This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept ...This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.展开更多
Labelled transition systems(LTSs) are widely used to formally describe system behaviour.The labels of LTS are extended to offer a more satisfactory description of behaviour by refining the abstract labels into multiva...Labelled transition systems(LTSs) are widely used to formally describe system behaviour.The labels of LTS are extended to offer a more satisfactory description of behaviour by refining the abstract labels into multivariate polynomials.These labels can be simplified by numerous numerical approximation methods.Those LTSs that can not apply failures semantics equivalence in description and verification may have a chance after using approximation on labels.The technique that combines approximation and failures semantics equivalence effectively alleviates the computational complexity and minimizes LTS.展开更多
Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. ...The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. Among those, a lot of solutions are new.展开更多
By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system....By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.展开更多
Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial s...Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial systems (or polynomial equations).By solving Lorenz equations,it is shown that our algo-rithm is efficient and powerful.展开更多
Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference positi...Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference position using the data provided by the Po- sitioning and Orientation System (POS) and obtain the mathematical relationships between the image points and ground reference points. The second step is to apply polynomial distortion model and Bilinear Interpolation to get the final precise rectified images. In this step, a reference image is required and some ground control points (GCPs) are selected. Experiments showed that the final rectified images are satisfactory, and that our two-step rectification algorithm is very effective.展开更多
This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis fo...This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi Bézier curves and discuss some of their properties. At last, we give an example and extend the range of the parameter variable t to arbitrary close interval [r, s] （r〈s）.展开更多
The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a repr...The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a representation of the Wiener model is the need to estimate the nonlinear function from the input and output data, without the intermediate signal availability. This paper presents a methodology for the nonlinear system identification of a Wiener type model, using methods for subspaces and polynomials of Chebyshev. The subspace methods used are MOESP （multivariable output-error state space） and N4SID （numerical algorithms for subspace state space system identification）. A simulated example is presented to compare the performance of these algorithms.展开更多
Wheel/rail relationship is a fundamental problem of railway system. Wear of wheel profiles has great effect on vehicle performance. Thus, it is important not just for the analysis of wear characteristics but for its p...Wheel/rail relationship is a fundamental problem of railway system. Wear of wheel profiles has great effect on vehicle performance. Thus, it is important not just for the analysis of wear characteristics but for its prediction. Actual wheel profiles of the high-speed trains on service were measured in the high-speed line and the wear characteristics were analyzed which came to the following results. The wear location was centralized from-15 mm to 25 mm. The maximum wear value appeared at the area of 5 mm from tread center far from wheel flange and it was less than 1.5 mm. Then, wheel wear was fitted to get the polynomial functions on different locations and operation mileages. A binary numerical prediction model was raised to predict wheel wear. The prediction model was proved by vehicle system dynamics and wheel/rail contact geometry. The results show that the prediction model can reflect wear characteristics of measured profiles and vehicle performances.展开更多
The continuous changing impacts appeared in all solution understanding approaches in the projects management field （especially in the construction field of work） by adopting dynamic solution paths. The paper will de...The continuous changing impacts appeared in all solution understanding approaches in the projects management field （especially in the construction field of work） by adopting dynamic solution paths. The paper will define what argue to be a better relational model for project management constraints （time, cost and scope）. This new model will increase the success factors of any complex program/project. This is a qualitative research adopting a new avenue of investigation by following different approach of attributing project activities with social phenomena, and supporting phenomenon with field of observations rather than mathematical method by emerging solution from human, and ants＇ colonies successful practices. The results will show the correct approach of relation between the triple constraints considering the relation as multi agents system having specified communication channels based on agents locations. Information will be transferred between agents, and action would be taken based on constraint agents locations in the project structure allowing immediate changes abilities in order to overcome issues of over budget, behind schedule and additional scope impact. This is complex adaptive system having self organized technique, and cybernetic control. Resulted model can be used for improving existing project management methodologies.展开更多
In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness o...In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness of the syzygy criterion, but the proof for the correctness of the rewritten criterion was left. Since then, F5 has been studied extensively. Some proofs for the correctness of F5 were proposed, but these proofs are valid only under some extra assumptions. In this paper, we give a proof for the correctness of F5B, an equivalent version of F5 in Buchberger＇s style. The proof is valid for both homogeneous and non-homogeneous polynomial systems. Since this proof does not depend on the computing order of the S-pairs, any strategy of selecting S-pairs could be used in F5B or F5. Furthermore, we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs.展开更多
In this paper, we study the number of limit cycles appeared in Hopf bifurcations of a Lienard system with multiple parameters. As an application to some polynomial Lienard systems of the form x= y, y= -gin（x） - fn...In this paper, we study the number of limit cycles appeared in Hopf bifurcations of a Lienard system with multiple parameters. As an application to some polynomial Lienard systems of the form x= y, y= -gin（x） - fn（X）y, we obtain a new lower bound of maximal number of limit cycles which appear in Hopf bifurcation for arbitrary degrees m and n.展开更多
文摘随着企业现代化管理水平的提高,企业中使用计算机辅助管理的水平,也正在日益提高。一些大型的,中型的,或比较先进的企业,计算机辅助管理的水平,正在由单项系统向多项系统过渡,进而向综合处理的管理信息系统(MIS)发展,这是一种趋势。综合 MIS,它的特点是水平高,功能强。相应的技术要求也高,投资额大,成功与失败的因素很复杂,因而风险性很大。为了降低风险度,减少不必要的失误,有必要对企业实施以计算机为基础的综合 MIS
文摘This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.
基金National Natural Science Foundation of China(No.11371003)Natural Science Foundations of Guangxi,China(No.2011GXNSFA018154,No.2012GXNSFGA060003)+2 种基金Science and Technology Foundation of Guangxi,China(No.10169-1)Scientific Research Project from Guangxi Education Department,China(No.201012MS274)Open Research Fund Program of Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis,China(No.HCIC201301)
文摘Labelled transition systems(LTSs) are widely used to formally describe system behaviour.The labels of LTS are extended to offer a more satisfactory description of behaviour by refining the abstract labels into multivariate polynomials.These labels can be simplified by numerous numerical approximation methods.Those LTSs that can not apply failures semantics equivalence in description and verification may have a chance after using approximation on labels.The technique that combines approximation and failures semantics equivalence effectively alleviates the computational complexity and minimizes LTS.
文摘Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
基金The project supported by Scientific Reseaxch Fund of Education Department of Heilongjiang Province of China under Grant No. 11511008
文摘The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. Among those, a lot of solutions are new.
文摘By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.
文摘Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial systems (or polynomial equations).By solving Lorenz equations,it is shown that our algo-rithm is efficient and powerful.
基金Project (No. 02DZ15001) supported by Shanghai Science and Technology Development Funds, China
文摘Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference position using the data provided by the Po- sitioning and Orientation System (POS) and obtain the mathematical relationships between the image points and ground reference points. The second step is to apply polynomial distortion model and Bilinear Interpolation to get the final precise rectified images. In this step, a reference image is required and some ground control points (GCPs) are selected. Experiments showed that the final rectified images are satisfactory, and that our two-step rectification algorithm is very effective.
基金Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000)
文摘This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi Bézier curves and discuss some of their properties. At last, we give an example and extend the range of the parameter variable t to arbitrary close interval [r, s] （r〈s）.
文摘The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a representation of the Wiener model is the need to estimate the nonlinear function from the input and output data, without the intermediate signal availability. This paper presents a methodology for the nonlinear system identification of a Wiener type model, using methods for subspaces and polynomials of Chebyshev. The subspace methods used are MOESP （multivariable output-error state space） and N4SID （numerical algorithms for subspace state space system identification）. A simulated example is presented to compare the performance of these algorithms.
基金Project(U1234208)supported by the Major Program of the National Natural Science Foundation of ChinaProject(2013J008-A)supported by the Research and Development Plan of Major Tasks in Science and Technology China Railways Co.Ltd.,China
文摘Wheel/rail relationship is a fundamental problem of railway system. Wear of wheel profiles has great effect on vehicle performance. Thus, it is important not just for the analysis of wear characteristics but for its prediction. Actual wheel profiles of the high-speed trains on service were measured in the high-speed line and the wear characteristics were analyzed which came to the following results. The wear location was centralized from-15 mm to 25 mm. The maximum wear value appeared at the area of 5 mm from tread center far from wheel flange and it was less than 1.5 mm. Then, wheel wear was fitted to get the polynomial functions on different locations and operation mileages. A binary numerical prediction model was raised to predict wheel wear. The prediction model was proved by vehicle system dynamics and wheel/rail contact geometry. The results show that the prediction model can reflect wear characteristics of measured profiles and vehicle performances.
文摘The continuous changing impacts appeared in all solution understanding approaches in the projects management field （especially in the construction field of work） by adopting dynamic solution paths. The paper will define what argue to be a better relational model for project management constraints （time, cost and scope）. This new model will increase the success factors of any complex program/project. This is a qualitative research adopting a new avenue of investigation by following different approach of attributing project activities with social phenomena, and supporting phenomenon with field of observations rather than mathematical method by emerging solution from human, and ants＇ colonies successful practices. The results will show the correct approach of relation between the triple constraints considering the relation as multi agents system having specified communication channels based on agents locations. Information will be transferred between agents, and action would be taken based on constraint agents locations in the project structure allowing immediate changes abilities in order to overcome issues of over budget, behind schedule and additional scope impact. This is complex adaptive system having self organized technique, and cybernetic control. Resulted model can be used for improving existing project management methodologies.
基金supported by National Key Basic Research Project of China (Grant No.2011CB302400)National Natural Science Foundation of China (Grant Nos. 10971217 and 61121062)
文摘In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness of the syzygy criterion, but the proof for the correctness of the rewritten criterion was left. Since then, F5 has been studied extensively. Some proofs for the correctness of F5 were proposed, but these proofs are valid only under some extra assumptions. In this paper, we give a proof for the correctness of F5B, an equivalent version of F5 in Buchberger＇s style. The proof is valid for both homogeneous and non-homogeneous polynomial systems. Since this proof does not depend on the computing order of the S-pairs, any strategy of selecting S-pairs could be used in F5B or F5. Furthermore, we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs.
基金supported by National Natural Science Foundation of China (Grant No.11271261)
文摘In this paper, we study the number of limit cycles appeared in Hopf bifurcations of a Lienard system with multiple parameters. As an application to some polynomial Lienard systems of the form x= y, y= -gin（x） - fn（X）y, we obtain a new lower bound of maximal number of limit cycles which appear in Hopf bifurcation for arbitrary degrees m and n.
