# zbMATH — the first resource for mathematics

## Li, Quansheng

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 Author ID: li.quansheng Published as: Li, Q.; Li, Q. S.; Li, Quan-Sheng; Li, Quansheng
 Documents Indexed: 86 Publications since 1986

#### Co-Authors

 3 single-authored 1 Chang, Long 1 Jian, Yongjun 1 Su, Jie

#### Serials

 3 Journal of Chengdu University of Science and Technology 1 Acta Mechanica Sinica

#### Fields

 3 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX)

#### Citations contained in zbMATH Open

50 Publications have been cited 254 times in 246 Documents Cited by Year
Turbulent boundary layers up to Re$$\theta = 2500$$ studied through simulation and experiment. Zbl 1183.76457
Schlatter, P.; Örlü, R.; Li, Q.; Brethouwer, G.; Fransson, J. H. M.; Johansson, A. V.; Alfredsson, P. H.; Henningson, D. S.
2009
Entropy splitting for high-order numerical simulation of compressible turbulence. Zbl 1139.76332
Sandham, N. D.; Li, Q.; Yee, H. C.
2002
Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method. Zbl 1068.74090
Huang, Y. Q.; Li, Q. S.
2004
Testing serial correlation in semiparametric panel data models. Zbl 0943.62039
Li, Q.; Hsiao, C.
1998
Asymptotic-preserving schemes for multiscale hyperbolic and kinetic equations. Zbl 1366.82029
Hu, J.; Jin, Shi; Li, Q.
2017
Reliability analysis of structures using artificial neural network based genetic algorithms. Zbl 1194.74515
Cheng, Jin; Li, Q. S.
2008
An improved thermal lattice Boltzmann model for flows without viscous heat dissipation and compression work. Zbl 1145.82341
Li, Q.; He, Y. L.; Wang, Y.; Tang, G. H.
2008
Thermomechanical postbuckling of shear deformable laminated cylindrical shells with local geometric imperfections. Zbl 1049.74571
Shen, Hui-Shen; Li, Q. S.
2002
Three-dimensional non-free-parameter lattice-Boltzmann model and its application to inviscid compressible flows. Zbl 1229.76090
Li, Q.; He, Y. L.; Wang, Y.; Tang, G. H.
2009
Postbuckling of shear deformable laminated plates resting on a tensionless elastic foundation subjected to mechanical or thermal loading. Zbl 1079.74544
Shen, Huishen; Li, Q. S.
2004
Four-node incompatible plane and axisymmetric elements with quadratic completeness in the physical space. Zbl 1075.74649
Huang, Y. Q.; Li, Q. S.
2004
Free convection heat and mass transfer from an isothermal sphere to a micropolar regime with Soret/Dufour effects. Zbl 1205.80010
Bég, O. Anwar; Prasad, V. Ramachandra; Vasu, B.; Reddy, N. Bhaskar; Li, Q.; Bhargava, R.
2011
Lattice Boltzmann model for simulating viscous compressible flows. Zbl 1386.76128
Wang, Y.; He, Y. L.; Li, Q.; Tang, G. H.; Tao, W. Q.
2010
Why traction-free? Piezoelectric crack and Coulombic traction. Zbl 1168.74435
Li, Q.; Chen, Y. H.
2008
Classes of exact solutions for buckling of multi-step non-uniform columns with an arbitrary number of cracks subjected to concentrated and distributed axial loads. Zbl 1211.74109
Li, Q. S.
2003
Buckling of shallow spherical shells including the effects of transverse shear deformation. Zbl 1045.74524
Li, Q. S.; Liu, J.; Tang, J.
2003
Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions. Zbl 1032.74559
Shen, Hui Shen; Li, Q. S.
2002
Buckling of an elastically restrained multi-step non-uniform beam with multiple cracks. Zbl 1010.74547
Li, Q. S.
2002
Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading. Zbl 1011.74020
Li, Q. S.
2001
An artificial neural network approach to mechanism kinematic chain isomorphism identification. Zbl 1049.70545
Kong, F. G.; Li, Q.; Zhang, W. J.
1999
Unsteady separation from the leading edge of a thin airfoil. Zbl 1025.76516
Degani, A. T.; Li, Q.; Walker, J. D. A.
1996
A new dynamic one-equation subgrid-scale model for large eddy simulations. Zbl 1183.76778
Huang, Shenghong; Li, Q. S.
2010
Numerical simulations of gas resonant oscillations in a closed tube using lattice Boltzmann method. Zbl 1143.80332
Wang, Y.; He, Y. L.; Li, Q.; Tang, G. H.
2008
Some further development on the eigensystem approach for graph isomorphism detection. Zbl 1074.05059
He, P. R.; Zhang, W. J.; Li, Q.
2005
Calculation of vertical dynamic characteristics of tall buildings with viscous damping. Zbl 0920.73172
Li, Q. S.; Fang, J. Q.; Jeary, A. P.
1998
Numerical analysis for conservation laws using $$l_1$$ minimization. Zbl 1433.65176
Gelb, Anne; Hou, X.; Li, Q.
2019
Inflow turbulence generation methods with large eddy simulation for wind effects on tall buildings. Zbl 1390.76240
Yan, B. W.; Li, Q. S.
2015
Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel. Zbl 1346.76212
Su, Jie; Jian, Yong-Jun; Chang, Long; Li, Quan-Sheng
2013
Computer-aided nonlinear vehicle-bridge interaction analysis. Zbl 1368.74026
Li, Q.; Xu, Y. L.; Wu, D. J.; Chen, Z. W.
2010
Analytical evaluation of dynamic responses of time-varying systems. Zbl 1172.74028
Li, Q. S.
2009
A truly meshless method based on partition of unity quadrature for shape optimization of continua. Zbl 1178.74189
Zou, W.; Zhou, J. X.; Zhang, Z. Q.; Li, Q.
2007
A new approach for bending analysis of thin circular plates with large deflection. Zbl 1112.74417
Li, Q. S.; Liu, Jie; Xiao, H. B.
2004
Free vibration of SDOF systems with arbitrary time-varying coefficients. Zbl 0996.70016
Li, Q. S.
2001
Evaluation of 2D coupled galloping oscillations of slender structures. Zbl 0919.73147
Li, Q. S.; Fang, J. Q.; Jeary, A. P.
1998
Three-dimensional non-orthogonal MRT pseudopotential lattice Boltzmann model for multiphase flows. Zbl 07072846
Li, Q.; Du, D. H.; Fei, L. L.; Luo, Kai H.
2019
On Gorenstein injective and projective comodules. Zbl 1281.16040
Pan, Q. X.; Li, Q.
2013
Optimal estimator for distributed anonymous observers. Zbl 1163.62002
Li, Q.; Wong, W. S.
2009
Inherent relations between the Bueckner integral and the $$J_k$$-integral or the $$M$$-integral in piezoelectric materials containing multiple defects. Zbl 1168.74046
Li, Q.; Chen, Y.-H.
2009
Coupled double-distribution-function lattice Boltzmann model with an adjustable bulk viscosity. Zbl 1353.76076
Li, Q.; He, Y. L.; Gao, Y. J.
2008
Combinatorial optimal design of number and positions of actuators in actively controlled structures using genetic algorithms. Zbl 1236.93126
Li, Q. S.; Liu, D. K.; Tang, J.; Zhang, N.; Tam, C. M.
2004
An exact approach for free vibration analysis of rectangular plates with line-concentrated mass and elastic line-support. Zbl 1092.74529
Li, Q. S.
2003
Randomised Hough transform with error propagation for line and circle detection. Zbl 1035.68103
Li, Q.; Xie, Y.
2003
Frequency domain analysis of fluid-structure interaction in liquid-filled pipe systems by transfer matrix method. Zbl 1087.74533
Li, Q. S.; Yang, Ke; Zhang, Lixiang; Zhang, N.
2002
Fuzzy variational principle and its applications. Zbl 1027.74043
Yang, L. F.; Li, Q. S.; Leung, A. Y. T.; Zhao, Y. L.; Li, G. Q.
2002
The quintic finite element and finite strip with generalized degrees of freedom in structural analysis. Zbl 1049.74049
Li, Q. S.; Yang, L. F.; Ou, X. D.; Li, G. Q.; Liu, D. K.
2001
Analytical solutions for buckling of multi-step non-uniform columns with arbitrary distribution of flexural stiffness or axial distributed loading. Zbl 1006.74039
Li, Q. S.
2001
Exact solutions for free longitudinal vibration of bars with non-uniform cross-sections. Zbl 1012.74022
Li, Q. S.
2000
A new exact approach for determining natural frequencies and mode shapes of non-uniform shear beams with arbitrary distribution of mass or stiffness. Zbl 0968.74032
Li, Q. S.
2000
Exact solutions for longitudinal vibration of rods coupled by translational springs. Zbl 1030.74023
Li, Q. S.; Li, G. Q.; Liu, D. K.
2000
A generic Petri net model for flexible manufacturing systems and its use for FMS control software testing. Zbl 0945.90538
Zhang, W. J.; Li, Q.; Bi, Z. M.; Zha, X. F.
2000
Numerical analysis for conservation laws using $$l_1$$ minimization. Zbl 1433.65176
Gelb, Anne; Hou, X.; Li, Q.
2019
Three-dimensional non-orthogonal MRT pseudopotential lattice Boltzmann model for multiphase flows. Zbl 07072846
Li, Q.; Du, D. H.; Fei, L. L.; Luo, Kai H.
2019
Asymptotic-preserving schemes for multiscale hyperbolic and kinetic equations. Zbl 1366.82029
Hu, J.; Jin, Shi; Li, Q.
2017
Inflow turbulence generation methods with large eddy simulation for wind effects on tall buildings. Zbl 1390.76240
Yan, B. W.; Li, Q. S.
2015
Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel. Zbl 1346.76212
Su, Jie; Jian, Yong-Jun; Chang, Long; Li, Quan-Sheng
2013
On Gorenstein injective and projective comodules. Zbl 1281.16040
Pan, Q. X.; Li, Q.
2013
Free convection heat and mass transfer from an isothermal sphere to a micropolar regime with Soret/Dufour effects. Zbl 1205.80010
Bég, O. Anwar; Prasad, V. Ramachandra; Vasu, B.; Reddy, N. Bhaskar; Li, Q.; Bhargava, R.
2011
Lattice Boltzmann model for simulating viscous compressible flows. Zbl 1386.76128
Wang, Y.; He, Y. L.; Li, Q.; Tang, G. H.; Tao, W. Q.
2010
A new dynamic one-equation subgrid-scale model for large eddy simulations. Zbl 1183.76778
Huang, Shenghong; Li, Q. S.
2010
Computer-aided nonlinear vehicle-bridge interaction analysis. Zbl 1368.74026
Li, Q.; Xu, Y. L.; Wu, D. J.; Chen, Z. W.
2010
Turbulent boundary layers up to Re$$\theta = 2500$$ studied through simulation and experiment. Zbl 1183.76457
Schlatter, P.; Örlü, R.; Li, Q.; Brethouwer, G.; Fransson, J. H. M.; Johansson, A. V.; Alfredsson, P. H.; Henningson, D. S.
2009
Three-dimensional non-free-parameter lattice-Boltzmann model and its application to inviscid compressible flows. Zbl 1229.76090
Li, Q.; He, Y. L.; Wang, Y.; Tang, G. H.
2009
Analytical evaluation of dynamic responses of time-varying systems. Zbl 1172.74028
Li, Q. S.
2009
Optimal estimator for distributed anonymous observers. Zbl 1163.62002
Li, Q.; Wong, W. S.
2009
Inherent relations between the Bueckner integral and the $$J_k$$-integral or the $$M$$-integral in piezoelectric materials containing multiple defects. Zbl 1168.74046
Li, Q.; Chen, Y.-H.
2009
Reliability analysis of structures using artificial neural network based genetic algorithms. Zbl 1194.74515
Cheng, Jin; Li, Q. S.
2008
An improved thermal lattice Boltzmann model for flows without viscous heat dissipation and compression work. Zbl 1145.82341
Li, Q.; He, Y. L.; Wang, Y.; Tang, G. H.
2008
Why traction-free? Piezoelectric crack and Coulombic traction. Zbl 1168.74435
Li, Q.; Chen, Y. H.
2008
Numerical simulations of gas resonant oscillations in a closed tube using lattice Boltzmann method. Zbl 1143.80332
Wang, Y.; He, Y. L.; Li, Q.; Tang, G. H.
2008
Coupled double-distribution-function lattice Boltzmann model with an adjustable bulk viscosity. Zbl 1353.76076
Li, Q.; He, Y. L.; Gao, Y. J.
2008
A truly meshless method based on partition of unity quadrature for shape optimization of continua. Zbl 1178.74189
Zou, W.; Zhou, J. X.; Zhang, Z. Q.; Li, Q.
2007
Some further development on the eigensystem approach for graph isomorphism detection. Zbl 1074.05059
He, P. R.; Zhang, W. J.; Li, Q.
2005
Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method. Zbl 1068.74090
Huang, Y. Q.; Li, Q. S.
2004
Postbuckling of shear deformable laminated plates resting on a tensionless elastic foundation subjected to mechanical or thermal loading. Zbl 1079.74544
Shen, Huishen; Li, Q. S.
2004
Four-node incompatible plane and axisymmetric elements with quadratic completeness in the physical space. Zbl 1075.74649
Huang, Y. Q.; Li, Q. S.
2004
A new approach for bending analysis of thin circular plates with large deflection. Zbl 1112.74417
Li, Q. S.; Liu, Jie; Xiao, H. B.
2004
Combinatorial optimal design of number and positions of actuators in actively controlled structures using genetic algorithms. Zbl 1236.93126
Li, Q. S.; Liu, D. K.; Tang, J.; Zhang, N.; Tam, C. M.
2004
Classes of exact solutions for buckling of multi-step non-uniform columns with an arbitrary number of cracks subjected to concentrated and distributed axial loads. Zbl 1211.74109
Li, Q. S.
2003
Buckling of shallow spherical shells including the effects of transverse shear deformation. Zbl 1045.74524
Li, Q. S.; Liu, J.; Tang, J.
2003
An exact approach for free vibration analysis of rectangular plates with line-concentrated mass and elastic line-support. Zbl 1092.74529
Li, Q. S.
2003
Randomised Hough transform with error propagation for line and circle detection. Zbl 1035.68103
Li, Q.; Xie, Y.
2003
Entropy splitting for high-order numerical simulation of compressible turbulence. Zbl 1139.76332
Sandham, N. D.; Li, Q.; Yee, H. C.
2002
Thermomechanical postbuckling of shear deformable laminated cylindrical shells with local geometric imperfections. Zbl 1049.74571
Shen, Hui-Shen; Li, Q. S.
2002
Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions. Zbl 1032.74559
Shen, Hui Shen; Li, Q. S.
2002
Buckling of an elastically restrained multi-step non-uniform beam with multiple cracks. Zbl 1010.74547
Li, Q. S.
2002
Frequency domain analysis of fluid-structure interaction in liquid-filled pipe systems by transfer matrix method. Zbl 1087.74533
Li, Q. S.; Yang, Ke; Zhang, Lixiang; Zhang, N.
2002
Fuzzy variational principle and its applications. Zbl 1027.74043
Yang, L. F.; Li, Q. S.; Leung, A. Y. T.; Zhao, Y. L.; Li, G. Q.
2002
Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading. Zbl 1011.74020
Li, Q. S.
2001
Free vibration of SDOF systems with arbitrary time-varying coefficients. Zbl 0996.70016
Li, Q. S.
2001
The quintic finite element and finite strip with generalized degrees of freedom in structural analysis. Zbl 1049.74049
Li, Q. S.; Yang, L. F.; Ou, X. D.; Li, G. Q.; Liu, D. K.
2001
Analytical solutions for buckling of multi-step non-uniform columns with arbitrary distribution of flexural stiffness or axial distributed loading. Zbl 1006.74039
Li, Q. S.
2001
Exact solutions for free longitudinal vibration of bars with non-uniform cross-sections. Zbl 1012.74022
Li, Q. S.
2000
A new exact approach for determining natural frequencies and mode shapes of non-uniform shear beams with arbitrary distribution of mass or stiffness. Zbl 0968.74032
Li, Q. S.
2000
Exact solutions for longitudinal vibration of rods coupled by translational springs. Zbl 1030.74023
Li, Q. S.; Li, G. Q.; Liu, D. K.
2000
A generic Petri net model for flexible manufacturing systems and its use for FMS control software testing. Zbl 0945.90538
Zhang, W. J.; Li, Q.; Bi, Z. M.; Zha, X. F.
2000
An artificial neural network approach to mechanism kinematic chain isomorphism identification. Zbl 1049.70545
Kong, F. G.; Li, Q.; Zhang, W. J.
1999
Testing serial correlation in semiparametric panel data models. Zbl 0943.62039
Li, Q.; Hsiao, C.
1998
Calculation of vertical dynamic characteristics of tall buildings with viscous damping. Zbl 0920.73172
Li, Q. S.; Fang, J. Q.; Jeary, A. P.
1998
Evaluation of 2D coupled galloping oscillations of slender structures. Zbl 0919.73147
Li, Q. S.; Fang, J. Q.; Jeary, A. P.
1998
Unsteady separation from the leading edge of a thin airfoil. Zbl 1025.76516
Degani, A. T.; Li, Q.; Walker, J. D. A.
1996
all top 5

#### Cited by 547 Authors

 11 Sandham, Neil D. 11 Yee, Helen C. 9 Schlatter, Philipp 9 Sjogreen, Bjorn 8 Ferreira, António Joaquim Mendes 8 Roque, C. M. C. 7 Hu, Xuemei 6 Örlü, Ramis 5 He, Yaling 5 Sandberg, Richard D. 5 Wang, Zhizhong 4 Carrera, Erasmo 4 Cinefra, Maria 4 Henningson, Dan S. 4 Sung, Hyung Jin 4 Yao, Yufeng 3 Caddemi, Salvatore 3 Caliò, Ivo 3 Del Rey Fernández, David C. 3 Hu, Zhiwei 3 Krishnan, Lijesh 3 Li, Qin 3 Liu, Feng 3 Lu, Jianfeng 3 Natal Jorge, Renato Manuel 3 Nguyen-Xuan, Hung 3 Parsani, Matteo 3 Ruban, Anatoly I. 3 Shariyat, M. 3 Shen, Huishen 3 Sun, MingBo 3 Thai, Chien Hoang 3 Touber, Emile 2 Alfredsson, Per Henrik 2 Ashrafizaadeh, Mahmud 2 Bernardini, Matteo 2 Carpenter, Mark H. 2 Cen, Song 2 Chen, Ke 2 Chen, Rongqian 2 Chen, Xiaoming 2 Dalcín, Lisandro D. 2 Farmanborda, Muster Satis 2 Fu, Xiangrong 2 Glaubitz, Jan 2 Grigorenko, Alexander Ya. 2 Hosein, Aiblaastin 2 Hu, Jingwei 2 Huang, Zhensheng 2 Hwang, Jinyul 2 Kuna, Meinhard 2 Kuo, Peien 2 Li, Jianbo 2 Li, Qi 2 Li, Qin Shu 2 Li, Qing 2 Li, Qun 2 Liu, Feng 2 Liu, Qing 2 Liu, Xiaohui 2 Marusic, Ivan 2 Monty, Jason P. 2 Neves, A. M. A. 2 Nguyen-Thanh, Nhon 2 Nguyen-Thoi, Trung 2 Piccardo, Giuseppe 2 Pirozzoli, Sergio 2 Qiu, Ruofan 2 Rabczuk, Timon 2 Rashidi, Mohammad Mehdi 2 Ricoeur, Andreas 2 Roberts, Graham T. 2 Rostami, Behnam 2 Shu, Chang 2 Soares, C. M. M. 2 Sreenivasan, Katepalli R. 2 Talebitooti, Mostafa 2 Tubino, Federica 2 Vinuesa, Ricardo 2 Vovkodav, O. V. 2 Wang, Guofu 2 Wei, Chuanhua 2 Wright, Stephen J. 2 Xiang, Yang 2 Yang, Jin 2 Yaremchenko, Sergiy N. 2 You, Yancheng 2 Yu, Kaiping 2 Yuan, Xianju 2 Zakerzadeh, Hamed 2 Zaki, Tamer A. 2 Zeng, Zhong 2 Zhang, Liangqi 2 Zhang, Riquan 2 Zhang, Xiangxiong 2 Zhao, Rui 2 Zhu, Chengxiang 1 Alashti, R. Akbari 1 Ali, Mohamed M. 1 Anh, Vu Thi Thuy ...and 447 more Authors
all top 5

#### Cited in 72 Serials

 43 Journal of Fluid Mechanics 18 Computers and Fluids 14 Computer Methods in Applied Mechanics and Engineering 14 Journal of Computational Physics 13 Applied Mathematical Modelling 9 Acta Mechanica 9 European Journal of Mechanics. A. Solids 7 Computers & Mathematics with Applications 7 Mathematical Problems in Engineering 6 Journal of Scientific Computing 5 Journal of Vibration and Control 4 International Journal of Solids and Structures 4 Meccanica 4 Communications in Statistics. Theory and Methods 4 Physics of Fluids 3 Applied Mathematics and Computation 3 International Journal for Numerical Methods in Engineering 3 Applied Mathematics and Mechanics. (English Edition) 3 Computational Mechanics 3 Archive of Applied Mechanics 3 Engineering Analysis with Boundary Elements 3 Multiscale Modeling & Simulation 2 International Journal for Numerical Methods in Fluids 2 Physica A 2 Shock Waves 2 Acta Mathematicae Applicatae Sinica. English Series 2 Communications in Statistics. Simulation and Computation 2 SIAM Journal on Scientific Computing 2 International Applied Mechanics 2 Mechanism and Machine Theory 2 European Journal of Mechanics. B. Fluids 2 International Journal of Modern Physics C 2 Journal of Systems Science and Complexity 2 International Journal of Computational Methods 2 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Modern Physics Letters B 1 International Journal of Engineering Science 1 International Journal of Systems Science 1 Journal of Engineering Mathematics 1 Journal of the Franklin Institute 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Theoretical and Computational Fluid Dynamics 1 Information Sciences 1 Journal of Econometrics 1 Journal of Optimization Theory and Applications 1 Mechanics Research Communications 1 SIAM Journal on Numerical Analysis 1 Statistics & Probability Letters 1 Journal of Time Series Analysis 1 Applied Numerical Mathematics 1 Econometric Reviews 1 Applied Mathematics Letters 1 Economics Letters 1 Pattern Recognition 1 Continuum Mechanics and Thermodynamics 1 Communications in Numerical Methods in Engineering 1 Statistical Papers 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 International Journal of Computational Fluid Dynamics 1 Journal of Shanghai University 1 Flow, Turbulence and Combustion 1 Engineering Computations 1 Econometric Theory 1 Journal of Turbulence 1 Journal of Applied Mathematics 1 AStA. Allgemeines Statistisches Archiv 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Acta Mechanica Sinica 1 Frontiers of Mathematics in China 1 Arabian Journal for Science and Engineering 1 International Journal of Applied and Computational Mathematics 1 SN Partial Differential Equations and Applications
all top 5

#### Cited in 22 Fields

 114 Fluid mechanics (76-XX) 83 Mechanics of deformable solids (74-XX) 51 Numerical analysis (65-XX) 21 Statistics (62-XX) 13 Partial differential equations (35-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Operations research, mathematical programming (90-XX) 6 Mechanics of particles and systems (70-XX) 6 Classical thermodynamics, heat transfer (80-XX) 4 Systems theory; control (93-XX) 3 Computer science (68-XX) 3 Biology and other natural sciences (92-XX) 2 Combinatorics (05-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)