线性

Then we found bijections between quadratic form finite automata and input memory linear automata which lead to a way to produce all weakly invertible or weak inverse quadratic form finite automata. In the last section of chapter three, we extend these results to a more general class of nonlinear finite automata (called qusi-quadratic form finite automata).

然后我们建立了建立全体二次型有限自动机与全体输入存储线性有限自动机之间的的一个一一对应L，由于L保持弱逆性（3.20定理），由此我们得到了产生全体可逆二次型有限自动机的方法：要产生一个具有某种可逆性的二次型有限自动机只需产生一个具有同种可逆性的输入存储线性有限自动机，然后作其二次型提升即可。

Presents the design of longitudinal control for ASTOVL lift-fan aircraft, a multi-variable, strong-coupling, complicated nonlinear system to make the system nonlinear offset and decouple, and the method used for linear system in designing the system to gain expectant flying qualities and the combination of aerodynamic control surfaces with thrust vectors to delay the control surfaces getting into saturation, and the minimum N-norm generalized inverse theorem of weighted generalized inverse adopted to apportion the moments commands, which make the control surfaces gain appropriate deflection and the simulation results to verify the dynamic inverse control laws designed really make the system nonlinear offset and decouple; when one command is given, only this output will response, and others do not response; when all commands are given together, the responses will be just the linear superpose of the response of each command, therefore the operation of the pilot will be simplified greatly.

摘 要： ASTOVL升力风扇飞机是多变量、强耦合、复杂的非线性系统，采用非线性动态逆理论设计控制律以实现系统的非线性对消及解耦，然后，采用线性系统的设计方法对系统进行设计，以使系统获得期望的飞行品质。同时，考虑到ASTOVL升力风扇飞机是由气动舵面和推力矢量融合作用的，为了延缓各舵面进入饱和的时间，采用加权广义逆中的极小N-范数广义逆定理分配力矩指令，从而使各舵面达到适当的偏转角。并将所设计的控制律进行了仿真，结果验证了所设计的动态逆控制律使系统实现了非线性对消和解耦，单个指令作用时，只有该项响应，其余不受影响；所有指令作用时，其结果就等于单个指令作用时的线性叠加，这样使驾驶员的操纵大大简化而易于控制，从而大大降低了飞行事故率。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

The main characteristic of this kind of quadratic forms is their orthogonality depends on the linear dependency of the elements which produce them (2. 17 theorem), and this is the very reason we can establish the invertibility theory over quadratic finite automata by R〓R〓 transformation methods.

这类二次型的主要特点是它们的正交性由它们的生成元的线性相关性决定（2.17定理），这是可以用线性R〓R〓变换方法建立二次型有限自动机弱逆性理论的根本原因。

This paper studies the properities of weakly invertible Linear finite automata through zero state,and obtains some results of weakly invertibility of Linear finite automata and description of the minimal linear finite sub-automata.

通过零状态研究了线性有限自动机的一些性质，得到了线性有限自动机弱可逆的一些结果，并给出了最小线性子有限自动机的描述，最后给出了算法实现。

The diffusion structure has important impact on the rate of the diffusion and safety intensity for block cipher.Using the linear transform which has branch numbers as large as possible as the diffusion structure is a main method to devise block cipher.The linear transform is usually achieved by constructing the invertible matrix.

扩散结构的好坏直接影响了分组密码的扩散速度和安全强度，以分支数尽可能大的线性变换为分组密码算法的扩散结构是设计分组密码的一种重要方法，线性变换的构造可通过可逆矩阵的构造完成。

Eliminating the restriction of the characteristic of field ,the forms of invertible linear operator preserving inverses of matrices over full matrix space with at least four elements are described.

去掉了域的特征限制，刻画了至少包含4个元素的任意域 F上的全矩阵空间Mn的保逆的可逆线性算子形式。利用保幂等的结论证明了f为Mn上保持逆矩阵的可逆线性算子当且仅当存在P∈GLn，使得f=εPAP-1，A∈Mn，ε=±1∈F；或者存在P∈GLn，使得f=εPATP-1，A∈Mn，ε=±1∈F

As a DC/DC basic structure is adopted, the operational amplifier leads the non inverting input end voltage of the error amplifier to follow the input voltage linearly, thus realizing the linear following relation between the output voltage and the input voltage.

由于采用DC/DC的基础结构，增加运算放大器使误差放大器的同相输入端电压与输入电压线性跟随，从而实现输出电压与输入电压的线性跟随关系。

With increasing loading, the reduction degrees of average correlative coefficients of linear fitting functions of isochronous stress axial strain curve and isochronous stress-radial strain curve are 0.97% and 0.67% respectively, which indicates the linear correlation decreases commonly.

随加载应力水平的提高，应力－轴向应变等时曲线和应力－径向应变等时曲线线性拟合函数的平均相关系数下降幅度分别为0.97%和0.67%，线性相关性普遍降低。

The average correlative coefficients of linear regression function for isochronous stress- axial strain curve are 3.92% higher than that of average correlative coefficients of linear regression function for isochronous stress- radial strain curve, so nonlinear creep property of the fine sandstone specimen in axial direction is correspondingly weaker than that in radial direction.

应力－轴向应变等时曲线线性回归函数的平均相关系数高出应力－径向应变等时曲线线性回归函数的平均相关系数3.92%，因此其轴向非线性蠕变特性相对于径向非线性蠕变特性更弱。

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％。