三向量

This is my last OpenGL for a project to use the "three-dimensional vector space / point" and related functions, they can use a definition of space vector / points, for the vector translation, zooming and rotation, the use of correlation function can also achieve two vector by the fork, get a Vectors absolute length of a vector unit, received a 3:00 decision vector perpendicular to the plane, a space to be the distance between two points, two vector to be the plot points, to be the angle between two vectors, such as operating for the use of user-friendly, each function is detailed Notes, it is particularly important if the calculation vector plot points, fork also took note, we hope to have useful.

这是我过去进行一个OpenGL项目时使用到的"三维空间向量/点"类及相关函数，使用它们可以定义一个空间向量/点，实现向量的平移，缩放和旋转等，使用相关函数还可以实现两向量的叉乘，得到一个向量的绝对长度，将一个向量单位化，得到一个三点决定的平面的垂直向量，得到空间中两点的距离，得到两向量的点积，得到两向量的夹角等操作，为方便用户的使用，每个函数都有详细的注释，特别重要的向量计算如点积，叉乘还有相关说明，希望对大家有所用处。

Using the theories of probability, algebra and spectral theory comprehensively, we investigate some related characteristics of logic functions in cryptography: Firstly, we introduce m order generalized s - correlation immunity of Boolean vector functions and prove that the higher order generalized ε- correlation immunity can guarantee the lower order generalized ε- correlation immunity. Then by applying decomposition formula of joint distribution of Boolean random vectors, we give a spectrum criterion of m order generalized e - correlation immunity of Boolean vector functions. Furthermore, we show that the algebraic degree of m order generalized e - correlation immune Boolean vector functions is not restricted by the correlation immune orders.

本文主要运用概率论的思想和方法，并结合代数学和频谱理论的相关知识，对密码学中逻辑函数的有关性质进行了研究，主要包括以下三个方面的内容：首先，对布尔向量函数的相关免疫性进行了拓展，给出了k维布尔向量函数m阶广义ε-相关免疫的概念，证明了布尔向量函数的高阶广义ε-相关免疫性蕴含低阶广义ε-相关免疫性，并根据布尔随机向量联合分布分解式得到了布尔向量函数m阶广义ε-相关免疫的一个谱判别条件，还说明了m阶广义ε-相关免疫布尔向量函数的代数次数不受相关免疫阶数的制约。

During the process of model smoothing, there is an uncertain weight threshold, which is discussed in detail for scientific evaluating.2. In the part of "3D Model Segmentation", the vector of Gauss-Mean curvature, that of Max-Min curvature, that of RMS-Absolute curvature are compared through their performances in segmentation.

在三维模型分割方面，对高斯-均值曲率向量、最大-最小曲率向量、RMS-绝对曲率向量等三种特征向量在分割中的性能，以及指定聚类数目对分割结果的影响通过试验进行了比较。

The results were summarized as follows:(1) the 4-week interval retest reliability for the Decidedness, Comfort, and Reasons scales were .69,.80, and .89, respectively, and for the subscales of the Reasons scale ranged between .78 and .85;(2) the alpha coefficients for the three scales were .85,.91,.97, and for the subscales of the Reasons scale ranged between .78 and .93;(3) there was a positive correlation between the Decidedness scale and the Comfort scale, and both scales were negatively correlated with the Reasons scale;(4) career indecision was found to be correlated as expected with state-trait anxiety, career beliefs, and perceived career barriers;(5) there were no significant differences between social science group and natural science group;(6) the only significant gender difference was found on the Career Choice Importance scale of the Reasons scale; and (7) there were significant grade differences on all the CCFI scale scores, with higher school grade level students showing greater decidedness.

本量表共分三部分：定向量表，安适量表及原因量表。其中，原因量表尚包含「环境资讯」、「抉择时机」、「双趋冲突」、「焦虑犹豫」、「科系因素」、「外在阻力」及「自我认识」七个分量表。做答方式采六点计分，从「非常不符合」到「非常符合」。信度方面，间隔四周的再测信度，定向量表为。69，安适量表为。80，原因量表为。89（分量表介於。78至。85间）。Cronbach alpha系数，定向量表为。85，安适量表为。91，原因量表为。97（分量表介於。78至。93间）。在效度方面，定向量表与安适量表呈显著正相关(r=。67)；两量表与原因量表呈显著负相关(r=-。77及-。75)；原因量表各分量表的内部相关低於各分量表与总分的相关。大学生的生涯定向程度、对生涯定向状态的安适程度及生涯未定向原因的类型三者与特质焦虑、情境焦虑、生涯信念及职业抉择阻力有关。

In this thesis, we mainly study the theory of vector optimization in three aspects: the spectral scalarization of Euclidean Jordan algebra vector optimization, the robust methods for solving uncertain multiobjective linear optimization problem and the application in game theory.

本文共分四章，主要致力于向量优化三个方面的研究：欧几里德若当代数向量优化的谱标量化、不确定多目标线性优化问题的鲁棒方法和向量优化在对策论中的应用。

This is a project to use the three-dimensional space vector/point type and related functions, they can be defined using a space vector/point, the realization of vector translation, scaling and rotation, the use of correlation function can also be the realization of the two vectors fork x, the absolute length of a vector, a vector unit, and get a three-point decision to the vertical plane of the vector, be the distance between two points in space, by the two vectors point multiplication by the two vectors angle, such as operations, for the use of user-friendly, each function are detailed notes, I hope all of you useless.

详细说明：这是一个项目时使用到的"三维空间向量/点"类及相关函数，使用它们可以定义一个空间向量/点，实现向量的平移，缩放和旋转等，使用相关函数还可以实现两向量的叉乘，得到一个向量的绝对长度，将一个向量单位化，得到一个三点决定的平面的垂直向量，得到空间中两点的距离，得到两向量的点积，得到两向量的夹角等操作，为方便用户的使用，每个函数都有详细的注释，希望对大家有所用处。

The method relies on the facts that the row vectors composed of all the image points span, the same linear subspace as the row vectors composed of 3D space points span and that a basis of the subspace can consist of two row vectors composed of all the image points and one row vector in 3D space that is orthogonal to the former. The row vector can be determined, and the 3D reconstruction is accomplished. The novelty lies in the fact that the method can treat all the image points uniformly.

利用所有图像序列构成的行向量生成的子空间之和与三维空间点构成的行向量生成的子空间是同一线性子空间、同时由所有图像点构成的2个行向量外加一个行向量就可以组成该子空间的一个基底的特性，线性地求取子空间中的行向量，最后完成三维重建。

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

By the definition of Darboux type vector and rectifying Darboux type vector ,we constructed the rectifying type developable surfaces and Darboux type developable surfaces and tangential Darboux type developable surfaces ,and study these three developable surfaces relationship with Minkowski slant helices and Minkowski conical geodesic curves. Bying applying the singularity theoerical knowledge, We give a classification of special developable surfaces under the condition of the existence of such a special curve as geodesic.

通过定义三维Minkowski空间中的达布型向量以及修正达布型向量，构造出三维Minkowski空间中的三类可展曲面，即修正型可展曲面、达布型可展曲面和切达布型可展曲面，研究Minkowski斜螺线和Minkowski锥面测地线这两种特殊曲线和这些曲面的关系，并研究Minkowski斜螺线和Minkowski锥面测地线作为这些曲面的测地线的条件下，运用奇点理论的知识，对这三种可展曲面进行奇点分类。

A positive and negative projection method of object to be tested based on universal pattern display card includes using 3D texture to present rebuilt body data of object to be tested, calculating out directional vector array of ray outgoing point to detectors, storing said vector array into pattern display card to form directional vector texture, rotating directional vector texture and directional vector around rotary shaft to realize once of positive projection course on any projective angle, using 3D texture index technique to let virtual slab set position be not limited any more in negative projection course.

本发明属于投影探测与成像技术领域，其特点在于该方法含有以下步骤：把被测物体的重建体数据用三维纹理存储表示；预先计算射线出射点至平面探测器上个探测器之间的方向向量数组，并存储到通用图形显示卡中形成方向向量纹理；利用方向向量纹理与方向向量绕旋转轴旋转来实现任一投影角度的正投影过程的一次完成，无中间结果转存；在反投影过程中，利用三维纹理索引技术使虚拟切片组的放置位置不再受到限制。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。