise linear Lagrange polynomial interpolation and piecewise cubic polynomial interpolation using the Taylor expansions.

中文摘要：本文利用Taylor展开得到三角形上线性Lagrange插值和三次Lagrange插值的导数余项公式，对这些余项公式进行分析，给出了两类能以四阶精度逼近被插函数在对称点的导数值的格式，一种是在均匀剖分时其分片线性插值的相邻单元的导数值的后处理格式，一种是在六片强正规剖分时的三次插值在对称点上的导数值的后处理格式，使得在已知原函数在各节点的值后，通过一个简单的线性计算就可得到原函数在对称点的导数的一个超逼近值，将以往提出的平均导数的二阶精度提高到四阶。

The main topics are: set theory foundation, Lebesgue measure and Lebesgue integral, basic theories on linear normed spaces and Hilbert spaces and introduction to linear bounded operators.

本课程基本内容包括集合论基础、Lebesgue测度与Lebesgue积分、线性赋范空间与Albert空间的基本理论和有界线性算子简介。

The result indicates that the output power oscillates and weakens along with increasing input power,and its oscillation period depends on the distance between the medium and beam focal point.Limiter′s limiting ability will decrease if waist size of the incident Gaussian beam and the aperture size increase.With a fixed input power scope,medium′s best limiting position will move towards the focal point if waist size of Gaussian beam and the aperture size increase,but the best limiting position will change a lot with different input power scopes.

结果表明：限幅器的出射功率随入射功率的增加衰减振荡，其振荡周期取决于介质相对于光束焦点的位置；限幅器的限幅能力随入射光束腰半径和光阑孔径的变大而减弱；入射功率范围固定，入射光束腰半径和光阑孔径增大时，介质的最佳限幅位置向入射光束的焦点靠近，但是在某些入射功率范围内会存在多个最佳限幅位置；光限幅器的箝位输出功率随光阑线性透过率的增加存在线性增加和非线性增加两个不同区域，实际应用中应在线性增加区域确定光阑孔径的大小。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。