线性

For the characteristic of the ring permanent magnet torque motor used in direct drive numerical control round table suffering from the effect of load disturbances and parameters variations, a multi-objective mixed H2/H∞ static output feedback controller, which makes all poles of the closed-loop system be located within a prescribed linear matrix inequality region D to achieve pole placement, is designed based on LMI.

针对直接驱动数控转台用环形永磁力矩电机易受负载扰动及自身参数变化影响的特点，文中基于线性矩阵不等式(linear matrix inequality， LMI)，设计了一个多目标混合H2/H￥静态输出反馈控制器，该控制器可使闭环系统的极点均落在预先选定的线性矩阵不等式区域D内来实现极点配置。

On the base of analysis of one dimensional linear interpolation method, two dimensional linear interpolation method in oblique angled rectilinear coordinate system is obtained.

在分析一维线性插值的基础上，得到了任意斜角直线坐标系下二维线性插值的一般计算公式以及有唯一解的条件，并将其应用于平面温度场的计算。

The computational complexity of the algorithm is polynomial growing with the sample size and the solution is the maximal margin one in the high dimensional space.

其主要的内容是：当问题是线性可分时，给出一个求解最大间隔解的方法以及当问题不是线性可分时，提出利用一核函数将样本集映

To develop the missile quasi-linear model, a state space model is established for missile dynamics, and function substitution method is used to describe the nonlinear dynamics of missile as linear combinations of functions of given time-varying parameters. With the minimizing variation range of model parameters over the whole design envelope as the optimum aim, linear programming optimum arithmetic is used to determine the model parameters at selected grid points.

为了建立导弹准线性化模型，将导弹动力学描述为状态空间形式；采用函数替换方法将导弹的非线性动力学描述为关于特定时变参数的函数的线性组合形式；以整个设计区间内模型参数变化范围最小为优化目标，采用线性规划优化算法确定了所选网格点上的模型参数。

Especially for multifrequence problems, both the order for the approximation of nonlinear functions and the iterative numbers for neural network learning will be decreased by several times.

利用这种新方法可以直接分析、辨识线性系统、双线性系统的稳定性和未知参数，并可直接求取性能指标下的最优控制律。

As to nonparametric and semiparametric regression models, the most widely used regression methods include, spline method(such as smoothing spline, penalized spline and so on); local smoothness, such as Nadaraya-Watson kernel estimate, Gasser-Muller estimate, local polynomial method; the third is orthogonal series, including Fourier series and so on.

所以三次光滑样条应用比较广泛。本文应用三次光滑样条方法来估计单指标部分线性模型中单指标参数和变系数部分线性模型中的函数系数。

This paper presents an improved method that uses the orthogonal least square algorithm to estimate both the structure and the parameters in the linear models from linearizing locally the whole nonlinear space.

本文在对非线性空间进行局部线性化的基础上，采用正交最小二乘方法对线性模型同时进行结构选择与参数辨识，改善了数值的病态特性，增强了算法的稳定性。

First, we give the relation of Birkhoff orthogonality and functionals in Banach space, then use functionals as a tool to investigate the relations of Birkhoff orthogonality and underling Banach space.

首先，建立了Banach空间中两个元素的Birkhoff正交性和线性泛函的关系，然后以线性泛函为主要工具，讨论了Birkhoff正交性和Banach空间结构的关系。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

Therefore, it is necessary to study these parallel problems. For the linear register systems, this paper presents a (1, N) parallel method with uniform calculating formulas by using the method of matrix equations, and studies to simplify XOR circuits. Comparing with the existing parallel methods for linear shift registers, this method for linear register systems doesn't need to expand the transition matrix, and has the same calculations for arbitrary N, which reduces the complexity.

对一般的线性寄存器系统，本文应用向量矩阵方程的研究方法提出了一种通用的、具有统一计算公式的(1， N)并行方法，研究了其中异或电路的化简，相对于已有的线性移位寄存器的并行方法而言，本文提出的方法不需要扩展矩阵，对任意的N计算公式均是统一的形式，减少了问题复杂性，具有更广泛的应用范围。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。