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1

Automated production of traditional proofs for theorems in Euclidean geometry I. The Hilbert intersection point theorems

Jing-Zhong Zhang, Shang-Ching Chou, Xiao-Shan Gao

Journal:

Annals of Mathematics and Artificial Intelligence

Year:

1995

Language:

english

File:

PDF, 1.55 MB

english, 1995

2

Generalized Stewart-Gough platforms and their direct kinematics

Xiao-Shan Gao,, Lei, D., Qizheng Liao,, Gui-Fang Zhang

Journal:

IEEE Transactions on Robotics

Year:

2005

Language:

english

File:

PDF, 708 KB

english, 2005

3

Complete solution classification for the perspective-three-point problem

Xiao-Shan Gao, Xiao-Rong Hou, Jianliang Tang, Hang-Fei Cheng

Journal:

IEEE Transactions on Pattern Analysis and Machine Intelligence

Year:

2003

Language:

english

File:

PDF, 982 KB

english, 2003

4

Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines

Yang, Zhengyuan, Shen, Li-Yong, Yuan, Chun-Ming, Gao, Xiao-Shan

Journal:

Computer-Aided Design

Year:

2015

Language:

english

File:

PDF, 1.30 MB

english, 2015

5

Beam parameters for end diffraction of slab waveguide

Lian-huang Li, Fu-yuan Guo, Yu-jia Peng, Xiao-shan Tang, Rui Gao

Journal:

Optik - International Journal for Light and Electron Optics

Year:

2011

Language:

english

File:

PDF, 313 KB

english, 2011

6

A C-tree decomposition algorithm for 2D and 3D geometric constraint solving

Xiao-Shan Gao, Qiang Lin, Gui-Fang Zhang

Journal:

Computer-Aided Design

Year:

2006

Language:

english

File:

PDF, 311 KB

english, 2006

7

Rational quadratic approximation to real algebraic curves

Xiao-Shan Gao, Ming Li

Journal:

Computer Aided Geometric Design

Year:

2004

Language:

english

File:

PDF, 637 KB

english, 2004

8

Inherently improper surface parametric supports

Eng-Wee Chionh, Xiao-Shan Gao, Li-Yong Shen

Journal:

Computer Aided Geometric Design

Year:

2006

Language:

english

File:

PDF, 137 KB

english, 2006

9

Geometric constraint solving with conics and linkages

Xiao-Shan Gao, Kun Jiang, Chang-Cai Zhu

Journal:

Computer-Aided Design

Year:

2002

Language:

english

File:

PDF, 946 KB

english, 2002

10

Solving spatial basic geometric constraint configurations with locus intersection

Xiao-Shan Gao, Christoph M. Hoffmann, Wei-Qiang Yang

Journal:

Computer-Aided Design

Year:

2004

Language:

english

File:

PDF, 314 KB

english, 2004

11

Solving geometric constraint systems. I. A global propagation approach

Xiao-Shan Gao, Shang-Ching Chou

Journal:

Computer-Aided Design

Year:

1998

Language:

english

File:

PDF, 1010 KB

english, 1998

12

Automated reasoning in differential geometry and mechanics using the characteristic set method

Shang-Ching Chou, Xiao-Shan Gao

Journal:

Journal of Automated Reasoning

Year:

1993

Language:

english

File:

PDF, 820 KB

english, 1993

13

Automated generation of Kempe linkages for algebraic curves and surfaces

Xiao-Shan Gao, Chang-Cai Zhu, Shang-Ching Chou, Jian-Xin Ge

Journal:

Mechanism and Machine Theory

Year:

2001

Language:

english

File:

PDF, 144 KB

english, 2001

14

A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering

Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang

Journal:

Journal of Automated Reasoning

Year:

2000

Language:

english

File:

PDF, 158 KB

english, 2000

15

Chow form for projective differential variety

Wei Li, Xiao-Shan Gao

Journal:

Journal of Algebra

Year:

2012

Language:

english

File:

PDF, 293 KB

english, 2012

16

Certified approximation of parametric space curves with cubic B-spline curves

Li-Yong Shen, Chun-Ming Yuan, Xiao-Shan Gao

Journal:

Computer Aided Geometric Design

Year:

2012

Language:

english

File:

PDF, 670 KB

english, 2012

17

Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming

Wei Fan, Xiao-Shan Gao, Chen-Han Lee…

Journal:

The International Journal of Advanced Manufacturing Technology

Year:

2013

Language:

english

File:

PDF, 948 KB

english, 2013

18

Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration

Ke Zhang, Chun-Ming Yuan, Xiao-Shan Gao

Journal:

The International Journal of Advanced Manufacturing Technology

Year:

2013

Language:

english

File:

PDF, 596 KB

english, 2013

19

Sparse difference resultant

Li, Wei, Yuan, Chun-Ming, Gao, Xiao-Shan

Journal:

Journal of Symbolic Computation

Year:

2015

Language:

english

File:

PDF, 868 KB

english, 2015

20

Extraordinary Optical Transmission in Metallic Nanostructures with a Plasmonic Nanohole Array of Two Connected Slot Antennas

Hu, Ying, Liu, Gui-qiang, Liu, Zheng-qi, Liu, Xiao-shan, Zhang, Xiang-nan, Cai, Zheng-jie, Liu, Mu-lin, Gao, Huo-gui, Gu, Gang

Journal:

Year:

2015

Language:

english

File:

PDF, 1.25 MB

english, 2015

21

ON THE NORMAL PARAMETERIZATION OF CURVES AND SURFACES

GAO, XIAO-SHAN, CHOU, SHANG-CHING

Journal:

International Journal of Computational Geometry & Applications

Year:

1991

Language:

english

File:

PDF, 552 KB

english, 1991

22

Intersection theory in differential algebraic geometry: Generic intersections and the differential Chow form

Gao, Xiao-Shan, Li, Wei, Yuan, Chun-Ming

Journal:

Transactions of the American Mathematical Society

Year:

2013

Language:

english

File:

PDF, 741 KB

english, 2013

23

Linear programming and windowing based feedrate optimization for spline toolpaths

Erkorkmaz, Kaan, Chen, Qing-Ge (Christina), Zhao, Ming-Yong, Beudaert, Xavier, Gao, Xiao-Shan

Journal:

CIRP Annals - Manufacturing Technology

Year:

2017

Language:

english

File:

PDF, 1.63 MB

english, 2017

24

A Zero Structure Theorem for Differential Parametric Systems

Xiao-Shan Gao, Shang-Ching Chou

Journal:

Journal of Symbolic Computation

Year:

1993

File:

PDF, 273 KB

1993

25

Implicitization of rational parametric equations

Xiao-Shan Gao, Shang-Ching Chou

Journal:

Journal of Symbolic Computation

Year:

1992

Language:

english

File:

PDF, 636 KB

english, 1992

26

Evolutionary programming based on non-uniform mutation

Xinchao Zhao, Xiao-Shan Gao, Ze-Chun Hu

Journal:

Applied Mathematics and Computation

Year:

2007

Language:

english

File:

PDF, 376 KB

english, 2007

27

Editorial

Arjeh M Cohen, Xiao-Shan Gao, Nobuki Takayama

Journal:

Journal of Symbolic Computation

Year:

2004

Language:

english

File:

PDF, 33 KB

english, 2004

28

A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs

Ruyong Feng, Xiao-Shan Gao

Journal:

Journal of Symbolic Computation

Year:

2006

Language:

english

File:

PDF, 400 KB

english, 2006

29

A characteristic set method for ordinary difference polynomial systems

Xiao-Shan Gao, Yong Luo, Chunming Yuan

Journal:

Journal of Symbolic Computation

Year:

2009

Language:

english

File:

PDF, 1020 KB

english, 2009

30

Rational solutions of ordinary difference equations

Ruyong Feng, Xiao-Shan Gao, Zhenyu Huang

Journal:

Journal of Symbolic Computation

Year:

2008

Language:

english

File:

PDF, 489 KB

english, 2008

31

Complete numerical isolation of real roots in zero-dimensional triangular systems

Jin-San Cheng, Xiao-Shan Gao, Chee-Keng Yap

Journal:

Journal of Symbolic Computation

Year:

2009

Language:

english

File:

PDF, 1.15 MB

english, 2009

32

Decomposition of ordinary difference polynomials

Mingbo Zhang, Xiao-Shan Gao

Journal:

Journal of Symbolic Computation

Year:

2009

Language:

english

File:

PDF, 884 KB

english, 2009

33

Minimal achievable approximation ratio for MAX-MQ in finite fields

Shang-Wei Zhao, Xiao-Shan Gao

Journal:

Theoretical Computer Science

Year:

2009

Language:

english

File:

PDF, 401 KB

english, 2009

34

Solving geometric constraint systems. II. A symbolic approach and decision of Rc-constructibility

Xiao-Shan Gao, Shang-Ching Chou

Journal:

Computer-Aided Design

Year:

1998

Language:

english

File:

PDF, 947 KB

english, 1998

35

Geometric constraint satisfaction using optimization methods

Jian-Xin Ge, Shang-Ching Chou, Xiao-Shan Gao

Journal:

Computer-Aided Design

Year:

1999

Language:

english

File:

PDF, 337 KB

english, 1999

36

An algorithm for solving partial differential parametric systems

Jimin Wang, Xiao-Shan Gao

Journal:

Discrete Applied Mathematics

Year:

2004

Language:

english

File:

PDF, 243 KB

english, 2004

37

Implicitization of differential rational parametric equations

Journal:

Journal of Symbolic Computation

Year:

2003

Language:

english

File:

PDF, 257 KB

english, 2003

38

Involutive directions and new involutive divisions

Yu-Fu Chen, Xiao-Shan Gao

Journal:

Computers & Mathematics with Applications

Year:

2001

Language:

english

File:

PDF, 959 KB

english, 2001

39

Automated generation of readable proofs with geometric invariants

Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang

Journal:

Journal of Automated Reasoning

Year:

1996

Language:

english

File:

PDF, 1.07 MB

english, 1996

40

Automated generation of readable proofs with geometric invariants

Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang

Journal:

Journal of Automated Reasoning

Year:

1996

Language:

english

File:

PDF, 913 KB

english, 1996

41

Automated reasoning in differential geometry and mechanics using the characteristic set method

Shang-Ching Chou, Xiao-Shan Gao

Journal:

Journal of Automated Reasoning

Year:

1993

Language:

english

File:

PDF, 989 KB

english, 1993

42

Automated production of traditional proofs in solid geometry

Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang

Journal:

Journal of Automated Reasoning

Year:

1995

Language:

english

File:

PDF, 1.67 MB

english, 1995

43

On the parameterization of algebraic curves

Xiao-Shan Gao, Shang-Ching Chou

Journal:

Applicable Algebra in Engineering, Communication and Computing

Year:

1992

Language:

english

File:

PDF, 658 KB

english, 1992

44

Decomposition of ordinary differential polynomials

Xiao-Shan Gao, Mingbo Zhang

Journal:

Applicable Algebra in Engineering, Communication and Computing

Year:

2008

Language:

english

File:

PDF, 316 KB

english, 2008

45

Quadratic approximation to plane parametric curves and its application in approximate implicitization

Ming Li, Xiao-Shan Gao, Shang-Ching Chou

Journal:

The Visual Computer

Year:

2006

Language:

english

File:

PDF, 465 KB

english, 2006

46

Affinity genetic algorithm

Xinchao Zhao, Xiao-Shan Gao

Journal:

Journal of Heuristics

Year:

2007

Language:

english

File:

PDF, 385 KB

english, 2007

47

Visually Dynamic Presentation of Proofs in Plane Geometry

Zheng Ye, Shang-Ching Chou, Xiao-Shan Gao

Journal:

Journal of Automated Reasoning

Year:

2010

Language:

english

File:

PDF, 1.25 MB

english, 2010

48

Visually Dynamic Presentation of Proofs in Plane Geometry

Zheng Ye, Shang-Ching Chou, Xiao-Shan Gao

Journal:

Journal of Automated Reasoning

Year:

2010

Language:

english

File:

PDF, 897 KB

english, 2010

49

On the Probability of the Number of Solutions for the P4P Problem

Xiao-Shan Gao, Jianliang Tang

Journal:

Journal of Mathematical Imaging and Vision

Year:

2006

Language:

english

File:

PDF, 397 KB

english, 2006

50

Generating Symbolic Interpolants for Scattered Data with Normal Vectors

Ming Li, Xiao-Shan Gao, Jin-San Cheng

Journal:

Journal of Computer Science and Technology

Year:

2005

File:

PDF, 746 KB

2005