对偶性

Then presents a new classification algorithm based on theorem of Information granularity?3. introduces the distillation of text character in text clustering ,presents an iteration procedure to obtain the weight of riles and words.

随后从理论的层面来剖析聚类/分类算法，并介绍了一种基于粒度的分类算法；四、介绍了在文本处理中如何提取文本特征，给出了一种权重计算的对偶性策略。

In this paper, the computation of original likelihood function is transformed into the optimal problem of its low bound through the conjugate representation of the convex function, and a additional parameter is introduced to control the smoothing degree of low bound, and so the performance of local optimal solution can be improved.

我们利用凸泛函的对偶性，将原似然函数的复杂计算问题转化为对其下界函数的优化问题，从而降低学习算法的复杂性；并通过引入一个参数来控制下界函数的光滑程度来改善局部最优解的性能；指出了传统的期望最大化算法(Expectation Maximization Algorithm)是变分学习算法的特殊情况。

Based on the important idea of duality between plane and point geometries,two direct explicit methods of computer-aided design for developable surface s were proposed,the developable surface s were represented using control planes with appropriate basis functions.

为了克服传统方法在可展曲面设计上的缺陷，方便地解决工程中经常遇到的可展曲面位置和形状难以调整和控制的问题，基于3D射影空间中点和平面间的对偶性这一重要思想，提出了两种直接、简单的可展曲面设计方法。

It order to overcome the difficulties in representation of developable surface s utilizing traditional approaches,based the concept of duality between points and planes in 3D projective space, a direct explicit method of computer-aided design for developable surface s was presented.

基于三维射影空间中点和平面间的对偶性，提出了计算机辅助设计五次样条上可展曲面的一种简单且有效的方法，通过采用该方法，可利用具有B啨zier和B样条基的控制平面设计可展曲面。

Also the new method is extended to current-fed inverters and medium frequency power supplies according to the principle of circuit duality.

然后利用电路对偶性原理将这一方法推广到电流型逆变器及中频电源中。

The standard applied modes of geometric flatness in new GPS(geometrical product specification),including the duality principle and common operation technology in new GPS system,and the expression,algorithm,data processing issues of the theoretical,specification and verification model,were investigated.

研究了新一代GPS中几何平面度标准的应用模式，包括新一代GPS体系的对偶性及共性操作技术以及公称、规范和验证模型的表示、算法和数据处理。开发了试验性软件系统，通过可视化方法表示了它们的关系，实现了GPS几何平面度标准在烟机零件中的具体应用。为进一步应用新一代GPS标准以及规范表达产品的设计、制造、检验所要求的统一公差信息提供了较好的借鉴

GPS (Geometrical product specification and verification); database; general ; GPS matrix model; duality principle; LSC; norm theory

工程科技II，工业通用技术及设备，工业通用技术与设备GPS；数据库；通用； GPS；矩阵模型；对偶性原理；最小二乘法；范数

After that, we discuss the weak duality theorem and the strong duality theorem concerning Benson efficient solutions.

接着讨论了Benson真有效解的强弱对偶性定理。

The high resolution image of full hole can be obtained from the being processed imaging logging information, and the morphological features about intersecting lines of fracture face and borehole present monocyclic sine curve.

成像测井数据经处理后可得到全井壁高分辨率的图像，而裂缝面与井筒的交线在图像上的形态特征呈现为单周期的正弦曲线，应用哈夫变换的点－线对偶性拾取图像中的裂缝角度等信息，可得到较好的处理结果。

Under the conditions of Ambrosetti-Rabinowitz type superlinear and odd duality, we show that the systems have at least one nontrivial solution and infinitely many solutions.

在Ambrosetti-Rabinowitz型超线性条件及具备奇对偶性条件下，得到了方程组分别有一个解及无穷多个解的存在性结果。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。