函数

An interpretation is just the inverse of the mapping that a representation provides, that is, an interpretation is a function g from ∑* to D for some alphabet ∑ and some set D.

这个解释函数与物化函数相反，把符号串映射回信息对象。也就是，解释函数是∑*到 D 的函数 g，基于一个字母表∑和集合 D。

After certifying the irreality of ideal filtering function, we can get a better filter selecting a proper window function. Comparing two actual filters, we designate a good"Panama hat"filtering function. Meanwhile, an effectively linear interpolating function is introduced to raise the image reconstruction quality. Describing its realizing steps on the micro-computer briefly, we reconstructed some images from the anlogue projections of some models. The number of projection views is 180, 100 same interval parallel lines per view; the size of reconstructed images is 64×64 pixels with 64 gray levels; the reconstructing speeds are 40" on PC-386 and 12"on PC-486, respectively; each pixel is 0.31mm.

在证明了理想滤波器的不可实现性之后，得知通过选择适当的窗函数可获得很好的滤波函数，经过两个实际滤波器的效果对比，我们选取了较好的"巴拿马帽"形滤波函数，同时也介绍了一个有效的提高重建质量的线性内插函数，概要地叙述了平行射束图象重建的计算机具体实现步骤后，对几个物体的模拟投影数据进行了重建：投影角为180°，每视角下有100个平行投影数据点，在386微机上重建尺寸为64×64，时间约为40秒；在486/33MHz微机上只用了12秒，图象的象点精度是0.31mm。

In this paper,fractal interpolation function is expressed as a wavelet series,and its mother function is defined by the translation of iterated function system.

把分形插值函数表示成小波类型级数的形式，其"母函数"是由迭代函数系的位移函数决定，并估计了它的余项和误差。

The present method is applied to two-dimensional potential problems and the corresponding discrete equations are derived. Because the shape functions so-obtained possess the Kronecker delta property, the essential boundary conditions can be enforced as the FEM; furthermore, the Heaviside step function is used as the test function, there is no domain integral, and only a regular boundary integral is involved.

因为滑动Kriging插值方法构造的形函数满足Kronecker函数性质，所以本文建立的改进的无网格局部Petrov-Galerkin法可以像有限元法一样直接施加边界条件；由于采用Heaviside分段函数作为局部弱形式的权函数，因此在计算刚度矩阵时只涉及边界积分，而没有区域积分。

Results show that radial basis function and point interpolation methods possess Kronecker Delta function property, but the robustness is poor in some cases; the MLS approximation function does not possess Kronecker Delta function property, but it has good robustness. Differences among the three discretization schemes of meshless method are as follows:the collocation method requires no numerical integration and very little computational time while its robustness is poor; Galerkin method is not a truly meshless method due to the background meshes required for integration; the Petrov-Galerkin method is a truly meshless method and need numerical integration in each sub-domain, so it needs more computational time.

分析结果显示：径向基函数和点插值法均具有d 函数属性，但计算稳定性差；移动最小二乘近似函数不具有d 函数属性，但计算比较稳定；无网格方法中的3种离散方法不同之处在于：配点法不需要积分，计算量小，计算稳定性差；Galerkin方法需要借助背景网格进行积分，它不是真正的无网格方法；Petrov-Galerkin方法，是一种真正的无网格方法，它需要对每个子域进行积分，计算工作量较大。

This thesis mainly discuss following issues, Theory and simple expressions for array covariance matrixes are derived when angular spread functions are symmetric distribution functions, i. e. the Uniform distribution, the Gauss distribution, the Laplace distribution and the Von Mises distribution, and a non-symmetric distribution function, i. e. the Gamma distribution. And the relation between the effective signal subspace and the array number, or and the nominal angle of the distributed source, the angular spread, the distributed functions, and the Signal-to-Noise Ratio is gained. The dimension of the effective signal subspace increases with increment of the array number. And it is more obvious to the non-symmetric distribution. The dimension of the effective signal subspace decreases with increment of the nominal angle. And the distributed source is equal to a point source as θ=π/2. The dimension of the effective signal subspace increases with increment of the angular spread.

本论文针对阵列信号处理中广泛存在的分布源现象，主要讨论了以下问题：推导了角度分布函数分别为对称的均匀分布、高斯分布、拉普拉斯分布、Von Mises分布和非对称的伽马分布时，分布源阵列接收信号协方差阵的严格模型和简化模型，得到了单个分布源的有效信号子空间随阵元数、分布源中心角、分布角、角度分布函数和信噪比的变化规律：随着阵元数的增加，对所有角度分布函数的有效信号子空间维数也随着增加，且非对称分布函数的有效信号子空间充满整个空间的可能性更大；随着分布源中心角逐步增加，有效信号子空间维数逐步减小，当θ=π/2时，等价于点源情形；随着分布源分布角逐渐加大，有效信号子空间维数也随之增加，直到有效信号子空间充满整个空间；随着信噪比的增加，有效信号子空间维数有一定程度的减少。

The third aspect: we consider comparison of Minimum Norm Quadratic Unbiased Estimator and ordinary least squares estimator of in the multivariate normal linear model Y ~ N{XB, V, where the design matrix A' need not have full rank and the dispersion matrix V can be singular.

使用的损失函数有二次损失函数、嫡损失函数和对称损失函数。论文基于以下三个准则：二次损失风险准则、嫡损失风险准则和对称损失风险准则，将MINQUE和LSE进行比较。

This paper has utilized the mathematic inductive method and Leibniz theorem to study the unity advanced derivation of complex-special Function and original function, acquired their united expression.

用数学归纳法和莱布尼兹公式对一类复杂函数的高阶导数与原函数的统一性进行了研究，获得了该类函数的高阶导数及原函数的统一表述公式。

The existence of potential 〓、Ω is proved in linear functional space theories.

用线性函数空间理论证明了位函数〓、Ω的存在性；指出了现有文献在退化矢量位〓的唯一性证明中所存在的问题，并重新给予了证明；证明了位函数〓、Ω在导体与导体、导体与非导体界面上自然满足分界面条件；针对汽轮发机端部的轴对称涡流场，讨论了位函数〓、Ω的泛函及有限元代数方程组的形成。

Quantifying similarity/difference between two objects plays an important role in many contexts The quality of the similarity/difference scores can be improved by considering the semantic information related to the features of objects A flexible semantic distance function called X Dist is proposed, which can utilize the semantic information to measure the difference between two objects based on a solution to the transportation problem from linear optimization With a ground distance function for single features being a metric, X Dist is also a metric This property is very useful for making searching efficient, but is not investigated in the previous research Moreover, the experimental results show X Dist can be as good as the previously studied similarity measures in nearest neighbor searching, discriminative power and computing speed

量化对象间相似性/差别的方法具有广泛的用途，利用相关的语义信息能够得到更好的量化结果提出了一个量化对象间语义差别的距离函数XDist，它基于线性优化中的运输问题模型和相关的语义信息量化两个对象之间的差别在量化特征的差别函数是度量的情况下，XDist是一个度量，在提高搜索的效率方面具有优势，弥补了以往研究的不足，而且实验初步表明，此函数在最近邻查询效果、差别分辨力和计算速度方面能与已有函数相媲美1 引言量化对象间相似性/差别的方法具有广泛的用途，例如数据挖掘中的聚类；信息检索中的相似文档查询；协同过滤中的相似用户查询；CBR中的相似案例查询集合是对象特征表示的常用结构，集合的元素是与对象特征相关的项，它们可以

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。