A Type of Triangular Ball Surface and its Properties

1IntroductionIntheCONSURFsystemll--3]developedbyA.A.Ball,thebasisfunctionsforcubicpolynomialsweredefinedbyandhencecubicBallcurveswithcontrolpointsPi(i=0,1,2,3)canberepresentedasp(u)=Z?=.B!(u)Pi,0Su51.TwotypesofhigherdegreegeneralizedBallbasisfunctionsandcorrespondingcurveshavebeenderivedbyWangl4]andSaidls]independently.InWang'spaper,generalizedBailbasisfunctionsofarbitrarydegreeweredefinedasfollows'.ifnisanevennumber.ifnisanoddnumberwherew~2u(1--u),05u51.Aparametriccurveofdegreentcall…     

The triangular pyramid: Routing and topological properties

In this paper, a new topology for multicomputer interconnection networks, based on triangular mesh, is proposed. The new network, referred to as the triangular pyramid (or tripy for short), has L levels of triangular mesh. We study some basic important properties of the proposed network as well as introduce a routing algorithm for the tripy network based on the routing of triangular meshes. We prove that this form of pyramidal network is Hamiltonian, Hamiltonian-connected, and pancyclic. We also prove that the proposed network is 6-colorable and conduct a brief comparison of the tripy and its traditional pyramid counterpart. Our results show that the proposed network has higher scalability, connectivity, and total network bandwidth while preserving the important properties of the traditional pyramid network.     

Unifying representation of Bézier curve and two kinds of generalized ball curves

This paper presents a new basis,the WSB basis,which unifies the Bernstein basis,Wang-Ball basis and Said-Ball basis,and therefore the Bézier curve,Wang-Ball curve and Said-Ball curve are the special cases of the WSB curve based on the WSB basis.In addition,the relative degree elevation formula,recursive algorithm and conversion formula between the WSB basis and the Bernstein basis are given.     

A synthetic method for knowledge management performance evaluation based on triangular fuzzy number and group support systems

The purpose of this paper is to propose a systematic method to solve knowledge management performance evaluation (KMPE) problems. This method includes an integrated evaluation process starting from the measurement to the output of KMPE and combines subjective and objective indicators together. Firstly, we established an index system, involving the process of knowledge management, the organizational knowledge structure, economic benefits and efficiency. And based on this index system, a synthetic evaluation method is presented, using triangular fuzzy number to measure indexes and facilitating the KMPE with a group support system (GSS). To know better of the proposed method, we have an example to illustrate. Finally, the empirical study conducted in this paper indicates that the evaluation method has strong practicability and operability. Besides, the evaluation is enabled by using a group support system: the more objective scoring can be achieved due to synchronic/asynchronous and anonymous participation; Decision-makers improve their efficiency by the clear demonstration analysis results. The systematic method of KMPE based on the index system is able to improve organizations’ efficiency in performance evaluation process.     

煤化工产业及其硬密封球阀的选型运用

介绍了煤化工行业的现代化工艺技术和整个煤化工行业的国内外发展趋势,同时分析了煤化工行业里硬密封球阀的经济性和发展前景.根据煤化工行业的特殊性对硬密封球阀的核心部件的工艺方法进行了简单介绍,然后对煤化工行业中常用的硬密封球阀的结构特点进行了简单分析,基本确定了硬密封球阀的适用工况.     

Computing exact rational offsets of quadratic triangular Bézier surface patches

The offset surfaces to non-developable quadratic triangular Bézier patches are rational surfaces. In this paper we give a direct proof of this result and formulate an algorithm for computing the parameterization of the offsets. Based on the observation that quadratic triangular patches are capable of producing C¹ smooth surfaces, we use this algorithm to generate rational approximations to offset surfaces of general free-form surfaces.     

知识挖掘与它的链式特征

利用S-粗集与它的属性迁移,提出f、■知识、挖掘度概念,讨论了属性迁移与知识挖掘的数量关系;给出了f、■知识链式定理和f、■知识最小、最大挖掘度定理。最后,给出了■知识挖掘的实例分析。     

Multi-degree reduction of triangular Bézier surfaces with boundary constraints

Given a triangular Bézier surface of degree n, the problem of multi-degree reduction by a triangular Bézier surface of degree m with boundary constraints is investigated. This paper considers the continuity of triangular Bézier surfaces at the three corners, so that the boundary curves preserve endpoints continuity of any order . The l₂- and L₂-norm combined with the constrained least-squares method are used to get the matrix representations for the control points of the degree reduced surfaces. Both methods can be applied to piecewise continuous triangular patches or to only a triangular patch with the combination of surface subdivision. And the resulting piecewise approximating patches are globally C⁰ continuous. Finally, error estimation is given and numerical examples demonstrate the effectiveness of our methods.     

General IF-sets with triangular norms and their applications to group decision making

A concept of general IF-sets, i.e. “intuitionistic” fuzzy sets according to Atanassov, with triangular norm-based hesitation degrees is introduced and developed. That concept is used to construct flexible algorithms of group decision making which involve relative scalar cardinalities defined by means of generalized sigma counts of fuzzy sets. Two cases of group decisions, based on individual or social fuzzy preference relations, are considered.     

Smooth tool path generation for 5-axis machining of triangular mesh surface with nonzero genus

NC machining of a nonzero genus triangular mesh surface is being more widely confronted than before in the manufacturing field. At present, due to the complexity of geometry computation related to tool path generation, only one path pattern of iso-planar type is adopted in real machining of such surface. To improve significantly 5-axis machining of the nonzero genus mesh surface, it is necessary to develop a more efficient and robust tool path generation method. In this paper, a new method of generating spiral or contour-parallel tool path is proposed, which is inspired by the cylindrical helix or circle which are a set of parallel lines on the rectangular region obtained by unwrapping the cylinder. According to this idea, the effective data structure and algorithm are first designed to transform a nonzero genus surface into a genus-0 surface such that the conformal map method can be used to build the bidirectional mapping between the genus-0 surface and the rectangular region. In this rectangular region, the issues of spiral or contour-parallel tool path generation fall into the category of simple straight path planning. Accordingly, the formula for calculating the parameter increment for the guide line is derived by the difference scheme on the mesh surface and an accuracy improvement method is proposed based on the edge curve interpolation for determining the cutter contact (CC) point. These guarantee that the generated tool path can meet nicely the machining requirement. To improve further the kinematic and dynamic performance of 5-axis machine tool, a method for optimizing tool orientation is also preliminarily investigated. Finally, the experiments are performed to demonstrate the proposed method and show that it can generate nicely the spiral tool path or contour-parallel tool path on the nonzero genus mesh surface and also can guarantee the smooth change of tool orientation.     

A scaled feedback stabilization of power integrator triangular systems

Using unbounded time-varying scaling of the states we design C¹ feedback laws for power integrator triangular systems which globally asymptotically stabilize (GAS) the origin despite the uncontrollability of the linearization. With bounded scaling the feedback laws achieve global practical stability (GPS). For a trade-off between GAS/GPS of the origin and unboundedness/boundedness of the scaling we construct a dynamic version of these feedback laws.     

A mathematical model for simulating and manufacturing ball end mill

The performance of ball end mill cutters in cutting operations is influenced by the configuration of the rake and clearance faces in the ball component. From the mathematical design of a cutting edge curve, the rake face can be defined by the rake angle and the width of the rake face at each cross section along the cutting edge. We propose the fundamental conditions that must govern the engagement between the grinding wheel and the designed rake face in order to avoid interference while machining a ball end mill. As a result, a new mathematical model for determining the wheel location and a software program for simulating the generation of the rake face of a ball end mill are proposed. In addition, methods for grinding the clearance face in both concave and flat-shapes are introduced. The flute surface generated by a disk wheel during the grinding process is determined on the basis of a tangency condition. The results of the experiment and the simulation are compared to validate the proposed model.     

一种新的信息系统三角模糊自适应评价模型

目前的信息系统评价模型采用通用评价因子来评价不同领域中的系统,不能全面衡量不同信息系统的质量。提出了新的评价模型使用了动态制定不同领域的评价因子,同时提出了一种带有模糊评判调节因子的NTFAHP法,并对模糊综合评价方法进行了改进,将两者相结合,建立了适应现代信息系统的新评价算法。设计了该评价模型的原型系统,利用原型系统实施工程实例的可计算化评价,其实验结果的准确性、可靠性和稳定性有了明显改善和提高。     

Modeling and analysis of singular systems via orthogonal triangular functions

This paper presents a new approach to singular system analysis by modeling the system in terms of orthogonal triangular functions (TFs). The proposed method is more accurate compared to block pulse function-based analysis with respect to mean integral square error (MISE). A numerical example involving four states of a singular system is treated and solutions obtained thereof. Four tables and relevant curves are presented to compare the respective coefficients in block pulse function (BPF) domain as well as in TF domain. The percentage error of the samples determined via TF domain are compared with the exact samples of the states. Furthermore, MISE for both BPF and TF analysis are computed and compared to reveal the efficiency of TF-based analysis.     

A general model for machinable features and its application to machinability evaluation of mechanical parts

This paper is intended to reveal the rationale in the machinability evaluation and to present an effective, systematic approach to the assessment of the machined parts in the early stage of design. By examining the inherent shaping mechanism of machining processes, a geometric feature model, termed ‘machining volume’, resulting from the cutter's movement that mimics the cutter's real motion trajectory in machining, is proposed with which a set of feature derivatives can be affiliated. The geometric and topological patterns of machining volume permit to capture and convey machinability constraints on a part shape, leading to a new, simple machinability evaluation method centered on machining volume. This method is dedicated to two kinds of inspection on the geometry of a part in design: one is to search for unmachinable surfaces that are beyond the capability of machining processes, and the other to detect machining interference between a cutter and a part. It shows a more useful means to characterize machinable features that result in the machinability evaluation with ease and efficiency.     

区间Ball曲线的边界及降阶

讨论了n次区间Ball曲线的边界的构成;同时通过讨论区间多项式的降阶,利用线性规划法及最佳一致逼近法,给出了区间Ball曲线的的降阶算法．若利用线性规划法得到的区间曲线不能达到预期的误差,则可以结合细分的技术实现．     

Using multivariate resultants to find the implicit equation of a rational surface

Given a parametrization of a rational surface, the absence of base points is shown to be a necessary and sufficient condition for the auxiliary resultant to be a power of the implicit polynomial. The method of resultants also reveals other important properties of rational surface representations, including the coefficients of the implicit equation, the relationship between the implicit and parametric degrees, the degree of each coordinate variable of the implicit equation, and the number of correspondence of the parametrization.     

Thermodynamic and surface properties of liquid Ge–Si alloys

In the present work, the surface tension of liquid Si and Ge has been measured by the pendant/sessile drop combined method over the temperature range of 1723–1908 K and 1233–1313 K, respectively. The new surface tension data, the molar volumes and the melting temperatures of silicon and germanium as well as the excess Gibbs energy data of the Ge–Si liquid phase are the inputs for Calphad type modelling to study the mixing behaviour in alloy melts. The energetics of mixing in liquid Ge–Si system has been analysed through the study of the concentration dependence of various thermodynamic (activity, enthalpy of mixing, Gibbs energy of mixing), surface (surface tension and surface composition) and transport (diffusivity) properties as well as the microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the framework of statistical mechanical theory in conjunction with the Quasi-Lattice Theory (QLT).     

Computer modelling and finite element analysis of spiral triangular strands

In this paper a new mathematical geometric model of spiral triangular wire strands with a construction of (3 + 9) and (3 + 9 + 15) wires is proposed and an accurate computational two-layered triangular strand 3D solid modelling, which is used for a finite element analysis, is presented. The present geometric model fully considers the spatial configuration of individual wires in the strand. The three dimensional curve geometry of wires axes in the individual layers of the triangular strand consists of straight linear and helical segments. The derived mathematical representation of this curve is in the form of parametric equations with variable input parameters which facilitate the determination of the centreline of an arbitrary circular wire of the right and left hand lay triangular one and two-layered strands. Derived geometric equations were used for the generation of accurate 3D geometric and computational strand models. The correctness of the derived parametric equations and performance of the generated strand model are controlled by visualizations. The 3D computational model was used for a finite element behaviour analysis of the two-layered triangular strand subjected to tension loadings. Illustrative examples are presented to highlight the benefits of the proposed geometric parametric equations and computational modelling procedures by using the finite element method.