尺度

Concretely, starting from a short sequence primal masks possessing Hermite interpolation properties, a necessary and sufficient conditions such that primal masks satisfies the preassigned order of sum rules are established, then a dual masks with short support, symmetry and any preassigned order of sum rules is constructed, it follows that two multiscaling functions are obtained and then multiwavelets and dual multiwavelets are derived. From which, a general design framework is obtained for constructing biorthogonal multiwavelets system with multiplicity 2r associated with Hermite interpolation functions.

具体的，从具有Hermite插值性质的短序列尺度符号出发，首先建立它具有指定阶和规则的充要条件，然后构造出短支撑、对称的具有指定阶和规则的对偶尺度符号，从而得到一对对偶的尺度函数，再构造出相应的双正交多小波。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component. For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper. For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space state informatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision. Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为（n-1）维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料（单质材料作为特殊的功能梯度材料看待）、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为(n-1)维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

They found that the marine atmosphere and the coastal ocean actually exchange buoyance and momentum within the meso-scale spatial and temporal domains of both fluids, spanning two to two thousand kilometers and ten minutes to ten hours on the atmospheric side and one to one thousand kilometers and seconds to two weeks on the ocean side.

他们在长期的研究中发现，在大陆沿海和近海区域的大气和海洋之间的相互作用实际上是在多种中尺度范围(空间尺度：对大气，2-2000km；对海洋，1-1000km；时间尺度：对大气，10分钟到10小时的量级；对海洋，几秒到两个星期)内的热量和动量的相互交换。

The transverse wave disturbance along tangential base flow of circular vortex is discussed By using numerical method we study this instability of baroclinic flow which is mesoscale inertia wave instability on the cylindrical coordinate The influence of stratification stability N 2 , Coriolis parameter f 0 , the vertical shear of tangential wind z of the ambinent atmosphere and the latent heat on the growth rate of instability is studied From the above analysis and calculation, we can learn that there are Eady mode and mesoscale mode of transverse wave instability in circular vortex as well Furthermore we also learn that distribution character of mesoscale mode disturbance field of transverse wave instability, anomalistic "cats eye" structure of lower level and the character of the slowly spreading disturbance converges at low level and the quickly spreading disturbance converges at high level

作者中文名：李红金；陆汉城；宋晓亮；李鲲摘要：讨论涡旋大气中，存在沿切向基流传播的横波型扰动，并采用数值方法讨论了柱坐标系下圆形涡旋系统斜压气流中这类扰动的不稳定，这是一类中尺度的重力惯性波的不稳定。研究了涡旋环境大气的层结稳定度参数N2、切向风垂直切变Vz、凝结潜热、涡旋特性及科里奥利参数f0对不稳定增长率的影响。圆形涡旋中同样存在横波不稳定的Eady模态和中尺度模态，得到了中尺度模态的扰动场分布特征：流场的不规则"猫眼"结构及慢速传播的扰动均集中在低层，而快速传播的扰动均集中在高层的扰动特征。

In the second chapter, the basic micro-dimensional statically determinate mechanism, and Boundary Element Method and its special resource program are introduced. In the third chapter, kinds of roller bearing longevity prolonging methods and elastic roll bend equivalent statically determinate roll system are discussed.

第二章阐述轧机微尺度理论的基础－微尺度静定机构学和边界元法及其专用程序，第三章论述二辊及四辊轧机轧辊弹性弯曲辊颈的倾斜的微尺度行为等效静定辊系和各类滚动轴承延寿机理。

When the receiving aperture is much larger than the scattering disk scale, the aperture-smooth effect is remarkable and the derived variance approximates the result given by weak-fluctuation theory for any zenith; when the receiving aperture is much smaller than the scattering disk scale, the low-pass filter effect of the scattering disk scale is dominating and weak-fluctuation theory is valid only for small zeniths.

散射盘尺度和接收孔径对到达角起伏起平滑作用，当接收孔径远大于散射盘尺度时，由于孔径平滑作用，导出的表达式在任意天顶角都可以近似为弱起伏理论给出的结果；当接收孔径小于散射盘尺度时，散射盘尺度的平滑作用明显，接收孔径的平滑作用相对较小，传统的到达角起伏理论仅在小天顶角是适用的，在大天顶角必须用新导出的方差表达式。

Also the multi-scale entropy processing and analysis of conductance fluctuating signals acquired by VMEA sensor for five flow patterns with water as the continuous liquid are conducted. The study result indicates that the increase of f o makes oil in water type slug flow occur at lower U sg; for low flow velocity, the continuous liquid inversion occurs at about f o=0.9 and the increase of U sg makes the inversion point move to low oil volume fraction; the multi-scale entropy detail describes the nonlinear dynamic characteristics of oil-gas-water flow patterns and the rate of MSE at low scales sensitively indicates the variation of flow patterns and can act as the efficient criterion of three-phase flow patterns identification.

对水为连续相的5种流型VMEA传感器波动信号进行了多尺度熵分析，研究结果表明：含油率增加可使水包油段塞流在较低气相表观速度下产生；较低流速下的油水相态逆转可发生在油液比为0.9左右，气相流速增加使得逆转点向含油率低的方向偏移；多尺度熵细节可以刻画油气水三相流非线性动力学特性，而低尺度的多尺度熵变化率敏感地反映流型转变，是划分油气水三相流流型的有效准则。

At the present time, their size has arrived at nanometer scale, and it approximately takes several picoseconds, or even shorter time, for free carriers to transport during such small distances. Therefore, research of carrier dynamics in silicon on shorter and shorter time scale is urgently developed. Processes on such short time scale are difficultly measured by traditional electronic method, so ultrafast spectroscopy method is the only choice of carrying out such experiments. Additionally, application of photoelectric detectors is severely influenced by laser.

近年来，硅半导体器件尺寸不断变小，目前已经缩小到了纳米尺度，载流子在这个尺度内的输运时间大约在ps量级，这促使人们需要对越来越短的时间尺度内硅的载流子动力学进行研究，传统的电子学方法很难对这么短时间尺度内发生的现象进行测量，超快光谱探测几乎成了进行这类研究的唯一测试手段。

In recent years, size of silicon devices has been decreasing. At the present time, their size has arrived at nanometer scale, and it approximately takes several picoseconds, or even shorter time, for free carriers to transport during such small distances. Therefore, research of carrier dynamics in silicon on shorter and shorter time scale is urgently developed. Processes on such short time scale are difficultly measured by traditional electronic method, so ultrafast spectroscopy method is the only choice of carrying out such experiments. Additionally, application of photoelectric detectors is severely influenced by laser.

近年来，硅半导体器件尺寸不断变小，目前已经缩小到了纳米尺度，载流子在这个尺度内的输运时间大约在ps量级，这促使人们需要对越来越短的时间尺度内硅的载流子动力学进行研究，传统的电子学方法很难对这么短时间尺度内发生的现象进行测量，超快光谱探测几乎成了进行这类研究的唯一测试手段。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。