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1

A complete algorithm for automated discovering of a class of inequality-type theorems

Lu Yang, Xiaorong Hou, Bican Xia

Journal:

SCIENCE CHINA Information Sciences

Year:

2001

Language:

english

File:

PDF, 970 KB

english, 2001

2

A new result on the p-irreducibility of binding polynomials

Bican Xia, Lu Yang

Journal:

Computers & Mathematics with Applications

Year:

2004

Language:

english

File:

PDF, 422 KB

english, 2004

3

On Solving Parametric Polynomial Systems

Moreno Maza, Marc, Xia, Bican, Xiao, Rong

Journal:

Mathematics in Computer Science

Year:

2012

Language:

english

File:

PDF, 369 KB

english, 2012

4

DISCOVERER

Journal:

ACM Communications in Computer Algebra

Year:

2007

Language:

english

File:

PDF, 164 KB

english, 2007

5

[ACM Press the 2005 international symposium - Beijing, China (2005.07.24-2005.07.27)] Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05 - Stability analysis of biological systems with real solution classification

Wang, Dongming, Xia, Bican

Year:

2005

Language:

english

File:

PDF, 218 KB

english, 2005

6

An Algorithm for Isolating the Real Solutions of Semi-algebraic Systems

Bican Xia, Lu Yang

Journal:

Journal of Symbolic Computation

Year:

2002

Language:

english

File:

PDF, 298 KB

english, 2002

7

A semi-algebraic approach for asymptotic stability analysis

Zhikun She, Bican Xia, Rong Xiao, Zhiming Zheng

Journal:

Nonlinear Analysis Hybrid Systems

Year:

2009

Language:

english

File:

PDF, 547 KB

english, 2009

8

Real solution isolation using interval arithmetic

Bican Xia, Ting Zhang

Journal:

Computers & Mathematics with Applications

Year:

2006

File:

PDF, 1.04 MB

2006

9

Termination of linear programs with nonlinear constraints

Bican Xia, Zhihai Zhang

Journal:

Journal of Symbolic Computation

Year:

2010

Language:

english

File:

PDF, 465 KB

english, 2010

10

A complete algorithm for counting real solutions of polynomial systems of equations and inequalities

Bican Xia, Xiaorong Hou

Journal:

Computers & Mathematics with Applications

Year:

2002

Language:

english

File:

PDF, 561 KB

english, 2002

11

Symbolic decision procedure for termination of linear programs

Bican Xia, Lu Yang, Naijun Zhan, Zhihai Zhang

Journal:

Formal Aspects of Computing

Year:

2011

Language:

english

File:

PDF, 293 KB

english, 2011

12

Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems

Qiang Guan, Long Wang, BiCan Xia, Lu Yang, WenSheng Yu, ZhenBing Zeng

Journal:

SCIENCE CHINA Information Sciences

Year:

2007

Language:

english

File:

PDF, 648 KB

english, 2007

13

Real solution isolation with multiplicity of zero-dimensional triangular systems

ZhiHai Zhang, Tian Fang, BiCan Xia

Journal:

SCIENCE CHINA Information Sciences

Year:

2011

Language:

english

File:

PDF, 189 KB

english, 2011

14

Recent advances in program verification through computer algebra

Lu Yang, Chaochen Zhou, Naijun Zhan, Bican Xia

Journal:

Frontiers of Computer Science

Year:

2010

Language:

english

File:

PDF, 241 KB

english, 2010

15

A New Method for Real Root Isolation of Univariate Polynomials

Ting Zhang, Bican Xia

Journal:

Mathematics in Computer Science

Year:

2007

Language:

english

File:

PDF, 274 KB

english, 2007

16

Condition number based complexity estimate for solving polynomial systems

Zhikun She, Bican Xia, Zhiming Zheng

Journal:

Journal of Computational and Applied Mathematics

Year:

2011

Language:

english

File:

PDF, 264 KB

english, 2011

17

Triangular decomposition of semi-algebraic systems

Changbo Chen, James H. Davenport, John P. May, Marc Moreno Maza, Bican Xia, Rong Xiao

Journal:

Journal of Symbolic Computation

Year:

2013

Language:

english

File:

PDF, 383 KB

english, 2013

18

Computing with semi-algebraic sets: Relaxation techniques and effective boundaries

Chen, Changbo, Davenport, James H., Moreno Maza, Marc, Xia, Bican, Xiao, Rong

Journal:

Journal of Symbolic Computation

Year:

2013

Language:

english

File:

PDF, 493 KB

english, 2013

19

Discovering polynomial Lyapunov functions for continuous dynamical systems

She, Zhikun, Li, Haoyang, Xue, Bai, Zheng, Zhiming, Xia, Bican

Journal:

Journal of Symbolic Computation

Year:

2013

Language:

english

File:

PDF, 436 KB

english, 2013

20

Generic regular decompositions for generic zero-dimensional systems

Tang, XiaoXian, Chen, ZhengHong, Xia, BiCan

Journal:

SCIENCE CHINA Information Sciences

Year:

2014

Language:

english

File:

PDF, 304 KB

english, 2014

21

[IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - Stabilization of the Belgian Chocolate System via Low-order Controllers

Guannan, He, Long, Wang, Bican, Xia, Wensheng, Yu

Year:

2006

Language:

english

File:

PDF, 464 KB

english, 2006

22

Special algorithm for stability analysis of multistable biological regulatory systems

Hong, Hoon, Tang, Xiaoxian, Xia, Bican

Journal:

Journal of Symbolic Computation

Year:

2015

Language:

english

File:

PDF, 1.72 MB

english, 2015

23

Smaller SDP for SOS decomposition

Dai, Liyun, Xia, Bican

Journal:

Journal of Global Optimization

Year:

2015

Language:

english

File:

PDF, 1.04 MB

english, 2015

24

Computing the real solutions of polynomial systems with the RegularChains library in Maple

Chen, Changbo, Davenport, James H., Lemaire, François, Maza, Marc Moreno, Xia, Bican, Xiao, Rong, Xie, Yuzhen

Journal:

ACM Communications in Computer Algebra

Year:

2012

Language:

english

File:

PDF, 227 KB

english, 2012

25

Proving inequalities and solving global optimization problems via simplified CAD projection

Han, Jingjun, Jin, Zhi, Xia, Bican

Journal:

Journal of Symbolic Computation

Year:

2016

Language:

english

File:

PDF, 599 KB

english, 2016

26

[ACM Press the 36th international symposium - San Jose, California, USA (2011.06.08-2011.06.11)] Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11 - Computing with semi-algebraic sets represented by triangular decomposition

Chen, Changbo, Davenport, James H., Moreno Maza, Marc, Xia, Bican, Xiao, Rong

Year:

2011

Language:

english

File:

PDF, 524 KB

english, 2011

27

[ACM Press the 39th International Symposium - Kobe, Japan (2014.07.23-2014.07.25)] Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14 - Constructing fewer open cells by GCD computation in CAD projection

Han, Jingjun, Dai, Liyun, Xia, Bican

Year:

2014

Language:

english

File:

PDF, 198 KB

english, 2014

28

Generic regular decompositions for parametric polynomial systems

Chen, Zhenghong, Tang, Xiaoxian, Xia, Bican

Journal:

Journal of Systems Science and Complexity

Year:

2015

Language:

english

File:

PDF, 279 KB

english, 2015

29

Automated Inequality Proving and Discovering || Proving Inequalities Beyond the Tarski Model

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 256 KB

english, 2016

30

Automated Inequality Proving and Discovering || Real Root Isolation

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 306 KB

english, 2016

31

Automated Inequality Proving and Discovering || Real Root Counting

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 340 KB

english, 2016

32

Automated Inequality Proving and Discovering || Successive Difference Substitution

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 311 KB

english, 2016

33

Automated Inequality Proving and Discovering || Zero Decomposition of Polynomial System

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 397 KB

english, 2016

34

Automated Inequality Proving and Discovering || Real Root Classification

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 534 KB

english, 2016

35

Automated Inequality Proving and Discovering || Open Weak CAD

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 3.13 MB

english, 2016

36

Automated Inequality Proving and Discovering || Basics of Elimination Method

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 295 KB

english, 2016

37

Automated Inequality Proving and Discovering || Dimension-Decreasing Algorithm

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 252 KB

english, 2016

38

Automated Inequality Proving and Discovering || Triangularization of Semi-Algebraic System

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 258 KB

english, 2016

39

Automated Inequality Proving and Discovering || SOS Decomposition

Xia, Bican, Yang, Lu

Year:

2016

Language:

english

File:

PDF, 361 KB

english, 2016

40

Open weak CAD and its applications

Han, Jingjun, Dai, Liyun, Hong, Hoon, Xia, Bican

Journal:

Journal of Symbolic Computation

Year:

2016

Language:

english

File:

PDF, 1.71 MB

english, 2016

41

Barrier certificates revisited

Dai, Liyun, Gan, Ting, Xia, Bican, Zhan, Naijun

Journal:

Journal of Symbolic Computation

Year:

2016

Language:

english

File:

PDF, 1.20 MB

english, 2016

42

[IEEE 2016 European Control Conference (ECC) - Aalborg, Denmark (2016.6.29-2016.7.1)] 2016 European Control Conference (ECC) - Computing reachable sets of linear vector fields revisited

Gan, Ting, Chen, Mingshuai, Li, Yangjia, Xia, Bican, Zhan, Naijun

Year:

2016

Language:

english

File:

PDF, 734 KB

english, 2016

43

Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Wang, Qiuye, Li, Yangjia, Xia, Bican, Zhan, Naijun

Journal:

Journal of Systems Science and Complexity

Year:

2017

Language:

english

File:

PDF, 271 KB

english, 2017

44

Reachability Analysis for Solvable Dynamical Systems

Gan, Ting, Chen, Mingshuai, Li, Yangjia, Xia, Bican, Zhan, Naijun

Journal:

IEEE Transactions on Automatic Control

Year:

2017

Language:

english

File:

PDF, 1.70 MB

english, 2017

45

A Hybrid Procedure for Finding Real Points on a Real Algebraic Set

Wang, Yu, Xia, Bican

Journal:

Journal of Systems Science and Complexity

Year:

2019

File:

PDF, 280 KB

2019

46

[ACM Press the 2019 - Beijing, China (2019.07.15-2019.07.18)] Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation - ISSAC '19 - An Effective Framework for Constructing Exponent Lattice Basis of Nonzero Algebraic Numbers

Zheng, Tao, Xia, Bican

Year:

2019

Language:

english

File:

PDF, 1.37 MB

english, 2019

47

[ACM Press the 2019 - Beijing, China (2019.07.15-2019.07.18)] Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation - ISSAC '19 - A New Sparse SOS Decomposition Algorithm Based on Term Sparsity

Wang, Jie, Li, Haokun, Xia, Bican

Year:

2019

Language:

english

File:

PDF, 1.45 MB

english, 2019

48

Logcf: An Efficient Tool for Real Root Isolation

Dai, Liyun, Fan, Zhe, Xia, Bican, Zhang, Hanwen

Journal:

Journal of Systems Science and Complexity

Year:

2019

File:

PDF, 371 KB

2019

49

Safety Verification for Random Ordinary Differential Equations

Xue, Bai, Franzle, Martin, Zhan, Naijun, Bogomolov, Sergiy, Xia, Bican

Journal:

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Year:

2020

File:

PDF, 1.65 MB

2020

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