内积空间

College of Guandong Business, Guanzhou 510320, China）Abstract: Since large-scale vertical quench furnace is voluminous, whose working condition is a typically complex process with distributed parameter, nonlinear, multi-inputs/multi-outputs, close coupled variables, etc, dynamically decoupling control algorithm of temperature distributed parameter system in the furnace was presented, by which the whole system was decoupled to several subsystems and the implementation of controller was simplified. With finite difference approximation, the space and time step size was solved to ensure the convergency of finite difference approximation. After decoupling, the subsystems were controlled with self-learning PID control algorithm. The results show that the temperature control precision and homogeneity are improved; the overshoot and process in temperature rising period are reduced simultaneity.

摘 要：针对大型立式淬火炉体积庞大，工况复杂，炉内温度分布呈本征非均匀性，具有多输入/多输出、非线性、强耦合等特性，难以实现炉内温度高精度高均匀性控制目标等问题，提出一种温度分布参数系统动态解耦控制算法，其原理是：采用有限维逼近方法将对象解耦为多个独立的子系统，简化控制器的实现过程；通过分析有限维逼近方法的收敛性，获得保证收敛性的空间和时间步长应满足的条件；解耦后的子系统采用自学习PID控制算法，实现炉内温度高精度和高均匀性控制以及升温过程的快速性和小超调。

Asynchronous loading of control parameters · Rapid (25ns per pixel) rotation, warping, panning, and scaling of images · Three-dimensional image addressing capability · General third-order polynomial transformations in two dimensions on-chip · Three-dimensional transformation of up to order 1.5 also supported · Flexible, user-congurable pixel datapath timing structure · Static convolutional ltering of up to 16 x 16 Pixel, 256 x 256 pixel or 256 x 256 x 256 pixel windows · User-selectable source image subpixel resolution of 2-8 to 2-16 · Pin-compatible upgrade to TMC2302 · 24-bit (optional 36-bit) positioning precision within the source image space, 48-bit internal precision · Low power CMOS process · Available in a 120-pin Plastic Pin Grid Array and 120-lead Metric Quad Flat Pack

1第1页，本页显示记录1-11，共11条记录分1页显示·异步控制参数加载·快速（25ns的每个像素）旋转，弯曲，平移，缩放和图像·三维图像处理能力·一般二维三阶多项式变换片·三高达1.5三维变换命令也支持·灵活，用户可配置的数据通道的静态时序结构·高达16 × 16像素滤波卷积像素，256 × 256像素或256 × 256 × 256像素（3通）窗口·用户可选的源图像亚像素分辨率的2-8 2-16·引脚兼容的升级TMC2302·24位（可选36位）的定位源图像的空间内，48位内部高精度·低功耗CMOS精密加工·提供120引脚塑料针栅阵列和120引脚公制四方扁平封装

First ,it is proved that a positive Hermite form corresponds uniquely to a positive self2adjoint operator in a complete random inner product module ,then this result leads directly to the proof of the main result of...

值得指出的是：完备随机内积模上Friedrichs 定理的证明中所涉及的一系列基本概念与方法都是以随机共轭空间理论为出发点的，与经典情形完全不同。

If the knowledge was closely related the many disciplines or many branches of a discipline,then this knowledge is certainly important,but the quadratic form,european space inner product,Jensen inequality are basic content of algebra,real letters,calculus in higher mathematics.

如果某一知识跟很多学科或者一个学科的很多分支有着密切联系，那么这个知识肯定是很重要的，而二次型、欧式空间内积、詹森不等式都是高等数学中代数、实函、微积分的基本内容。

Reproducing kernel Hilbert space ; inner product ; orthonormal basis

再生核Hilbert空间；内积；正交基

Based on the analysis of conventional phase difference detection method,a new algorithm of phase difference detection is presented according to Fourier series decomposition method and the characteristic that inner product of two orthogonal vectors in a linear space is zero.

在分析现有相位差检测算法的基础上，应用Fourier级数分解方法与线性空间中正交向量内积为零的特性，推导出了一种新的相位差检测算法。

The intensification phenomenon at 1-meter scale was not found. The larval density in water column might be highly heterogeneous even in very small scale. On the other hand, we consistently found higher settlement density in sand areas than in reef areas. This phenomenon may well have been caused by the intensification

本研究结果在1公尺的空间尺度下并没有发现附苗强化现象，但是礁区的附苗密度却如预期低於砂区，推测可能是1公尺空间尺度内幼生数量过於不均匀，相差5倍的附苗板面积不足以造成幼生附苗密度的变异，而礁区与砂区则由於面积相差相当大因此可以发现附苗强化现象。

By using the analysis method,this paper gets a inequality about the relation of the interior product and the norm in the separable,complex Hilbert space.

用分析法得到了可分复Hilbert空间中一个内积与范数关系的不等式，由此不等式可推出几个可以看作是Cauchy-Schwarz不等式的反向不等

On the analogy between plane elasticity and plate bending theory, moment functions of plate bending in polar coordinates are introduced as original variables to establish a symplectic space in circumferential direction for the bending of annular sector plate with an appropriate definition of symplectic inner product.

根据平面弹性与薄板弯曲问题的相似性原理，极坐标系板弯曲的弯矩函数被引入作为原变量，并通过恰当的辛内积定义建立了环扇形薄板弯曲问题的一个辛几何空间。

There are three features in the minibasins induced by gravitational sliding on the slope: the firstly, feature is surface of unconformity developed by onlap on minibasin margins or surface of unconformity truncated by mass transport-complex are sequence boundary in the study area; the secondly , accommodation of gravity flow is controlled by up lift rate and sedimentation rate , and styles of filling in the minibasins are dominated by the interrelationship between the two factors; and the third , there are two stacking patterns that consists of upward of turbidite fan-hemipelagic drape mud or mass-transport complexes-turbidite fan-hemipelagic drape mud.

认为在深水陆坡重力滑动作用所形成的微盆地内，层序边界表现为微盆地边缘上超不整合面或重力流对下伏地层的侵蚀不整合；逆冲构造隆升速率与沉积速率共同控制了重力流可容空间和沉积充填样式；沉积垂向演化以块状搬运复合体一浊积扇－深海披覆泥或浊积扇－深海披覆泥为特征。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。