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## Xu, Yuesheng

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 Author ID: xu.yuesheng Published as: Xu, Yuesheng; Xu, Y.; Xu, Yue Sheng Homepage: http://thecollege.syr.edu/people/faculty/pages/math/xu-yuesheng.html External Links: MGP · ORCID · Google Scholar · dblp
 Documents Indexed: 173 Publications since 1984, including 4 Books
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#### Co-Authors

 3 single-authored 27 Micchelli, Charles A. 26 Chen, Zhongying 22 Shen, Lixin 12 Jiang, Ying 12 Weinstein, Stanley E. 10 Wu, Bin 9 Kaneko, Hideaki 8 Zhang, Haizhang 6 Cao, Yanzhao 6 Lu, Yao 6 Zeng, Xueying 6 Zhao, Yunhe 5 Chen, Qiuhui 5 Swetits, John J. 5 Wang, Rui 5 Yang, Hongqi 4 Li, Si 4 Li, Zheng 4 Lu, Jian 4 Song, Guohui 4 Ubhaya, Vasant A. 4 Zhang, Na 4 Zou, Qingsong 3 Chen, Feishe 3 Chen, Xiangling 3 Król, Andrzej 3 Li, Qia 3 Ma, Yunyun 3 Noren, Richard D. 3 Sauer, Thomas 3 Wang, Bo 3 Xu, Chen 2 Bogacki, Przemyslaw 2 Brenner, Marty 2 Deutsch, Frank 2 Fang, Weifu 2 Ford, William F. 2 Huang, Min 2 Liu, Jianqiang 2 Liu, Songtao 2 Qian, Tao 2 Riemenschneider, Sherman D. 2 Schneider, Reinhold 2 Suter, Bruce W. 2 Wang, Yi 2 Yan, Dunyan 2 Ye, Qi 2 Zeng, Taishan 2 Zhang, Yuanyuan 2 Zhou, Aihui 1 Arman, L. 1 Brenner, Susanne Cecelia 1 Brunner, Hermann 1 Cai, Haotao 1 Chen, Jieyang 1 Chen, Yun 1 Cheng, Raymond 1 Dahmen, Wolfgang A. 1 Dai, Daoqing 1 Ding, Shengpei 1 Diogo, Teresa 1 Dumrongpokaphan, Thongchai 1 Fermo, Luisa 1 Ford, Neville J. 1 Guan, Wenchao 1 Han, Guoqiang 1 Herdman, Terry L. 1 Hu, Rizhang 1 Huang, Jiasheng 1 Huang, Norden E. 1 Ken, Hayami 1 Kerr, Gilbert 1 Lenbury, Yongwimon 1 Li, Yonghai 1 Li, Yuesheng 1 Li, Zhiwen 1 Lian, Qiaofang 1 Lima, Pedro Miguel 1 Liu, Bao 1 Liu, Liping 1 Liu, Xiaoxia 1 Liu, Youming 1 Liu, Yuzhen 1 Long, Wenting 1 Ma, Fuming 1 Mao, Dong 1 Nelakanti, Gnaneshwar 1 Ouncharoen, Rujira 1 Padilla, Peter A. 1 Peng, Silong 1 Pennline, James A. 1 Pereverzyev, Sergiy jun. 1 Rahpeymaii, Farzad 1 Ross Schmidtlein, C. 1 Shen, Zuowei 1 Shu, Shi 1 Tao, Qian 1 Vai Mang I 1 Wang, Jiong 1 Wang, Zhuo ...and 16 more Co-Authors
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#### Serials

 19 Advances in Computational Mathematics 15 Journal of Integral Equations and Applications 10 Journal of Computational and Applied Mathematics 10 SIAM Journal on Numerical Analysis 9 Inverse Problems 8 Mathematics of Computation 8 Applied and Computational Harmonic Analysis 7 Journal of Scientific Computing 6 Journal of Complexity 6 International Journal of Numerical Analysis and Modeling 5 Journal of Approximation Theory 5 Applied Numerical Mathematics 5 Journal of Machine Learning Research (JMLR) 4 Proceedings of the American Mathematical Society 3 Applicable Analysis 3 Journal of Mathematical Analysis and Applications 3 Analysis and Applications (Singapore) 3 Inverse Problems and Imaging 2 Numerical Functional Analysis and Optimization 2 Applied Mathematics and Mechanics. (English Edition) 2 Journal of Computational Mathematics 1 Archives of Mechanics 1 Computing 1 Integral Equations and Operator Theory 1 Memoirs of the American Mathematical Society 1 Numerische Mathematik 1 Results in Mathematics 1 Constructive Approximation 1 Northeastern Mathematical Journal 1 Numerical Methods for Partial Differential Equations 1 SIAM Journal on Matrix Analysis and Applications 1 CAD. Computer-Aided Design 1 Science in China. Series A 1 Multidimensional Systems and Signal Processing 1 Linear Algebra and its Applications 1 Numerical Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Acta Mathematica Sinica. English Series 1 Communications on Pure and Applied Analysis 1 Pacific Journal of Optimization 1 Lecture Notes in Pure and Applied Mathematics 1 Cambridge Monographs on Applied and Computational Mathematics 1 Frontiers of Mathematics in China 1 Mathematical Modelling of Natural Phenomena 1 SIAM Journal on Imaging Sciences 1 Advances in Adaptive Data Analysis 1 Science China. Mathematics 1 IEEE Transactions on Circuits and Systems I: Regular Papers 1 Applied and Numerical Harmonic Analysis
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#### Fields

 123 Numerical analysis (65-XX) 47 Integral equations (45-XX) 30 Approximations and expansions (41-XX) 28 Information and communication theory, circuits (94-XX) 21 Computer science (68-XX) 19 Harmonic analysis on Euclidean spaces (42-XX) 17 Partial differential equations (35-XX) 10 Functional analysis (46-XX) 10 Operator theory (47-XX) 9 Operations research, mathematical programming (90-XX) 7 Biology and other natural sciences (92-XX) 6 Ordinary differential equations (34-XX) 5 Statistics (62-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 General and overarching topics; collections (00-XX) 3 Potential theory (31-XX) 3 Integral transforms, operational calculus (44-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of deformable solids (74-XX) 2 Systems theory; control (93-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX)

#### Citations contained in zbMATH Open

145 Publications have been cited 1,809 times in 906 Documents Cited by Year
Proximity algorithms for image models: denoising. Zbl 1216.94015
Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng
2011
A hybrid collocation method for Volterra integral equations with weakly singular kernels. Zbl 1042.65106
Cao, Yanzhao; Herdman, Terry; Xu, Yuesheng
2003
Universal kernels. Zbl 1222.68266
Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang
2006
Gauss-type quadratures for weakly singular integrals and their application to Fredholm integral equations of the second kind. Zbl 0799.65023
Kaneko, Hideaki; Xu, Yuesheng
1994
Fast collocation methods for second kind integral equations. Zbl 1016.65107
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
2002
Higher-order finite volume methods for elliptic boundary value problems. Zbl 1266.65180
Chen, Zhongying; Wu, Junfeng; Xu, Yuesheng
2012
Using the matrix refinement equation for the construction of wavelets on invariant sets. Zbl 0815.42019
Micchelli, Charles A.; Xu, Yuesheng
1994
Superconvergence of the iterated Galerkin methods for Hammerstein equations. Zbl 0860.65138
Kaneko, Hideaki; Xu, Yuesheng
1996
The Petrov-Galerkin method for second kind integral equations. II: Multiwavelet schemes. Zbl 0915.65134
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
1997
The Petrov-Galerkin and iterated Petrov-Galerkin methods for second-kind integral equations. Zbl 0911.65143
Chen, Zhongying; Xu, Yuesheng
1998
Reproducing kernel Banach spaces for machine learning. Zbl 1235.68217
Zhang, Haizhang; Xu, Yuesheng; Zhang, Jun
2009
Reconstruction and decomposition algorithms for biorthogonal multiwavelets. Zbl 0872.42010
Micchelli, Charles A.; Xu, Yuesheng
1997
Multilevel augmentation methods for solving operator equations. Zbl 1077.65053
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2005
Wavelet Galerkin methods for second-kind integral equations. Zbl 0913.65129
Micchelli, Charles A.; Xu, Yuesheng; Zhao, Yunhe
1997
A multilevel method for solving operator equations. Zbl 0990.65059
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
2001
A construction of interpolating wavelets on invariant sets. Zbl 1051.65009
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
1999
An implementation of fast wavelet Galerkin methods for integral equations of the second kind. Zbl 1047.65112
Fang, Weifu; Wang, Yi; Xu, Yuesheng
2004
A multilevel augmentation method for solving ill-posed operator equations. Zbl 1088.65051
Chen, Zhongying; Xu, Yuesheng; Yang, Hongqi
2006
A B-spline approach for empirical mode decompositions. Zbl 1092.94007
Chen, Qiuhui; Huang, Norden; Riemenschneider, Sherman; Xu, Yuesheng
2006
Numerical solutions for weakly singular Hammerstein equations and their superconvergence. Zbl 0764.65085
Kaneko, Hideaki; Noren, Richard D.; Xu, Yuesheng
1992
The Bedrosian identity for the Hilbert transform of product functions. Zbl 1101.44002
Xu, Yuesheng; Yan, Dunyan
2006
Hybrid collocation methods for Fredholm integral equations with weakly singular kernels. Zbl 1119.65122
Cao, Yanzhao; Huang, Min; Liu, Liping; Xu, Yuesheng
2007
Nonlinear functionals of wavelet expansions – adaptive reconstruction and fast evaluation. Zbl 0962.65118
Dahmen, Wolfgang; Schneider, Reinhold; Xu, Yuesheng
2000
Degenerate kernel method for Hammerstein equations. Zbl 0711.65118
Kaneko, Hideaki; Xu, Yuesheng
1991
Fourier spectrum characterization of Hardy spaces and applications. Zbl 1169.42003
Qian, Tao; Xu, Yuesheng; Yan, Dunyan; Yan, Lixin; Yu, Bo
2009
Proximity algorithms for the L1/TV image denoising model. Zbl 1275.65014
Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng; Zeng, Xueying
2013
Discrete wavelet Petrov–Galerkin methods. Zbl 0998.65120
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
2002
Regularity of the solution of Hammerstein equations with weakly singular kernel. Zbl 0706.45005
Kaneko, Hideaki; Noren, Richard; Xu, Yuesheng
1990
A construction of higher-order finite volume methods. Zbl 1307.65144
Chen, Zhongying; Xu, Yuesheng; Zhang, Yuanyuan
2015
Singularity preserving Galerkin methods for weakly singular Fredholm integral equations. Zbl 0819.65139
Cao, Yanzhao; Xu, Yuesheng
1994
A fast Fourier-Galerkin method for solving singular boundary integral equations. Zbl 1175.65140
Cai, Haotao; Xu, Yuesheng
2008
Multilevel augmentation methods for differential equations. Zbl 1123.65075
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2006
Fast Fourier-Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition. Zbl 1193.65206
Jiang, Ying; Xu, Yuesheng
2010
Fast multilevel augmentation methods for solving Hammerstein equations. Zbl 1195.65224
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2009
Orthonormal bases with nonlinear phases. Zbl 1213.42126
Qian, Tao; Wang, Rui; Xu, Yuesheng; Zhang, Haizhang
2010
Fast discrete algorithms for sparse Fourier expansions of high dimensional functions. Zbl 1184.65124
Jiang, Ying; Xu, Yuesheng
2010
Multiscale methods for Fredholm integral equations. Zbl 1332.65188
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
2015
A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models. Zbl 1273.65085
Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng
2012
Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction. Zbl 1270.94018
Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng
2012
Multi-step fixed-point proximity algorithms for solving a class of optimization problems arising from image processing. Zbl 1326.65069
Li, Qia; Shen, Lixin; Xu, Yuesheng; Zhang, Na
2015
Multiplicative noise removal in imaging: an exp-model and its fixed-point proximity algorithm. Zbl 1360.94043
Lu, Jian; Shen, Lixin; Xu, Chen; Xu, Yuesheng
2016
The discrete Petrov-Galerkin method for weakly singular integral equations. Zbl 0974.65122
Chen, Zhongying; Xu, Yuesheng; Zhao, Jiansheng
1999
Multi-parameter Tikhonov regularization for linear ill-posed operator equations. Zbl 1174.65018
Chen, Zhongying; Lu, Yao; Xu, Yuesheng; Yang, Hongqi
2008
Superconvergence of the iterated hybrid collocation method for weakly singular Volterra integral equations. Zbl 1141.65091
Huang, Min; Xu, Yuesheng
2006
Refinable kernels. Zbl 1222.68337
Xu, Yuesheng; Zhang, Haizhang
2007
Superconvergence of the iterated degenerate kernel method. Zbl 1020.65099
Kaneko, H.; Padilla, P.; Xu, Y.
2001
A fast wavelet collocation method for integral equations on polygons. Zbl 1104.65132
Wang, Yi; Xu, Yuesheng
2005
Fast collocation methods for solving ill-posed integral equations of the first kind. Zbl 1167.65073
Chen, Zhongying; Xu, Yuesheng; Yang, Hongqi
2008
Multi-parameter regularization methods for high-resolution image reconstruction with displacement errors. Zbl 1374.94240
Lu, Yao; Shen, Lixin; Xu, Yuesheng
2007
Integral equation models for image restoration: high accuracy methods and fast algorithms. Zbl 1256.94012
Lu, Yao; Shen, Lixin; Xu, Yuesheng
2010
Multi-level iteration methods for solving integral equations of the second kind. Zbl 1041.65107
Fang, Weifu; Ma, Fuming; Xu, Yuesheng
2002
An extrapolation method for a class of boundary integral equations. Zbl 0851.65077
Xu, Yuesheng; Zhao, Yunhe
1996
A fast Fourier-Galerkin method solving a boundary integral equation for the biharmonic equation. Zbl 1307.31008
Jiang, Ying; Wang, Bo; Xu, Yuesheng
2014
Aggregation of regularized solutions from multiple observation models. Zbl 1369.65078
Chen, Jieyang; Pereverzyev, Sergiy jun.; Xu, Yuesheng
2015
Multilevel preconditioning for the finite volume method. Zbl 1250.65132
Li, Yonghai; Shu, Shi; Xu, Yuesheng; Zou, Qingsong
2012
Wavelet inpainting with the $$\ell_{0}$$ sparse regularization. Zbl 1338.65061
Shen, Lixin; Xu, Yuesheng; Zeng, Xueying
2016
Generalized Mercer kernels and reproducing kernel Banach spaces. Zbl 1455.68009
Xu, Yuesheng; Ye, Qi
2019
Galerkin methods based on Hermite splines for singular perturbation problems. Zbl 1107.65064
Liu, Song-Tao; Xu, Yuesheng
2006
Fast numerical collocation solutions of integral equations. Zbl 1137.65067
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2007
Two-dimensional empirical mode decomposition by finite elements. Zbl 1149.74395
Xu, Y.; Liu, Bao; Liu, J.; Riemenschneider, S.
2006
Optimal learning of bandlimited functions from localized sampling. Zbl 1180.65182
Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang
2009
Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs. Zbl 1193.65232
Wang, Bo; Wang, Rui; Xu, Yuesheng
2010
Degree reduction of Bézier curves by uniform approximation with endpoint interpolation. Zbl 0837.65007
Bogacki, Przemyslaw; Weinstein, Stanley E.; Xu, Yuesheng
1995
Adaptive wavelet methods for elliptic operator equations with nonlinear terms. Zbl 1025.65058
Xu, Yuesheng; Zou, Qingsong
2003
Fast Boolean approximation methods for solving integral equations in high dimensions. Zbl 1085.65126
Xu, Yuesheng; Zhou, Aihui
2004
Error control strategies for numerical integrations in fast collocation methods. Zbl 1079.65132
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2005
A fast collocation method for eigen-problems of weakly singular integral operators. Zbl 1203.65284
Chen, Zhongying; Nelakanti, Gnaneshwar; Xu, Yuesheng; Zhang, Yongdong
2009
A construction of refinable sets for interpolating wavelets. Zbl 0921.65097
Micchelli, Charles A.; Sauer, Thomas; Xu, Yuesheng
1998
Correction method and extrapolation method for singular two-point boundary value problems. Zbl 0971.65066
Han, Guoqiang; Wang, Jiong; Ken, Hayami; Xu, Yuesheng
2000
Deterministic convergence of an online gradient method for neural networks. Zbl 1066.68111
Wu, Wei; Xu, Yuesheng
2002
An intracellular delay-differential equation model of the HIV infection and immune control. Zbl 1337.92205
Dumrongpokaphan, T.; Lenbury, Y.; Ouncharoen, R.; Xu, Y.
2007
Fast multilevel augmentation methods for nonlinear boundary integral equations. Zbl 1236.65147
Chen, Xiangling; Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2011
Refinement of reproducing kernels. Zbl 1235.68211
Xu, Yuesheng; Zhang, Haizhang
2009
On the characterization and computation of best monotone approximation in $$L_ p[0,1]$$ for $$1\leq p<\infty$$. Zbl 0693.41016
Swetits, J. J.; Weinstein, S. E.; Xu, Yuesheng
1990
Piecewise linear spectral sequences. Zbl 1061.42020
Liu, Youming; Xu, Yuesheng
2005
B-spline quasi-interpolation on sparse grids. Zbl 1221.65034
Jiang, Ying; Xu, Yuesheng
2011
Optimal $${\mathcal H}_2$$ model reduction for large scale MIMO systems via tangential interpolation. Zbl 1213.93089
Xu, Yuesheng; Zeng, Taishan
2011
Noisy 1-bit compressive sensing: models and algorithms. Zbl 1331.65085
Dai, Dao-Qing; Shen, Lixin; Xu, Yuesheng; Zhang, Na
2016
An analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1099.65116
Schneider, Reinhold; Xu, Yuesheng; Zhou, Aihui
2006
Numerical solutions for weakly singular Fredholm integral equations of the second kind. Zbl 0716.65118
Kaneko, Hideaki; Xu, Yuesheng
1991
The Moreau envelope approach for the L1/TV image denoising model. Zbl 1283.94010
Chen, Feishe; Shen, Lixin; Xu, Yuesheng; Zeng, Xueying
2014
Fast collocation methods for high-dimensional weakly singular integral equations. Zbl 1144.65084
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2008
Multiplicative noise removal with a sparsity-aware optimization model. Zbl 1375.94022
Lu, Jian; Shen, Lixin; Xu, Chen; Xu, Yuesheng
2017
Higher-order finite volume methods. II: Inf-sup condition and uniform local ellipticity. Zbl 1293.65142
Chen, Zhongying; Xu, Yuesheng; Zhang, Yuanyuan
2014
A second-order hybrid finite volume method for solving the Stokes equation. Zbl 1368.65153
Chen, Zhongying; Xu, Yuesheng; Zhang, Jiehua
2017
Multivariate filter banks having matrix factorizations. Zbl 1043.42026
Chen, Qiuhui; Micchelli, Charles A.; Peng, Silong; Xu, Yuesheng
2003
Constrained best approximation in Hilbert space III. Applications of $$n$$-convex functions. Zbl 0995.41500
Deutsch, F.; Ubhaya, V. A.; Ward, J. D.; Xu, Yuesheng
1996
Quadratures for improper integrals and their applications in integral equations. Zbl 0815.65034
Xu, Yuesheng; Zhao, Yunhe
1994
Asymptotic error analysis of a quadrature method for integral equations with Green’s function kernels. Zbl 0978.65126
Ford, William F.; Pennline, James A.; Xu, Yuesheng; Zhao, Yunhe
2000
The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels. Zbl 1381.45009
Brunner, Hermann; Ma, Yunyun; Xu, Yuesheng
2015
Multiscale collocation methods for ill-posed integral equations via a coupled system. Zbl 1244.65237
Chen, Zhongying; Ding, Shengpei; Xu, Yuesheng; Yang, Hongqi
2012
Best quasi-convex uniform approximation. Zbl 0729.41026
Weinstein, S. E.; Xu, Yuesheng
1990
Tree wavelet approximations with applications. Zbl 1081.42031
Xu, Yuesheng; Zou, Qingsong
2005
Shadow block iteration for solving linear systems obtained from wavelet transforms. Zbl 1086.65029
Lu, Yao; Shen, Lixin; Xu, Yuesheng
2005
Computing highly oscillatory integrals. Zbl 1376.65027
Ma, Yunyun; Xu, Yuesheng
2018
Quadratures for boundary integral equations of the first kind with logarithmic kernels. Zbl 0888.65122
Xu, Yuesheng; Zhao, Yunhe
1996
Limit values of derivatives of the Cauchy integrals and computation of the logarithmic potentials. Zbl 1063.65150
Xu, Y.; Chen, H.-L.; Zou, Q.
2004
Fast Fourier-Galerkin methods for nonlinear boundary integral equations. Zbl 1278.65187
Chen, Xiangling; Wang, Rui; Xu, Yuesheng
2013
Two-step fixed-point proximity algorithms for multi-block separable convex problems. Zbl 1368.65088
Li, Qia; Xu, Yuesheng; Zhang, Na
2017
Degenerate kernel schemes by wavelets for nonlinear integral equations on the real line. Zbl 0853.65142
Shen, Zuowei; Xu, Yuesheng
1995
Fixed-point proximity algorithm for minimal norm interpolation. Zbl 1440.15015
Li, Zheng; Micchelli, Charles A.; Xu, Yuesheng
2020
Multiplicative noise removal: nonlocal low-rank model and its proximal alternating reweighted minimization algorithm. Zbl 07292236
Liu, Xiaoxia; Lu, Jian; Shen, Lixin; Xu, Chen; Xu, Yuesheng
2020
Generalized Mercer kernels and reproducing kernel Banach spaces. Zbl 1455.68009
Xu, Yuesheng; Ye, Qi
2019
Functional reproducing kernel Hilbert spaces for non-point-evaluation functional data. Zbl 1423.46046
Wang, Rui; Xu, Yuesheng
2019
Computing highly oscillatory integrals. Zbl 1376.65027
Ma, Yunyun; Xu, Yuesheng
2018
Sparse support vector machines in reproducing kernel Banach spaces. Zbl 1405.65080
Li, Zheng; Xu, Yuesheng; Ye, Qi
2018
A fixed-point proximity approach to solving the support vector regression with the group Lasso regularization. Zbl 1407.65066
Li, Zheng; Song, Guohui; Xu, Yuesheng
2018
A fully discrete fast Fourier-Galerkin method solving a boundary integral equation for the biharmonic equation. Zbl 1401.31011
Jiang, Ying; Wang, Bo; Xu, Yuesheng
2018
Multiplicative noise removal with a sparsity-aware optimization model. Zbl 1375.94022
Lu, Jian; Shen, Lixin; Xu, Chen; Xu, Yuesheng
2017
A second-order hybrid finite volume method for solving the Stokes equation. Zbl 1368.65153
Chen, Zhongying; Xu, Yuesheng; Zhang, Jiehua
2017
Two-step fixed-point proximity algorithms for multi-block separable convex problems. Zbl 1368.65088
Li, Qia; Xu, Yuesheng; Zhang, Na
2017
A finite element method for the one-dimensional prescribed curvature problem. Zbl 1380.65361
Brenner, Susanne C.; Sung, Li-Yeng; Wang, Zhuo; Xu, Yuesheng
2017
High-resolution image reconstruction: an $$\mathrm{env}_{\ell^{1}}/\text{TV}$$ model and a fixed-point proximity algorithm. Zbl 1415.94031
Long, Wenting; Lu, Yao; Shen, Lixin; Xu, Yuesheng
2017
Multiplicative noise removal in imaging: an exp-model and its fixed-point proximity algorithm. Zbl 1360.94043
Lu, Jian; Shen, Lixin; Xu, Chen; Xu, Yuesheng
2016
Wavelet inpainting with the $$\ell_{0}$$ sparse regularization. Zbl 1338.65061
Shen, Lixin; Xu, Yuesheng; Zeng, Xueying
2016
Noisy 1-bit compressive sensing: models and algorithms. Zbl 1331.65085
Dai, Dao-Qing; Shen, Lixin; Xu, Yuesheng; Zhang, Na
2016
A collocation method solving integral equation models for image restoration. Zbl 1347.65197
Liu, Yuzhen; Shen, Lixin; Xu, Yuesheng; Yang, Hongqi
2016
Reducing staircasing artifacts in SPECT reconstruction by an infimal convolution regularization. Zbl 1374.92095
Wu, Zhifeng; Li, Si; Zeng, Xueying; Xu, Yuesheng; Krol, Andrzej
2016
A construction of higher-order finite volume methods. Zbl 1307.65144
Chen, Zhongying; Xu, Yuesheng; Zhang, Yuanyuan
2015
Multiscale methods for Fredholm integral equations. Zbl 1332.65188
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
2015
Multi-step fixed-point proximity algorithms for solving a class of optimization problems arising from image processing. Zbl 1326.65069
Li, Qia; Shen, Lixin; Xu, Yuesheng; Zhang, Na
2015
Aggregation of regularized solutions from multiple observation models. Zbl 1369.65078
Chen, Jieyang; Pereverzyev, Sergiy jun.; Xu, Yuesheng
2015
The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels. Zbl 1381.45009
Brunner, Hermann; Ma, Yunyun; Xu, Yuesheng
2015
A fast Fourier-Galerkin method solving a boundary integral equation for the biharmonic equation. Zbl 1307.31008
Jiang, Ying; Wang, Bo; Xu, Yuesheng
2014
The Moreau envelope approach for the L1/TV image denoising model. Zbl 1283.94010
Chen, Feishe; Shen, Lixin; Xu, Yuesheng; Zeng, Xueying
2014
Higher-order finite volume methods. II: Inf-sup condition and uniform local ellipticity. Zbl 1293.65142
Chen, Zhongying; Xu, Yuesheng; Zhang, Yuanyuan
2014
Fast computation of the multidimensional discrete Fourier transform and discrete backward Fourier transform on sparse grids. Zbl 1312.65233
Jiang, Ying; Xu, Yuesheng
2014
Orthogonal polynomial expansions on sparse grids. Zbl 1300.65009
Cao, Yanzhao; Jiang, Ying; Xu, Yuesheng
2014
Nesterov’s algorithm solving dual formulation for compressed sensing. Zbl 1293.65090
Chen, Feishe; Shen, Lixin; Suter, Bruce W.; Xu, Yuesheng
2014
Proximity algorithms for the L1/TV image denoising model. Zbl 1275.65014
Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng; Zeng, Xueying
2013
Fast Fourier-Galerkin methods for nonlinear boundary integral equations. Zbl 1278.65187
Chen, Xiangling; Wang, Rui; Xu, Yuesheng
2013
Fast optimal $$\mathcal H_2$$ model reduction algorithms based on Grassmann manifold optimization. Zbl 1283.65116
Xu, Yuesheng; Zeng, Taishan
2013
On computing with the Hilbert spline transform. Zbl 1268.41005
Micchelli, Charles A.; Xu, Yuesheng; Yu, Bo
2013
Finite rank kernels for multi-task learning. Zbl 1267.41003
Liu, Jianqiang; Micchelli, Charles A.; Wang, Rui; Xu, Yuesheng
2013
Higher-order finite volume methods for elliptic boundary value problems. Zbl 1266.65180
Chen, Zhongying; Wu, Junfeng; Xu, Yuesheng
2012
A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models. Zbl 1273.65085
Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng
2012
Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction. Zbl 1270.94018
Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng
2012
Multilevel preconditioning for the finite volume method. Zbl 1250.65132
Li, Yonghai; Shu, Shi; Xu, Yuesheng; Zou, Qingsong
2012
Multiscale collocation methods for ill-posed integral equations via a coupled system. Zbl 1244.65237
Chen, Zhongying; Ding, Shengpei; Xu, Yuesheng; Yang, Hongqi
2012
Refinement of operator-valued reproducing kernels. Zbl 1283.68310
Zhang, Haizhang; Xu, Yuesheng; Zhang, Qinghui
2012
Multilevel augmentation methods for nonlinear boundary integral equations II: Accelerated quadratures and Newton iterations. Zbl 1271.65145
Chen, Xiangling; Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2012
Proximity algorithms for image models: denoising. Zbl 1216.94015
Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng
2011
Fast multilevel augmentation methods for nonlinear boundary integral equations. Zbl 1236.65147
Chen, Xiangling; Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2011
B-spline quasi-interpolation on sparse grids. Zbl 1221.65034
Jiang, Ying; Xu, Yuesheng
2011
Optimal $${\mathcal H}_2$$ model reduction for large scale MIMO systems via tangential interpolation. Zbl 1213.93089
Xu, Yuesheng; Zeng, Taishan
2011
Filters of wavelets on invariant sets for image denoising. Zbl 1248.94017
Lian, Qiaofang; Shen, Lixin; Xu, Yuesheng; Yang, Lihua
2011
A fast algorithm for computing sample entropy. Zbl 1226.92003
Jiang, Ying; Mao, Dong; Xu, Yuesheng
2011
Fast Fourier-Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition. Zbl 1193.65206
Jiang, Ying; Xu, Yuesheng
2010
Orthonormal bases with nonlinear phases. Zbl 1213.42126
Qian, Tao; Wang, Rui; Xu, Yuesheng; Zhang, Haizhang
2010
Fast discrete algorithms for sparse Fourier expansions of high dimensional functions. Zbl 1184.65124
Jiang, Ying; Xu, Yuesheng
2010
Integral equation models for image restoration: high accuracy methods and fast algorithms. Zbl 1256.94012
Lu, Yao; Shen, Lixin; Xu, Yuesheng
2010
Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs. Zbl 1193.65232
Wang, Bo; Wang, Rui; Xu, Yuesheng
2010
Approximation of high-dimensional kernel matrices by multilevel circulant matrices. Zbl 1197.65045
Song, Guohui; Xu, Yuesheng
2010
Approximation of kernel matrices by circulant matrices and its application in kernel selection methods. Zbl 1191.65190
Song, Guohui; Xu, Yuesheng
2010
Reproducing kernel Banach spaces for machine learning. Zbl 1235.68217
Zhang, Haizhang; Xu, Yuesheng; Zhang, Jun
2009
Fourier spectrum characterization of Hardy spaces and applications. Zbl 1169.42003
Qian, Tao; Xu, Yuesheng; Yan, Dunyan; Yan, Lixin; Yu, Bo
2009
Fast multilevel augmentation methods for solving Hammerstein equations. Zbl 1195.65224
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2009
Optimal learning of bandlimited functions from localized sampling. Zbl 1180.65182
Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang
2009
A fast collocation method for eigen-problems of weakly singular integral operators. Zbl 1203.65284
Chen, Zhongying; Nelakanti, Gnaneshwar; Xu, Yuesheng; Zhang, Yongdong
2009
Refinement of reproducing kernels. Zbl 1235.68211
Xu, Yuesheng; Zhang, Haizhang
2009
Graded Galerkin methods for the high-order convection-diffusion problem. Zbl 1180.65093
Liu, Song-Tao; Xu, Yuesheng
2009
Multiparameter regularization for Volterra kernel identification via multiscale collocation methods. Zbl 1190.65200
Brenner, Marty; Jiang, Ying; Xu, Yuesheng
2009
A fast Fourier-Galerkin method for solving singular boundary integral equations. Zbl 1175.65140
Cai, Haotao; Xu, Yuesheng
2008
Multi-parameter Tikhonov regularization for linear ill-posed operator equations. Zbl 1174.65018
Chen, Zhongying; Lu, Yao; Xu, Yuesheng; Yang, Hongqi
2008
Fast collocation methods for solving ill-posed integral equations of the first kind. Zbl 1167.65073
Chen, Zhongying; Xu, Yuesheng; Yang, Hongqi
2008
Fast collocation methods for high-dimensional weakly singular integral equations. Zbl 1144.65084
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2008
On translation invariant operators which preserve the B-spline recurrence. Zbl 1283.41010
Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang
2008
Hybrid collocation methods for Fredholm integral equations with weakly singular kernels. Zbl 1119.65122
Cao, Yanzhao; Huang, Min; Liu, Liping; Xu, Yuesheng
2007
Refinable kernels. Zbl 1222.68337
Xu, Yuesheng; Zhang, Haizhang
2007
Multi-parameter regularization methods for high-resolution image reconstruction with displacement errors. Zbl 1374.94240
Lu, Yao; Shen, Lixin; Xu, Yuesheng
2007
Fast numerical collocation solutions of integral equations. Zbl 1137.65067
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2007
An intracellular delay-differential equation model of the HIV infection and immune control. Zbl 1337.92205
Dumrongpokaphan, T.; Lenbury, Y.; Ouncharoen, R.; Xu, Y.
2007
On the matrix completion problem for multivariate filter bank construction. Zbl 1128.65111
Chen, Qiuhui; Micchelli, Charles A.; Xu, Yuesheng
2007
Universal kernels. Zbl 1222.68266
Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang
2006
A multilevel augmentation method for solving ill-posed operator equations. Zbl 1088.65051
Chen, Zhongying; Xu, Yuesheng; Yang, Hongqi
2006
A B-spline approach for empirical mode decompositions. Zbl 1092.94007
Chen, Qiuhui; Huang, Norden; Riemenschneider, Sherman; Xu, Yuesheng
2006
The Bedrosian identity for the Hilbert transform of product functions. Zbl 1101.44002
Xu, Yuesheng; Yan, Dunyan
2006
Multilevel augmentation methods for differential equations. Zbl 1123.65075
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2006
Superconvergence of the iterated hybrid collocation method for weakly singular Volterra integral equations. Zbl 1141.65091
Huang, Min; Xu, Yuesheng
2006
Galerkin methods based on Hermite splines for singular perturbation problems. Zbl 1107.65064
Liu, Song-Tao; Xu, Yuesheng
2006
Two-dimensional empirical mode decomposition by finite elements. Zbl 1149.74395
Xu, Y.; Liu, Bao; Liu, J.; Riemenschneider, S.
2006
An analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1099.65116
Schneider, Reinhold; Xu, Yuesheng; Zhou, Aihui
2006
Multilevel augmentation methods for solving operator equations. Zbl 1077.65053
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2005
A fast wavelet collocation method for integral equations on polygons. Zbl 1104.65132
Wang, Yi; Xu, Yuesheng
2005
Error control strategies for numerical integrations in fast collocation methods. Zbl 1079.65132
Chen, Zhongying; Wu, Bin; Xu, Yuesheng
2005
Piecewise linear spectral sequences. Zbl 1061.42020
Liu, Youming; Xu, Yuesheng
2005
Tree wavelet approximations with applications. Zbl 1081.42031
Xu, Yuesheng; Zou, Qingsong
2005
Shadow block iteration for solving linear systems obtained from wavelet transforms. Zbl 1086.65029
Lu, Yao; Shen, Lixin; Xu, Yuesheng
2005
Biorthogonal multivariate filter banks from centrally symmetric matrices. Zbl 1079.65141
Chen, Qiuhui; Micchelli, Charles A.; Xu, Yuesheng
2005
An implementation of fast wavelet Galerkin methods for integral equations of the second kind. Zbl 1047.65112
Fang, Weifu; Wang, Yi; Xu, Yuesheng
2004
Fast Boolean approximation methods for solving integral equations in high dimensions. Zbl 1085.65126
Xu, Yuesheng; Zhou, Aihui
2004
Limit values of derivatives of the Cauchy integrals and computation of the logarithmic potentials. Zbl 1063.65150
Xu, Y.; Chen, H.-L.; Zou, Q.
2004
A hybrid collocation method for Volterra integral equations with weakly singular kernels. Zbl 1042.65106
Cao, Yanzhao; Herdman, Terry; Xu, Yuesheng
2003
Adaptive wavelet methods for elliptic operator equations with nonlinear terms. Zbl 1025.65058
Xu, Yuesheng; Zou, Qingsong
2003
Multivariate filter banks having matrix factorizations. Zbl 1043.42026
Chen, Qiuhui; Micchelli, Charles A.; Peng, Silong; Xu, Yuesheng
2003
Fast collocation methods for second kind integral equations. Zbl 1016.65107
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
2002
Discrete wavelet Petrov–Galerkin methods. Zbl 0998.65120
Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng
2002
Multi-level iteration methods for solving integral equations of the second kind. Zbl 1041.65107
Fang, Weifu; Ma, Fuming; Xu, Yuesheng
2002
Deterministic convergence of an online gradient method for neural networks. Zbl 1066.68111
Wu, Wei; Xu, Yuesheng
2002
The Aitken-Neville scheme in several variables. Zbl 1052.41001
Sauer, Thomas; Xu, Yuesheng
2002
...and 45 more Documents
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#### Cited by 1,243 Authors

 86 Xu, Yuesheng 35 Nelakanti, Gnaneshwar 28 Qian, Tao 27 Chen, Zhongying 26 Shen, Lixin 21 Zhang, Haizhang 19 Micchelli, Charles A. 17 Assari, Pouria 17 Long, Guangqing 17 Zou, Qingsong 15 Lu, Jian 15 Maleknejad, Khosrow 13 Jiang, Ying 13 Kaneko, Hideaki 13 Pedas, Arvet 13 Zhang, Zhimin 12 Chen, Qiuhui 12 Dehghan Takht Fooladi, Mehdi 11 Cai, Haotao 10 Li, Yonghai 9 Brunner, Hermann 9 Das, Payel 9 Panigrahi, Bijaya Laxmi 8 Chen, Jian 8 Chen, Xiangling 8 Tan, Lihui 8 Yang, Lihua 7 Huang, Jin 7 Li, Pingrun 7 Luo, Xingjun 7 Mandal, Moumita 7 Vainikko, Gennadi 7 Wang, Rui 7 Yang, Hongqi 7 Zeng, Xueying 6 Cao, Yanzhao 6 Deng, Guantie 6 Huang, Can 6 Lin, Rongrong 6 Noren, Richard D. 6 Sheng, Baohuai 6 Tamme, Enn 6 Weinstein, Stanley E. 6 Xu, Chen 6 Yan, Dunyan 6 Zhang, Na 6 Zhang, Yuanyuan 5 Allouch, Chafik 5 Jiang, Qingtang 5 Kant, Kapil 5 Li, Songhua 5 Lin, Wei 5 Liu, Songtao 5 Pereverzyev, Sergiy jun. 5 Sahani, Mitali Madhumita 5 Sbibih, Driss 5 Shen, Youjian 5 Song, Guohui 5 Tahrichi, Mohamed 5 Tang, Yuchao 5 Wang, Lilian 5 Wu, Bin 5 Wu, Tingting 5 Ye, Qi 5 Zhang, Yongdong 5 Zou, Yuru 4 Adibi, Hojatollah 4 Cao, Waixiang 4 Cerejeiras, Paula 4 Cheng, Sirui 4 Chui, Charles Kam-tai 4 Cui, Lihong 4 Deutsch, Frank 4 Dong, Qiaoli 4 Fermo, Luisa 4 Huang, Min 4 Kähler, Uwe 4 Kolk, Marek 4 Li, Fanchun 4 Li, Haichou 4 Li, Qia 4 Maleewong, Montri 4 Rane, Akshay S. 4 Rebelo, Magda S. 4 Suter, Bruce W. 4 Ubhaya, Vasant A. 4 Wang, Tongke 4 Wang, Xiang 4 Wu, Jiming 4 Xian, Jun 4 Yang, Min 4 Yang, Suhua 4 Ye, Peixin 4 Zeng, Chunmei 4 Zeng, Taishan 4 Zhang, Xiaoqun 4 Zhou, Yanhui 3 Cao, Wanrong 3 Cattani, Carlo 3 Černá, Dana ...and 1,143 more Authors
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#### Cited in 191 Serials

 73 Journal of Computational and Applied Mathematics 60 Applied Mathematics and Computation 49 Advances in Computational Mathematics 40 Journal of Integral Equations and Applications 33 Journal of Scientific Computing 31 Applied Numerical Mathematics 22 Applied and Computational Harmonic Analysis 18 Journal of Mathematical Analysis and Applications 17 Journal of Complexity 16 Computers & Mathematics with Applications 16 Journal of Approximation Theory 16 International Journal of Computer Mathematics 16 Mathematical Problems in Engineering 15 Numerical Functional Analysis and Optimization 14 Numerical Algorithms 14 Analysis and Applications (Singapore) 12 Inverse Problems 12 Mathematics of Computation 10 SIAM Journal on Numerical Analysis 10 International Journal of Wavelets, Multiresolution and Information Processing 9 Numerische Mathematik 9 Numerical Methods for Partial Differential Equations 9 Inverse Problems and Imaging 8 Applicable Analysis 8 Computational and Applied Mathematics 8 Abstract and Applied Analysis 8 Acta Mathematica Sinica. English Series 8 Journal of Applied Mathematics and Computing 7 Mathematical Methods in the Applied Sciences 7 Mathematics and Computers in Simulation 7 Applied Mathematical Modelling 7 SIAM Journal on Scientific Computing 7 Journal of Machine Learning Research (JMLR) 7 Science China. Mathematics 6 BIT 6 Engineering Analysis with Boundary Elements 6 Complex Variables and Elliptic Equations 6 Complex Analysis and Operator Theory 6 Advances in Applied Mathematics and Mechanics 5 Applied Mathematics Letters 5 Neural Computation 5 Journal of Inequalities and Applications 5 Mediterranean Journal of Mathematics 4 Journal of Computational Physics 4 The Annals of Statistics 4 Information Sciences 4 Proceedings of the American Mathematical Society 4 Science in China. Series A 4 Journal of Global Optimization 4 ETNA. Electronic Transactions on Numerical Analysis 4 Journal of Applied Mathematics 4 Advances in Difference Equations 4 SIAM Journal on Imaging Sciences 4 International Journal of Applied and Computational Mathematics 3 Calcolo 3 International Journal for Numerical Methods in Engineering 3 Acta Applicandae Mathematicae 3 Computer Aided Geometric Design 3 Computational Statistics and Data Analysis 3 Journal of Mathematical Imaging and Vision 3 The Journal of Analysis 3 Applied Mathematics. Series B (English Edition) 3 Journal of Inverse and Ill-Posed Problems 3 Bernoulli 3 Communications in Nonlinear Science and Numerical Simulation 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Frontiers of Mathematics in China 3 East Asian Journal on Applied Mathematics 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of the Franklin Institute 2 Ukrainian Mathematical Journal 2 Kybernetes 2 Mathematische Nachrichten 2 Results in Mathematics 2 Chinese Annals of Mathematics. Series B 2 Neural Networks 2 Multidimensional Systems and Signal Processing 2 Machine Learning 2 Japan Journal of Industrial and Applied Mathematics 2 Advances in Engineering Software 2 Computational Optimization and Applications 2 The Journal of Fourier Analysis and Applications 2 Journal of Vibration and Control 2 Positivity 2 Chaos 2 Fractional Calculus & Applied Analysis 2 Nonlinear Analysis. Real World Applications 2 Foundations of Computational Mathematics 2 International Journal of Computational Methods 2 Fixed Point Theory and Applications 2 Journal of Fixed Point Theory and Applications 2 Electronic Journal of Statistics 2 GEM - International Journal on Geomathematics 2 Journal of Applied Analysis and Computation 2 Mathematical Sciences 2 Journal of Function Spaces 1 Bulletin of the Australian Mathematical Society 1 Computers and Fluids 1 International Journal of Control 1 Journal of Mathematical Physics ...and 91 more Serials
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#### Cited in 47 Fields

 598 Numerical analysis (65-XX) 257 Integral equations (45-XX) 112 Information and communication theory, circuits (94-XX) 101 Partial differential equations (35-XX) 96 Harmonic analysis on Euclidean spaces (42-XX) 93 Computer science (68-XX) 83 Approximations and expansions (41-XX) 73 Operator theory (47-XX) 55 Functional analysis (46-XX) 54 Operations research, mathematical programming (90-XX) 50 Statistics (62-XX) 42 Ordinary differential equations (34-XX) 28 Fluid mechanics (76-XX) 27 Calculus of variations and optimal control; optimization (49-XX) 25 Functions of a complex variable (30-XX) 20 Probability theory and stochastic processes (60-XX) 19 Integral transforms, operational calculus (44-XX) 19 Mechanics of deformable solids (74-XX) 18 Biology and other natural sciences (92-XX) 13 Real functions (26-XX) 11 Systems theory; control (93-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 8 Potential theory (31-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Geophysics (86-XX) 5 General topology (54-XX) 4 Algebraic geometry (14-XX) 3 Special functions (33-XX) 3 Difference and functional equations (39-XX) 3 Convex and discrete geometry (52-XX) 3 Differential geometry (53-XX) 3 Optics, electromagnetic theory (78-XX) 2 Sequences, series, summability (40-XX) 2 Abstract harmonic analysis (43-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Mathematics education (97-XX)