Is CAD/CAM ready for AI?

In this paper we explore the possibility of merging CAD/CAM with Artificial Intelligence technology. A brief tutorial on expert systems is presented. Several observations are noted which link existing expert system applications with various CAD/CAM problems. In conclusion, these existing expert system applications may provide guidance for implementing AI solutions to certain CAD/CAM problems.     

Complex Angular Momentum Diagonalization of the Bethe-Salpeter Structure in General Quantum Field Theory

The Complex Angular Momentum (CAM) representation of (scalar) fourpoint functions has been previously established starting from the general principles of local relativistic Quantum Field Theory (QFT). Here, we carry out the diagonalization of the general t-channel Bethe-Salpeter (BS) structure of four-point functions in the corresponding CAM variable 5^t, for all negative values of the squared-energy variable t. This diagonalization is closely related to the existence of BS-equations for the absorptive parts in the crossed channels, interpreted as convolution equations with spectral properties. The production of Regge poles equipped with factorized residues involving Euclidean three-point functions appears as conceptually built-in in the analytic axiomatic framework of QFT. The existence of leading Reggeon terms governing the asymptotic behaviour of the four-point function at fixed t is strictly conditioned by the asymptotic behaviour of a g lobal Bethe-Salpeter kernel of the theory.     

INSTRUCTIONS TO AUTHORS

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INSTRUCTIONS TO AUTHORS

1. The Chinese Annals of Mathematics (CAM) Ser.B is a comprehensive mathematical journal carrying original papers on pure and applied mathematics. It aims at presenting the latest achievements in mathematical researches and promoting domestic and international academic exchanges.     

THE SUBDIVISION ALGORITHM FOR GENERATING CURVES AND ITS PROPERTIES

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Introducing knowledge processing technology to CAD/CAM

A method of introducing knowledge processing technology which will develop advanced CAD/CAM systems for engineering design programs is discussed. To achieve this objective it is necessary to establish the concept of an object model and a methodology for building it in computers.Trying engineering design and knowledge processing together is not an easy task. The reasons are two-fold: first, knowledge processing technology is still making rapid progress and we do not understand it yet completely, and second, in order to introduce knowledge processing technology into CAD/CAM we need to analyze the design-and-manufacturing process in detail and to find the best method to combine these two technologies. The task is further complicated because it can be done by those who have enough knowledge of both technologies only, and also because it may result in reorganization of the traditional design-and-manufacturing process.This paper describes the current state of knowledge processing technology as well as its limitations in achieving intelligent functions, and analyzes the manner of combining these two technologies.     

G3连续过渡曲面的构造

过渡曲面在CAD／CAM中具有十分重要的作用，其构造与风荷连续性，几何不变量密切相关。本文通过对几何不变量法曲率，测地挠率和几何连续关系的推导，得到构造G^3几何连续过渡曲面的充分条件，结合连接线定理，用超限插值法解决了两个参数面间G3几何连续时渡问题。     

高弹粘流在三维变厚度狭缝流道中流动的数值模拟

用有限块法对高弹粘流在三维变厚度狭缝流道中的流动进行数值模拟.求出流体流量在流道中的分布规律;通过对实际板材挤出模鱼尾型流道中设置阻流块对流动影响的计算,证实有限块法是简易可行的,从而为挤出模的计算机辅助设计提供了一个重要手段.     

Bzier曲线和曲面包围的面积和体积算法

§1.引言 曲线、曲面造型和立体造型的理论和方法是迅速发展的 CAD/CAM技术的重要基础之一.在造船、航空、汽车、模具、机械和建筑等行业的CAD系统中,经常需要计算平面上闭曲线包围的面积以及三维立体图形的表面积和体积.     

New control massic polygon of a B-rational curve resulting from a homographic change of parameter

We deal with the homographic and affine change of parameter of rational curves represented as BR-curves. Forcomputational purposes in CAGD and CAM we determine the new massic polygon through four different methods and we study the particular case of Bézier curves among the applications.     

Robots,CAM and O.R.

Microelectronics have greatly influenced the nature of manufacturing technology and systems. New factories make growing use of microcomputers and microprocessors in robots, C.N.C. machine tools and flexible manufacturing systems. The result is an increasing trend towards fully integrated computer-based manufacturing systems. As a consequence, O.R. software has a newer, more direct role in the modern factory than ever before. Fully integrated CAM systems are implemented by multi-disciplinary teams of engineers and management scientists. The O.R. practitioner can make a major contribution, for example in layout optimisation and plant simulations.     

A further generalisation of the planar cubic Bézier spiral

Spiral segments are useful in the design of fair curves. They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. Cubic Bézier curves are commonly used in curve and surface design because they are of low degree, are easily evaluated, and allow inflection points. This paper generalises earlier results on planar cubic Bézier spiral segments and examines techniques for curve design using the new results.     

Global Existence and Exponential Stability for a Quasilinear Wave Equation with Memory Damping at the Boundary

In this paper, we focus on the global well-posedness of a quasilinear wave equation with a memory boundary condition. Under conditions on the geometry of the domain and the relaxation function describing the memory properties of the boundary, we obtain the existence, regularity and uniqueness of the global solution to the system. We prove also that the energy of the global solution to the system decays exponentially. The research was supported by the National Natural Science Foundation of China under Grant 60504001, Programa Nacional de Ayudas Para la Movilidad under Grant SB2003-0271 in Spain and the SIMUMAT projet of the CAM (Spain). The author is grateful to Prof. Enrique Zuazua for fruitful discussion.     

The implementation of the finite-volume dynamical core in the community atmosphere model

A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the community atmosphere model (CAM) 3.0 is presented. These 3-D equations can be decoupled into a set of 2-D equations by the introduction of a floating vertical coordinate, resulting in considerable potential parallelism. Subsequent analysis of the data dependencies—in particular those arising from the polar singularity of the latitude-longitude coordinate system—suggests that two separate domain decompositions should be employed, each tailored for a different part of the model. The implementation requires that data be periodically redistributed between these two decompositions. Furthermore, data from nearest neighbors are kept in halo regions, which are updated between iterations. These data movements are optimized through one-sided communication primitives and multithreading. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.     

Spiral transitions

Spiral curves are free from singularities and curvature extrema. These are used in path smoothing applications to overcome the abrupt change in curvature and super-elevation of moving object that occurs between tangent and circular curve. Line to circle spiral transition is made of straight line segment and curvature continuous spiral curve. It is extendible to other important types of transitions like line to line and circle to circle. Although the problem of line to circle transition has been addressed by many researchers, there is no comprehensive literature review available. This paper presents state-of-the-art of line to circle spiral transition,applications in different fields, limitations of existing approaches, and recommendations to meet the challenges of compatibility with today's CAD/CAM soft wares, satisfaction of Hermite end conditions, approximation of discrete data for image processing, 3 D path smoothness for an unmanned aerial vehicle(UAV), and arc-length parametrization. Whole discussion is concluded with future research directions in various areas of applications.     

Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model

The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Recently, techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. It was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. The probability distribution functions (PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a Gaussian. Here, rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic models. Asymptotic Gaussian lower bounds are also established under suitable hypotheses.     

Design of a new dynamical core for global atmospheric models based on some efficient numerical methods

A careful study on the integral properties of the primitive hydrostatic balance equations for baroclinic atmosphere is carried out, and a new scheme to design the global adiabatic model of atmospheric dynamics is presented. This scheme includes a method of weighted equal-area mesh and a fully discrete finite difference method with quadratic and linear conservations for solving the primitive equation system. Using this scheme, we established a new dynamical core with adjustable high resolution acceptable to the available computer capability, which can be very stable without any filtering and smoothing. Especially, some important integral properties are kept unchanged, such as the anti-symmetries of the horizontal advection operators and the vertical convection operator, the mass conservation, the effective energy conservation under the standard stratification approximation, and so on. Some numerical tests on the new dynamical core, respectively regarding its global conservations and its integrated performances in climatic modeling, incorporated with the physical packages from the Community Atmospheric Model Version 2 (CAM2) of National Center for Atmospheric Research (NCAR), are included.     

Design of a new dynamical core for global atmospheric models based on some efficient numerical methods

A careful study on the integral properties of the primitive hydrostatic balance equations for baroclinic atmosphere is carried out, and a new scheme to design the global adiabatic model of atmospheric dynamics is presented. This scheme includes a method of weighted equal-area mesh and a fully discrete finite difference method with quadratic and linear conservations for solving the primitive equation system. Using this scheme, we established a new dynamical core with adjustable high resolution acceptable to the available     

Convex hull properties and algorithms

Convex hull (CH) is widely used in computer graphic, image processing, CAD/CAM, and pattern recognition. We investigate CH properties and derive new properties: (1) CH vertices’ coordinates monotonically increase or decrease, (2) The edge slopes monotonically decrease. Using these properties, we proposed two algorithms, i.e., CH algorithm for planar point set, and CH algorithm for two available CHs. The main ideas of the proposed algorithms are as follows. A planar point set is divided into several subsets by the extreme points, and vertices in these subsets are then separately calculated. During the computation, the CH properties are used to eliminate concave points. This can reduce the computational cost and then improves the speed. Our first algorithm can extract CH with O(nlogn) time, which is the lower bound of planar CH extraction, and the second algorithm can obtain CH with O(m+n) time at the worst case.     

Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

This paper studies the construction of geometric integrators for nonholonomic systems. We develop a formalism for nonholonomic discrete Euler–Lagrange equations in a setting that permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot). This work was partially supported by MEC (Spain) Grants MTM 2006-03322, MTM 2007-62478, MTM 2006-10531, project “Ingenio Mathematica” (i-MATH) No. CSD 2006-00032 (Consolider-Ingenio 2010) and S-0505/ESP/0158 of the CAM.