# zbMATH — the first resource for mathematics

## Liu, Xing

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 Author ID: liu.xing Published as: Liu, X.; Liu, Xing
 Documents Indexed: 79 Publications since 1987
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#### Co-Authors

 0 single-authored 7 Han, Hongyu 7 Peng, Daiyuan 3 Liu, Mingzhu 3 Potra, Florian-Alexandru 3 Zhou, Liang 3 Zhou, Limengnan 2 Ban, Xiaojuan 2 Deng, Weihua 2 Sun, Yijing 2 Wang, Xiaokun 2 Yu, Xueheng 2 Zhang, Mingjun 1 Bian, Enrong 1 Che, Haijun 1 Chen, Ke-wan 1 Chen, Zeyu 1 Cui, Xuyang 1 Guo, Cuihua 1 Guo, Rui 1 Han, Songcheng 1 Hao, Ying 1 He, Runzi 1 He, Xuefeng 1 Huang, Fusheng 1 Li, Guifang 1 Li, He Lin 1 Li, Shengqiang 1 Li, Song 1 Liu, Lipei 1 Liu, Weixin 1 Liu, Wenjun J. 1 Ma, Yanqin 1 Ma, Zheng 1 Peng, Enda 1 Song, Minghui 1 Song, Xiaobao 1 Su, Chengjian 1 Sun, Hao 1 Sun, Shulin 1 Tang, Yongchao 1 Teng, Wenshun 1 Tian, Bo 1 Tian, Desheng 1 Wang, Huijuan 1 Wang, Jun 1 Wang, Yanmei 1 Wei, Feng 1 Wen, Zhi-yu 1 Wu, Di 1 Wu, Lianghua 1 Xu, Yuting 1 Yang, Chengwu 1 Yang, Jingming 1 Yang, Zhen 1 Yin, Baoji 1 Yin, Xian-fang 1 Yuan, Chaowei 1 Zegarlinski, Boguslaw 1 Zhang, Aiguo 1 Zhang, Guilai 1 Zhang, Haiqiang 1 Zhang, Rong 1 Zhang, Sheng 1 Zhang, Yalan 1 Zhu, Jinfu 1 Zhu, Laiyi 1 Zhu, Xiaojie
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#### Serials

 4 Designs, Codes and Cryptography 3 Journal of Systems Engineering 3 Cryptography and Communications 2 Acta Automatica Sinica 2 Optimization Methods & Software 2 Systems Engineering and Electronics 2 Advances in Mathematics of Communications 2 Symmetry 1 IEEE Transactions on Information Theory 1 International Journal of Control 1 Journal of the Franklin Institute 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Journal of Computational and Applied Mathematics 1 Theoretical Computer Science 1 Applied Mathematics and Mechanics. (English Edition) 1 Mathematics in Practice and Theory 1 Applied Numerical Mathematics 1 Journal of Jiangxi Normal University. Natural Science Edition 1 Journal of Scientific Computing 1 Numerical Algorithms 1 Journal of Partial Differential Equations 1 SIAM Journal on Optimization 1 Journal of Nanjing University of Aeronautics and Astronautics 1 Computational and Applied Mathematics 1 Fractals 1 Transactions of Nanjing University of Aeronautics & Astronautics 1 Mathematical Problems in Engineering 1 Discrete Dynamics in Nature and Society 1 Journal of Systems Science and Complexity 1 Communications on Pure and Applied Analysis 1 Analysis in Theory and Applications 1 Control and Decision
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#### Fields

 13 Information and communication theory, circuits (94-XX) 7 Numerical analysis (65-XX) 7 Operations research, mathematical programming (90-XX) 6 Partial differential equations (35-XX) 6 Systems theory; control (93-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Probability theory and stochastic processes (60-XX) 3 Ordinary differential equations (34-XX) 3 Fluid mechanics (76-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functional analysis (46-XX)

#### Citations contained in zbMATH

39 Publications have been cited 200 times in 176 Documents Cited by Year
Multiple positive solutions for Kirchhoff type problems with singularity. Zbl 1270.35242
Liu, Xing; Sun, Yijing
2013
On complete convergence for arrays of row-wise negatively associated random variables. Zbl 1146.60025
Chen, P.; Hu, T.-C.; Liu, X.; Volodin, A.
2008
Existence of positive solutions for a Kirchhoff type problem with critical exponent. Zbl 1265.35077
Sun, Yijing; Liu, Xing
2012
Predictor-corrector methods for sufficient linear complementarity problems in a wide neighborhood of the central path. Zbl 1087.90078
Potra, Florian A.; Liu, Xing
2005
Corrector-predictor methods for sufficient linear complementarity problems in a wide neighborhood of the central path. Zbl 1128.90058
Liu, Xing; Potra, Florian A.
2006
Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates. Zbl 1033.74019
Liu, X.; Wang, Q.; Quek, S. T.
2002
Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties. Zbl 1355.94036
Liu, Xing; Peng, Daiyuan; Han, Hongyu
2014
Linear multistep methods for impulsive differential equations. Zbl 1248.65076
Liu, Xing; Song, M. H.; Liu, M. Z.
2012
Asymptotic stability of Runge-Kutta methods for nonlinear differential equations with piecewise continuous arguments. Zbl 1309.65084
Liu, Xing; Liu, Ming-Zhu
2015
On low-hit-zone frequency-hopping sequence sets with optimal partial Hamming correlation. Zbl 1355.94033
Han, Hongyu; Peng, Daiyuan; Liu, Xing
2014
Analytic and numerical exponential asymptotic stability of nonlinear impulsive differential equations. Zbl 1291.65237
Liu, Xing; Zhang, G. L.; Liu, M. Z.
2014
Linear multistep methods for impulsive delay differential equations. Zbl 1426.65085
Liu, X.; Zeng, Y. M.
2018
A two-stage resource allocation model for lifeline systems quick response with vulnerability analysis. Zbl 1346.91116
Zhang, C.; Liu, X.; Jiang, YP.; Fan, B.; Song, X.
2016
A new shock/discontinuity detector. Zbl 1280.76026
Oliveira, M.; Lu, P.; Liu, X.; Liu, Chaoqun
2010
Influence of temperature change on column buckling of multiwalled carbon nanotubes. Zbl 1217.82140
Zhang, Y. Q.; Liu, X.; Zhao, J. H.
2008
Blade penetration into a vortex core with and without axial core flow. Zbl 1065.76055
Liu, X.; Marshall, J. S.
2004
Training of Elman networks and dynamic system modelling. Zbl 0850.93186
Pham, D. T.; Liu, X.
1996
Elastic stability of plates with varying rigidities. Zbl 0825.73940
Harik, I. E.; Liu, X.; Ekambaram, R.
1991
Robust vehicle routing problem with hard time windows under demand and travel time uncertainty. Zbl 1391.90064
Hu, C.; Lu, J.; Liu, X.; Zhang, G.
2018
Adaptive terminal sliding mode based thruster fault tolerant control for underwater vehicle in time-varying ocean currents. Zbl 1395.93160
Zhang, Mingjun; Liu, Xing; Yin, Baoji; Liu, Weixin
2015
Sets of frequency hopping sequences under aperiodic Hamming correlation: upper bound and optimal constructions. Zbl 1300.94038
Liu, Xing; Peng, Daiyuan
2014
An efficient moving grid algorithm for large deformation. Zbl 1137.65411
Qin, N.; Liu, X.; Xia, H.
2005
Block appointment systems for outpatient clinics with multiple doctors. Zbl 1140.90450
Liu, L.; Liu, X.
1998
Physiological age, health costs, and their interrelation. Zbl 1403.62188
Govorun, M.; Jones, B. L.; Liu, X.; Stanford, D. A.
2018
Darboux transformation and soliton solutions for the generalized coupled variable-coefficient nonlinear Schrödinger-Maxwell-Bloch system with symbolic computation. Zbl 1274.35358
Guo, Rui; Tian, Bo; Liu, Xing; Zhang, Hai-Qiang; Liu, Wen-Jun
2012
Capacitated production planning with outsourcing in an OKP company. Zbl 1157.90394
Liu, X.; Tu, Y. L.
2008
Speed-up and slow-down collisions in laser-induced non-sequential multiple ionization. Zbl 1117.78305
Figueira de Morisson Faria, C.; Liu, X.
2007
Analytic solution to free vibration of rectangular plates. Zbl 0925.73258
Harik, I. E.; Liu, X.; Balakrishnan, N.
1992
Analytic and numerical stability of delay differential equations with variable impulses. Zbl 1428.34121
Liu, X.; Zeng, Y. M.
2019
Multi-objective Stackelberg game model for water supply networks against interdictions with incomplete information. Zbl 1403.90127
Jiang, J.; Liu, X.
2018
Frequency hopping sequences with optimal aperiodic Hamming correlation by interleaving techniques. Zbl 1357.94058
Liu, Xing; Peng, Daiyuan
2017
Hidden Markov model for municipal waste generation forecasting under uncertainties. Zbl 1346.62162
Jiang, P.; Liu, X.
2016
New lower bounds on the aperiodic Hamming correlations of frequency hopping sequences with low hit zone. Zbl 1393.94910
Han, Hongyu; Peng, Daiyuan; Liu, Xing
2015
Investigation of a novel elastic-mechanical wheel transmission under light duty conditions. Zbl 1338.70005
Chen, Yangzhi; Liu, X.; Chetwynd, D. G.; Huang, P.
2008
Frequency-dependent data weighting in global gravity field modeling from satellite data contaminated by non-stationary noise. Zbl 1138.86308
Ditmar, P.; Klees, R.; Liu, X.
2007
Classical aspects of laser-induced non-sequential double ionization above and below the threshold. Zbl 1154.78313
Figueira de Morisson Faria, C.; Liu, X.; Becker, W.
2006
A Stackelberg differential games solution to a problem of optimal intertemporal investment and tax rate design. Zbl 1121.91315
Zhang, Rong; Liu, Xing
2004
Modelling and prediction using GMDH networks of Adalines with nonlinear preprocessors. Zbl 0825.93040
Pham, D. T.; Liu, X.
1994
A hybrid approach to deductive uncertain inference. Zbl 0647.68095
Liu, X.; Gammerman, A.
1988
Analytic and numerical stability of delay differential equations with variable impulses. Zbl 1428.34121
Liu, X.; Zeng, Y. M.
2019
Linear multistep methods for impulsive delay differential equations. Zbl 1426.65085
Liu, X.; Zeng, Y. M.
2018
Robust vehicle routing problem with hard time windows under demand and travel time uncertainty. Zbl 1391.90064
Hu, C.; Lu, J.; Liu, X.; Zhang, G.
2018
Physiological age, health costs, and their interrelation. Zbl 1403.62188
Govorun, M.; Jones, B. L.; Liu, X.; Stanford, D. A.
2018
Multi-objective Stackelberg game model for water supply networks against interdictions with incomplete information. Zbl 1403.90127
Jiang, J.; Liu, X.
2018
Frequency hopping sequences with optimal aperiodic Hamming correlation by interleaving techniques. Zbl 1357.94058
Liu, Xing; Peng, Daiyuan
2017
A two-stage resource allocation model for lifeline systems quick response with vulnerability analysis. Zbl 1346.91116
Zhang, C.; Liu, X.; Jiang, YP.; Fan, B.; Song, X.
2016
Hidden Markov model for municipal waste generation forecasting under uncertainties. Zbl 1346.62162
Jiang, P.; Liu, X.
2016
Asymptotic stability of Runge-Kutta methods for nonlinear differential equations with piecewise continuous arguments. Zbl 1309.65084
Liu, Xing; Liu, Ming-Zhu
2015
Adaptive terminal sliding mode based thruster fault tolerant control for underwater vehicle in time-varying ocean currents. Zbl 1395.93160
Zhang, Mingjun; Liu, Xing; Yin, Baoji; Liu, Weixin
2015
New lower bounds on the aperiodic Hamming correlations of frequency hopping sequences with low hit zone. Zbl 1393.94910
Han, Hongyu; Peng, Daiyuan; Liu, Xing
2015
Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties. Zbl 1355.94036
Liu, Xing; Peng, Daiyuan; Han, Hongyu
2014
On low-hit-zone frequency-hopping sequence sets with optimal partial Hamming correlation. Zbl 1355.94033
Han, Hongyu; Peng, Daiyuan; Liu, Xing
2014
Analytic and numerical exponential asymptotic stability of nonlinear impulsive differential equations. Zbl 1291.65237
Liu, Xing; Zhang, G. L.; Liu, M. Z.
2014
Sets of frequency hopping sequences under aperiodic Hamming correlation: upper bound and optimal constructions. Zbl 1300.94038
Liu, Xing; Peng, Daiyuan
2014
Multiple positive solutions for Kirchhoff type problems with singularity. Zbl 1270.35242
Liu, Xing; Sun, Yijing
2013
Existence of positive solutions for a Kirchhoff type problem with critical exponent. Zbl 1265.35077
Sun, Yijing; Liu, Xing
2012
Linear multistep methods for impulsive differential equations. Zbl 1248.65076
Liu, Xing; Song, M. H.; Liu, M. Z.
2012
Darboux transformation and soliton solutions for the generalized coupled variable-coefficient nonlinear Schrödinger-Maxwell-Bloch system with symbolic computation. Zbl 1274.35358
Guo, Rui; Tian, Bo; Liu, Xing; Zhang, Hai-Qiang; Liu, Wen-Jun
2012
A new shock/discontinuity detector. Zbl 1280.76026
Oliveira, M.; Lu, P.; Liu, X.; Liu, Chaoqun
2010
On complete convergence for arrays of row-wise negatively associated random variables. Zbl 1146.60025
Chen, P.; Hu, T.-C.; Liu, X.; Volodin, A.
2008
Influence of temperature change on column buckling of multiwalled carbon nanotubes. Zbl 1217.82140
Zhang, Y. Q.; Liu, X.; Zhao, J. H.
2008
Capacitated production planning with outsourcing in an OKP company. Zbl 1157.90394
Liu, X.; Tu, Y. L.
2008
Investigation of a novel elastic-mechanical wheel transmission under light duty conditions. Zbl 1338.70005
Chen, Yangzhi; Liu, X.; Chetwynd, D. G.; Huang, P.
2008
Speed-up and slow-down collisions in laser-induced non-sequential multiple ionization. Zbl 1117.78305
Figueira de Morisson Faria, C.; Liu, X.
2007
Frequency-dependent data weighting in global gravity field modeling from satellite data contaminated by non-stationary noise. Zbl 1138.86308
Ditmar, P.; Klees, R.; Liu, X.
2007
Corrector-predictor methods for sufficient linear complementarity problems in a wide neighborhood of the central path. Zbl 1128.90058
Liu, Xing; Potra, Florian A.
2006
Classical aspects of laser-induced non-sequential double ionization above and below the threshold. Zbl 1154.78313
Figueira de Morisson Faria, C.; Liu, X.; Becker, W.
2006
Predictor-corrector methods for sufficient linear complementarity problems in a wide neighborhood of the central path. Zbl 1087.90078
Potra, Florian A.; Liu, Xing
2005
An efficient moving grid algorithm for large deformation. Zbl 1137.65411
Qin, N.; Liu, X.; Xia, H.
2005
Blade penetration into a vortex core with and without axial core flow. Zbl 1065.76055
Liu, X.; Marshall, J. S.
2004
A Stackelberg differential games solution to a problem of optimal intertemporal investment and tax rate design. Zbl 1121.91315
Zhang, Rong; Liu, Xing
2004
Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates. Zbl 1033.74019
Liu, X.; Wang, Q.; Quek, S. T.
2002
Block appointment systems for outpatient clinics with multiple doctors. Zbl 1140.90450
Liu, L.; Liu, X.
1998
Training of Elman networks and dynamic system modelling. Zbl 0850.93186
Pham, D. T.; Liu, X.
1996
Modelling and prediction using GMDH networks of Adalines with nonlinear preprocessors. Zbl 0825.93040
Pham, D. T.; Liu, X.
1994
Analytic solution to free vibration of rectangular plates. Zbl 0925.73258
Harik, I. E.; Liu, X.; Balakrishnan, N.
1992
Elastic stability of plates with varying rigidities. Zbl 0825.73940
Harik, I. E.; Liu, X.; Ekambaram, R.
1991
A hybrid approach to deductive uncertain inference. Zbl 0647.68095
Liu, X.; Gammerman, A.
1988
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#### Cited by 332 Authors

 11 Liao, Jiafeng 7 Tang, Chun-Lei 6 Han, Hongyu 6 Peng, Daiyuan 6 Shen, Aiting 6 Volodin, Andrei I. 5 Hu, Shuhe 5 Liu, Xing 5 Wang, Xuejun 5 Zhou, Limengnan 4 Darvay, Zsolt 4 Li, Hongying 4 Liang, Hongbin 4 Ma, Zheng 3 Chen, Pingyan 3 Kheirfam, Behrouz 3 Lei, Chunyu 3 Lesaja, Goran 3 Liu, Xinquan 3 Potra, Florian-Alexandru 3 Rajasekaran, Sundaramoorthy 3 Terlaky, Tamás 3 Wang, Guoqiang 3 Wilson, Antony John 3 Xie, Qilin 3 Yan, Baoqiang 3 Zhang, Peng 2 Alves, Claudianor Oliveira 2 Arefi, Mohammad Mehdi 2 Asadi, Soodabeh 2 Chu, Changmu 2 Hashemi, Sh. Hosseini 2 Hu, Tienchung 2 Illés, Tibor 2 Li, Xiaoqin 2 Liu, Jiu 2 Mansouri, Hossein 2 Naimen, Daisuke 2 Qian, Xiaotao 2 Qiu, Dehua 2 Rahimi, Gholam H. 2 Salahi, Maziar 2 Sung, Soohak 2 Tang, Chunlei 2 Wang, Changyuan 2 Wang, Dechen 2 Wang, Xinghui 2 Wu, Yi 2 Wu, Yongfeng 2 Zeng, Yumei 2 Zhang, Chengjian 2 Zhang, Guilai 2 Zhang, Sheng 2 Zhong, Xiaojing 1 Agarwal, Ravi P. 1 Al-Refa’ei, Mahmoud H. 1 Alimohammady, Mohsen 1 Amini-Dehak, Mohammad 1 Amiri, Hassan Kaffash 1 Antony, S. Joseph 1 Ashoori, A. R. 1 Atai, Ali Asghar 1 Azaiez, M. Naceur 1 Azaripour, S. 1 Baghani, Mostafa 1 Bai, Yanqin 1 Balakrishnan, Ganesh Priya 1 Balaras, Elias 1 Bambozzi de Oliveira, Maria Luísa 1 Bauer, Frank 1 Ben Yaghlane, Asma 1 Benali, Khaled 1 Beskese, Ahmet 1 Bezzarga, Mounir 1 Bock, Stefan 1 Boudjeriou, Tahir 1 Bozorgnia, Abolghasem 1 Broglia, Riccardo 1 Bruneel, Herwig 1 Cao, Xiongtao 1 Casorrán, Carlos 1 Chang, Kuang-Chao 1 Chang, Tai-Ping 1 Chao, Wen 1 Chen, Bocong 1 Chen, Chung-Lung 1 Chen, Frank Youhua 1 Chen, Jianhua 1 Chen, Jianqing 1 Chen, Yangzhi 1 Chen, Yiren 1 Chen, Zengqiang 1 Cheng, Bitao 1 Chitsaz, Maryam 1 Cho, Gyeong-Mi 1 Chronopoulos, Dimitrios 1 Cunha, M. A. B. 1 de Klerk, Etienne 1 De Vuyst, Stijn 1 Deng, Xin ...and 232 more Authors
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#### Cited in 92 Serials

 10 Applied Mathematical Modelling 10 European Journal of Operational Research 6 Computers & Mathematics with Applications 5 Journal of Mathematical Analysis and Applications 5 Applied Mathematics and Computation 5 Journal of Optimization Theory and Applications 5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 4 Acta Mechanica 4 Journal of Fluid Mechanics 4 Applied Mathematics Letters 4 Designs, Codes and Cryptography 3 Journal of the Franklin Institute 3 Journal of Mathematical Physics 3 Meccanica 3 Applied Mathematics. Series B (English Edition) 3 Optimization Methods & Software 3 Journal of Inequalities and Applications 3 Communications on Pure and Applied Analysis 3 Boundary Value Problems 3 Advances in Mathematics of Communications 3 Cryptography and Communications 2 Journal of Computational and Applied Mathematics 2 Journal of Differential Equations 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Insurance Mathematics & Economics 2 Applied Mathematics and Mechanics. (English Edition) 2 Applied Numerical Mathematics 2 Computers & Operations Research 2 Journal of Scientific Computing 2 Journal of Global Optimization 2 Computational Optimization and Applications 2 Electronic Journal of Differential Equations (EJDE) 2 Computational and Applied Mathematics 2 Discrete Dynamics in Nature and Society 1 Bulletin of the Australian Mathematical Society 1 Computers and Fluids 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 Journal of Mathematical Biology 1 Metrika 1 Periodica Mathematica Hungarica 1 Wave Motion 1 Annales Polonici Mathematici 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 Statistics & Probability Letters 1 Stochastic Analysis and Applications 1 International Journal of Production Research 1 Statistics 1 Optimization 1 Journal of Computer Science and Technology 1 Numerical Methods for Partial Differential Equations 1 Neural Computation 1 Applications of Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Annals of Physics 1 International Journal of Computer Mathematics 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Test 1 Topological Methods in Nonlinear Analysis 1 Statistical Papers 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Convex Analysis 1 Engineering Analysis with Boundary Elements 1 Mathematical Problems in Engineering 1 Journal of Vibration and Control 1 Nonlinear Dynamics 1 Abstract and Applied Analysis 1 Taiwanese Journal of Mathematics 1 Mechanism and Machine Theory 1 European Journal of Mechanics. A. Solids 1 CEJOR. Central European Journal of Operations Research 1 RAIRO. Operations Research 1 Journal of Modern Optics 1 Journal of Systems Science and Complexity 1 Advanced Nonlinear Studies 1 Mediterranean Journal of Mathematics 1 Stochastics 1 Complex Analysis and Operator Theory 1 Discrete and Continuous Dynamical Systems. Series S 1 Algorithms 1 Advances in Mathematical Physics 1 Mathematical Programming Computation 1 Journal of Probability and Statistics 1 Annals of Functional Analysis 1 Journal of the Operations Research Society of China 1 Advances in Nonlinear Analysis 1 East Asian Journal on Applied Mathematics 1 Journal of Function Spaces 1 AMM. Applied Mathematics and Mechanics. (English Edition)
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#### Cited in 24 Fields

 45 Partial differential equations (35-XX) 38 Operations research, mathematical programming (90-XX) 25 Mechanics of deformable solids (74-XX) 24 Probability theory and stochastic processes (60-XX) 22 Numerical analysis (65-XX) 11 Fluid mechanics (76-XX) 10 Information and communication theory, circuits (94-XX) 9 Ordinary differential equations (34-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Statistics (62-XX) 5 Computer science (68-XX) 4 Operator theory (47-XX) 4 Optics, electromagnetic theory (78-XX) 4 Biology and other natural sciences (92-XX) 4 Systems theory; control (93-XX) 3 Quantum theory (81-XX) 2 Integral equations (45-XX) 2 Mechanics of particles and systems (70-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX)