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## Lu, Jianfeng

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 Author ID: lu.jianfeng Published as: Lu, J.; Lu, J. F.; Lu, Jian-feng; Lu, Jianfeng; Lü, J.-F.; Lü, Jian-Feng; Lü, Jianfeng External Links: ORCID
 Documents Indexed: 145 Publications since 1986, including 2 Books
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#### Co-Authors

 1 single-authored 20 E, Weinan 13 Ying, Lexing 11 Lin, Lin 8 Li, Qin 7 Liu, Jianguo 7 Steinerberger, Stefan 7 Yang, Xu 5 Li, Yingzhou 5 Yang, Haizhao 4 Cao, Yu 4 Marzuola, Jeremy L. 4 Sun, Weiran 4 Yang, Jingyu 3 Cai, Zhenning 3 Ding, Jing 3 Gao, Yuan 3 Lai, Rongjie 3 Lu, Yulong 3 Ming, Pingbing 3 Thicke, Kyle 3 Watson, Alexander B. 3 Weinstein, Michael I. 2 Chen, Ke 2 Daubechies, Ingrid Chantal 2 Delgadillo, Ricardo 2 Dunson, David Brian 2 García-Cervera, Carlos J. 2 Han, Jianmin 2 Li, Lei 2 Li, Xiantao 2 Li, Xingjie Helen 2 Liu, Jingchen 2 Nolen, James H. 2 Peng, Hao 2 Sachs, Matthias 2 Vanden-Eijnden, Eric 2 Wang, Zhe 2 Wright, Stephen J. 2 Yang, Chao 2 Zhou, Xiang 1 Caelli, Terry M. 1 Cai, Ying 1 Car, Roberto 1 Chen, Hongxu 1 Chen, Huajie 1 Chen, Jingrun 1 Chen, Xiaoyun 1 Chen, Ziang 1 Cook, Alexis B. 1 Cornelis, Bruno 1 Dai, Jinwen 1 Dai, Shibin 1 Du, Haishun 1 Du, Qiang 1 Fan, Hong-Yi 1 Fang, Di 1 Gauckler, Ludwig J. 1 Ge, Rong 1 Goodfriend, Alex 1 Gu, Xingjian 1 Huang, Hui 1 Huang, Yufang 1 Jackson, Trachette L. 1 Jin, Lei 1 Khoo, Yuehaw 1 Kohn, Robert Vita 1 Lee, Holden 1 Li, Bo 1 Li, Cuiling 1 Li, Lian 1 Li, Tiejun 1 Li, Wuchen 1 Li, Xiaoou 1 Lin, Ling 1 Liu, Zibu 1 Lu, Yanting 1 Lu, Zhiqi 1 Ma, Zhixin 1 Mao, Anqi 1 Margetis, Dionisios 1 Mendl, Christian B. 1 Meza, Juan C. 1 Moroz, Vitaly 1 Muratov, Cyrill B. 1 Nishimura, Akihiko 1 Ocon, Noelle 1 Ortner, Christoph 1 Osher, Stanley Joel 1 Otto, Felix 1 Pan, Zhigeng 1 Ren, Weiqing 1 Rousset, Frédéric 1 Schratz, Katharina 1 Schweizer, Ben 1 Sen, Deborshee 1 Shen, Chunhua 1 Sogge, Christopher D. 1 Spiliopoulos, Konstantinos V. 1 Tian, Xiaochuan 1 Wang, Li ...and 19 more Co-Authors
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#### Serials

 15 Journal of Computational Physics 9 SIAM Journal on Scientific Computing 8 Multiscale Modeling & Simulation 7 Communications in Mathematical Sciences 6 Communications on Pure and Applied Mathematics 4 Journal of Mathematical Physics 4 Journal of Statistical Physics 4 Mathematics of Computation 3 Archive for Rational Mechanics and Analysis 3 International Journal of Heat and Mass Transfer 3 SIAM Journal on Numerical Analysis 3 Pattern Recognition 3 SIAM Journal on Mathematical Analysis 2 Nonlinearity 2 Biometrika 2 Chinese Annals of Mathematics. Series B 2 Journal of Nonlinear Science 2 Communications in Nonlinear Science and Numerical Simulation 2 Research in the Mathematical Sciences 2 Annals of Mathematical Sciences and Applications 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 Information Processing Letters 1 Physics Letters. A 1 ACM Transactions on Mathematical Software 1 Journal of Functional Analysis 1 Memoirs of the American Mathematical Society 1 Proceedings of the American Mathematical Society 1 Physica D 1 Acta Mathematicae Applicatae Sinica. English Series 1 Probability Theory and Related Fields 1 Constructive Approximation 1 Journal of Computer Science and Technology 1 Asymptotic Analysis 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Scientific Computing 1 The Annals of Applied Probability 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Proceedings of the National Academy of Sciences of the United States of America 1 Potential Analysis 1 Applied and Computational Harmonic Analysis 1 Journal of Huazhong University of Science and Technology 1 Methods and Applications of Analysis 1 Discrete and Continuous Dynamical Systems 1 Journal of Nanjing Normal University. Natural Science Edition 1 Acta Mathematica Sinica. English Series 1 IEEE Transactions on Image Processing 1 Control and Decision 1 Acta Numerica 1 Mathematical Biosciences and Engineering 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Journal of Guangxi Normal University. Natural Science Edition 1 Communications in Applied Mathematics and Computational Science 1 Communications in Computational Physics 1 SIAM Journal on Imaging Sciences 1 Communications in Theoretical Physics 1 Science China. Mathematics 1 SIAM Spotlights 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Transactions of Mathematics and its Applications
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#### Fields

 59 Numerical analysis (65-XX) 52 Partial differential equations (35-XX) 34 Statistical mechanics, structure of matter (82-XX) 29 Quantum theory (81-XX) 17 Mechanics of deformable solids (74-XX) 14 Computer science (68-XX) 13 Probability theory and stochastic processes (60-XX) 8 Fluid mechanics (76-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Statistics (62-XX) 6 Ordinary differential equations (34-XX) 6 Operator theory (47-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Biology and other natural sciences (92-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Approximations and expansions (41-XX) 3 Functional analysis (46-XX) 3 Optics, electromagnetic theory (78-XX) 3 Operations research, mathematical programming (90-XX) 3 Systems theory; control (93-XX) 2 Real functions (26-XX) 2 Integral equations (45-XX) 2 Mechanics of particles and systems (70-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX)

#### Citations contained in zbMATH Open

100 Publications have been cited 692 times in 526 Documents Cited by Year
Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Zbl 1213.42133
Daubechies, Ingrid; Lu, Jianfeng; Wu, Hau-Tieng
2011
A variational perspective on cloaking by anomalous localized resonance. Zbl 1366.78002
Kohn, R. V.; Lu, J.; Schweizer, B.; Weinstein, M. I.
2014
Nonexistence of a minimizer for Thomas–Fermi–Dirac–von Weizsäcker model. Zbl 1301.49002
Lu, Jianfeng; Otto, Felix
2014
Fast construction of hierarchical matrix representation from matrix-vector multiplication. Zbl 1218.65038
Lin, Lin; Lu, Jianfeng; Ying, Lexing
2011
Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Zbl 1182.65072
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Car, Roberto; E, Weinan
2009
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation. Zbl 1251.82008
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
Adaptive synchronization of different chaotic systems with fully unknown parameters. Zbl 1203.93161
Chen, Xiaoyun; Lu, Jianfeng
2007
Convergence of a force-based hybrid method in three dimensions. Zbl 1393.74166
Lu, Jianfeng; Ming, Pingbing
2013
SelInv – an algorithm for selected inversion of a sparse symmetric matrix. Zbl 1365.65069
Lin, Lin; Yang, Chao; Meza, Juan C.; Lu, Jianfeng; Ying, Lexing; E, Weinan
2011
Frozen Gaussian approximation for high frequency wave propagation. Zbl 1272.65075
Lu, Jianfeng; Yang, Xu
2011
Convergence of frozen Gaussian approximation for high-frequency wave propagation. Zbl 1387.35400
Lu, Jianfeng; Yang, Xu
2012
The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born Rule. Zbl 1253.74025
E, Weinan; Lu, Jianfeng
2011
Generalized (complete, lag, anticipated) synchronization of discrete-time chaotic systems. Zbl 1221.37216
Lu, Jianfeng
2008
Nakayama automorphism and applications. Zbl 1396.16004
Lü, J.-F.; Mao, X.-F.; Zhang, J. J.
2017
The Kohn-Sham equation for deformed crystals. Zbl 1435.74001
E, Weinan; Lu, Jianfeng
2013
Reactive trajectories and the transition path process. Zbl 1343.60074
Lu, Jianfeng; Nolen, James
2015
Frozen Gaussian approximation for general linear strictly hyperbolic systems: formulation and Eulerian methods. Zbl 1447.81130
Lu, Jianfeng; Yang, Xu
2012
Localized bases of eigensubspaces and operator compression. Zbl 1205.15017
E, Weinan; Li, Tiejun; Lu, Jianfeng
2010
Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model. Zbl 1277.81117
E, Weinan; Lu, Jianfeng
2010
Solving for high-dimensional committor functions using artificial neural networks. Zbl 07096498
Khoo, Yuehaw; Lu, Jianfeng; Ying, Lexing
2019
A convergent method for linear half-space kinetic equations. Zbl 1380.35006
Li, Qin; Sun, Weiran; Lu, Jianfeng
2017
A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. Zbl 1230.65039
Lin, Lin; Yang, Chao; Lu, Jianfeng; Ying, Lexing; E, Weinan
2011
Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces. Zbl 1365.35174
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng
2017
Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime. Zbl 1377.35145
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng
2017
Density matrix minimization with $${\ell}_1$$ regularization. Zbl 1327.65110
Lai, Rongjie; Lu, Jianfeng; Osher, Stanley
2015
Pole-based approximation of the Fermi-Dirac function. Zbl 1188.41007
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Weinan, E.
2009
Validity and regularization of classical half-space equations. Zbl 1367.35176
Li, Qin; Lu, Jianfeng; Sun, Weiran
2017
Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics. Zbl 1349.82096
Li, Qin; Lu, Jianfeng; Sun, Weiran
2015
Learning interacting particle systems: diffusion parameter estimation for aggregation equations. Zbl 1412.65171
Huang, Hui; Liu, Jian-Guo; Lu, Jianfeng
2019
Crystal image analysis using 2D synchrosqueezed transforms. Zbl 1336.74016
Yang, Haizhao; Lu, Jianfeng; Ying, Lexing
2015
Feature fusion: Parallel strategy vs. serial strategy. Zbl 1028.68152
Yang, Jian; Yang, Jing-yu; Zhang, David; Lu, Jian-feng
2003
Scaling limit of the Stein variational gradient descent: the mean field regime. Zbl 1417.35189
Lu, Jianfeng; Lu, Yulong; Nolen, James
2019
Thermodynamic limit of crystal defects with finite temperature tight binding. Zbl 1412.35279
Chen, Huajie; Lu, Jianfeng; Ortner, Christoph
2018
Convergence of phase-field free energy and boundary force for molecular solvation. Zbl 1384.35052
Dai, Shibin; Li, Bo; Lu, Jianfeng
2018
Half-space kinetic equations with general boundary conditions. Zbl 1360.35131
Li, Qin; Lu, Jianfeng; Sun, Weiran
2017
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost. Zbl 1349.81020
Lu, Jianfeng; Ying, Lexing
2015
Optimized local basis set for Kohn-Sham density functional theory. Zbl 1250.82002
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
Double delayed feedback control for the stabilization of unstable steady states in chaotic systems. Zbl 1221.37217
Lu, Jianfeng; Ma, Zhixin; Li, Lian
2009
The elastic continuum limit of the tight binding model. Zbl 1136.74003
E, Weinan; Lu, Jianfeng
2007
A quasi-nonlocal coupling method for nonlocal and local diffusion models. Zbl 06880667
Du, Qiang; Li, Xingjie Helen; Lu, Jianfeng; Tian, Xiaochuan
2018
Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: a mathematical justification of fewest switches surface hopping algorithms. Zbl 06869467
Lu, Jianfeng; Zhou, Zhennan
2018
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem. Zbl 1386.82053
Li, Lei; Liu, Jian-Guo; Lu, Jianfeng
2017
Decay estimates of discretized Green’s functions for Schrödinger type operators. Zbl 1354.65218
Lin, Lin; Lu, Jianfeng
2016
Strang splitting methods for a quasilinear Schrödinger equation: convergence, instability, and dynamics. Zbl 1326.35349
Lu, Jianfeng; Marzuola, Jeremy L.
2015
Multiple kernel clustering based on centered kernel alignment. Zbl 1373.68324
Lu, Yanting; Wang, Liantao; Lu, Jianfeng; Yang, Jingyu; Shen, Chunhua
2014
Geometrical modeling of granular structures in two and three dimensions. Application to nanostructures. Zbl 1176.74051
Benabbou, A.; Borouchaki, H.; Laug, P.; Lu, J.
2009
Fisher information regularization schemes for Wasserstein gradient flows. Zbl 1437.65055
Li, Wuchen; Lu, Jianfeng; Wang, Li
2020
Trigonometric integrators for quasilinear wave equations. Zbl 1403.65048
Gauckler, Ludwig; Lu, Jianfeng; Marzuola, Jeremy L.; Rousset, Frédéric; Schratz, Katharina
2019
Detecting localized eigenstates of linear operators. Zbl 1425.35128
Lu, Jianfeng; Steinerberger, Stefan
2018
Quasi-nonlocal coupling of nonlocal diffusions. Zbl 1422.65166
Li, Xingjie Helen; Lu, Jianfeng
2017
Semi-supervised linear discriminant analysis for dimension reduction and classification. Zbl 1412.68195
Wang, Sheng; Lu, Jianfeng; Gu, Xingjian; Du, Haishun; Yang, Jingyu
2016
Localized density matrix minimization and linear-scaling algorithms. Zbl 1349.82007
Lai, Rongjie; Lu, Jianfeng
2016
Efficient rare event simulation for failure problems in random media. Zbl 1320.65012
Liu, Jingchen; Lu, Jianfeng; Zhou, Xiang
2015
Stability of a force-based hybrid method with planar sharp interface. Zbl 1307.65148
Lu, Jianfeng; Ming, Pingbing
2014
Effective Maxwell equations from time-dependent density functional theory. Zbl 1210.81030
Weinan, E.; Lu, Jianfeng; Yang, Xu
2011
Load share and finite element stress analysis for double circular-arc helical gears. Zbl 0835.73064
Lu, J.; Litvin, F. L.; Chen, J. S.
1995
A dimension-free Hermite-Hadamard inequality via gradient estimates for the torsion function. Zbl 1436.26011
Lu, Jianfeng; Steinerberger, Stefan
2020
PEXSI-$$\Sigma$$: a Green’s function embedding method for Kohn-Sham density functional theory. Zbl 1400.82023
Li, Xiantao; Lin, Lin; Lu, Jianfeng
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
The Nakayama automorphism of a class of graded algebras. Zbl 1376.16038
Lü, J.-F.; Mao, X.-F.; Zhang, J. J.
2017
Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature. Zbl 1357.81085
Watson, Alexander B.; Lu, Jianfeng; Weinstein, Michael I.
2017
Fast algorithm for periodic density fitting for Bloch waves. Zbl 1381.65098
Lu, Jianfeng; Ying, Lexing
2016
Gauge-invariant frozen Gaussian approximation method for the Schrödinger equation with periodic potentials. Zbl 1346.81043
Delgadillo, Ricardo; Lu, Jianfeng; Yang, Xu
2016
Analysis of the divide-and-conquer method for electronic structure calculations. Zbl 1344.65053
Chen, Jingrun; Lu, Jianfeng
2016
Orbital-free density functional theory of out-of-plane charge screening in graphene. Zbl 1343.82074
Lu, Jianfeng; Moroz, Vitaly; Muratov, Cyrill B.
2015
Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase. Zbl 1278.81084
E, Weinan; Lu, Jian-feng; Yang, Xu
2013
A sub-linear scaling algorithm for computing the electronic structure of materials. Zbl 1133.35429
García-Cervera, Carlos J.; Lu, Jianfeng; E, Weinan
2007
Dynamic stress concentration around elliptic cavities in saturated poroelastic soil under harmonic plane waves. Zbl 1120.74521
Wang, J. H.; Zhou, X. L.; Lu, J. F.
2005
Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method. Zbl 1048.80009
Xu, B. Q.; Shen, Z. H.; Lu, J.; Ni, X. W.; Zhang, S. Y.
2003
Computerized design and generation of double circular-arc helical gears with low transmission errors. Zbl 0865.70002
Litvin, F. L.; Lu, J.
1995
Numerical methods for Kohn-Sham density functional theory. Zbl 07099162
Lin, Lin; Lu, Jianfeng; Ying, Lexing
2019
Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance. Zbl 1414.81141
Cao, Yu; Lu, Jianfeng; Lu, Yulong
2019
Phase-space sketching for crystal image analysis based on synchrosqueezed transforms. Zbl 07097233
Lu, Jianfeng; Yang, Haizhao
2018
Removal of canvas patterns in digital acquisitions of paintings. Zbl 1409.94095
Cornelis, Bruno; Yang, Haizhao; Goodfriend, Alex; Ocon, Noelle; Lu, Jianfeng; Daubechies, Ingrid
2017
Orbital minimization method with $$\ell^{1}$$ regularization. Zbl 1375.81099
Lu, Jianfeng; Thicke, Kyle
2017
Cubic scaling algorithms for RPA correlation using interpolative separable density fitting. Zbl 1375.81259
Lu, Jianfeng; Thicke, Kyle
2017
Sparsifying preconditioner for soliton calculations. Zbl 1349.65606
Lu, Jianfeng; Ying, Lexing
2016
Seamless multiscale modeling via dynamics on fiber bundles. Zbl 1133.65029
E, Weinan; Lu, Jianfeng
2007
Sound horizon of accretion onto a Kerr black hole. Zbl 0575.76126
Lu, J. F.
1986
Efficient posterior sampling for high-dimensional imbalanced logistic regression. Zbl 1457.62221
Sen, Deborshee; Sachs, Matthias; Lu, Jianfeng; Dunson, David B.
2020
A stochastic version of Stein variational gradient descent for efficient sampling. Zbl 1444.62043
Li, Lei; Li, Yingzhou; Liu, Jian-Guo; Liu, Zibu; Lu, Jianfeng
2020
Dirac operators and domain walls. Zbl 1442.35275
Lu, Jianfeng; Watson, Alexander B.; Weinstein, Michael I.
2020
Quadrature points via heat kernel repulsion. Zbl 1447.41013
Lu, Jianfeng; Sachs, Matthias; Steinerberger, Stefan
2020
Exponential decay of Rényi divergence under Fokker-Planck equations. Zbl 1428.35599
Cao, Yu; Lu, Jianfeng; Lu, Yulong
2019
Approximating pointwise products of Laplacian eigenfunctions. Zbl 1447.35228
Lu, Jianfeng; Sogge, Christopher D.; Steinerberger, Stefan
2019
A mathematical introduction to electronic structure theory. Zbl 1435.81001
Lin, Lin; Lu, Jianfeng
2019
Coordinatewise descent methods for leading eigenvalue problem. Zbl 1420.65051
Li, Yingzhou; Lu, Jianfeng; Wang, Zhe
2019
Stochastic dynamical low-rank approximation method. Zbl 1415.65015
Cao, Yu; Lu, Jianfeng
2018
Frozen Gaussian approximation for high frequency wave propagation in periodic media. Zbl 1417.35153
Delgadillo, Ricardo; Lu, Jianfeng; Yang, Xu
2018
Moderate deviation for random elliptic PDE with small noise. Zbl 1402.60032
Li, Xiaoou; Liu, Jingchen; Lu, Jianfeng; Zhou, Xiang
2018
A surface hopping Gaussian beam method for high-dimensional transport systems. Zbl 1398.81096
Cai, Zhenning; Lu, Jianfeng
2018
A concurrent global-local numerical method for multiscale PDEs. Zbl 1397.65232
Huang, Yufang; Lu, Jianfeng; Ming, Pingbing
2018
Point cloud discretization of Fokker-Planck operators for committor functions. Zbl 1431.65235
Lai, Rongjie; Lu, Jianfeng
2018
An asymptotic preserving method for transport equations with oscillatory scattering coefficients. Zbl 1395.65081
Li, Qin; Lu, Jianfeng
2017
Preconditioning orbital minimization method for planewave discretization. Zbl 1365.65273
Lu, Jianfeng; Yang, Haizhao
2017
Large eddy simulation of flow and mass exchange in an embayment with or without vegetation. Zbl 07162925
Lu, J.; Dai, H. C.
2016
Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation. Zbl 1349.82056
Lu, Jianfeng; Mendl, Christian B.
2015
Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model. Zbl 1278.82054
E, Weinan; Lu, Jianfeng
2012
Dynamical and thermal performance of molten salt pipe during filling process. Zbl 1167.80347
Lu, Jianfeng; Ding, Jing
2009
Quantum mechanics version of wavelet transform studied by virtue of IWOP technique. Zbl 1167.81462
Fan, Hong-Yi; Lü, Jian-Feng
2004
Fisher information regularization schemes for Wasserstein gradient flows. Zbl 1437.65055
Li, Wuchen; Lu, Jianfeng; Wang, Li
2020
A dimension-free Hermite-Hadamard inequality via gradient estimates for the torsion function. Zbl 1436.26011
Lu, Jianfeng; Steinerberger, Stefan
2020
Efficient posterior sampling for high-dimensional imbalanced logistic regression. Zbl 1457.62221
Sen, Deborshee; Sachs, Matthias; Lu, Jianfeng; Dunson, David B.
2020
A stochastic version of Stein variational gradient descent for efficient sampling. Zbl 1444.62043
Li, Lei; Li, Yingzhou; Liu, Jian-Guo; Liu, Zibu; Lu, Jianfeng
2020
Dirac operators and domain walls. Zbl 1442.35275
Lu, Jianfeng; Watson, Alexander B.; Weinstein, Michael I.
2020
Quadrature points via heat kernel repulsion. Zbl 1447.41013
Lu, Jianfeng; Sachs, Matthias; Steinerberger, Stefan
2020
Solving for high-dimensional committor functions using artificial neural networks. Zbl 07096498
Khoo, Yuehaw; Lu, Jianfeng; Ying, Lexing
2019
Learning interacting particle systems: diffusion parameter estimation for aggregation equations. Zbl 1412.65171
Huang, Hui; Liu, Jian-Guo; Lu, Jianfeng
2019
Scaling limit of the Stein variational gradient descent: the mean field regime. Zbl 1417.35189
Lu, Jianfeng; Lu, Yulong; Nolen, James
2019
Trigonometric integrators for quasilinear wave equations. Zbl 1403.65048
Gauckler, Ludwig; Lu, Jianfeng; Marzuola, Jeremy L.; Rousset, Frédéric; Schratz, Katharina
2019
Numerical methods for Kohn-Sham density functional theory. Zbl 07099162
Lin, Lin; Lu, Jianfeng; Ying, Lexing
2019
Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance. Zbl 1414.81141
Cao, Yu; Lu, Jianfeng; Lu, Yulong
2019
Exponential decay of Rényi divergence under Fokker-Planck equations. Zbl 1428.35599
Cao, Yu; Lu, Jianfeng; Lu, Yulong
2019
Approximating pointwise products of Laplacian eigenfunctions. Zbl 1447.35228
Lu, Jianfeng; Sogge, Christopher D.; Steinerberger, Stefan
2019
A mathematical introduction to electronic structure theory. Zbl 1435.81001
Lin, Lin; Lu, Jianfeng
2019
Coordinatewise descent methods for leading eigenvalue problem. Zbl 1420.65051
Li, Yingzhou; Lu, Jianfeng; Wang, Zhe
2019
Thermodynamic limit of crystal defects with finite temperature tight binding. Zbl 1412.35279
Chen, Huajie; Lu, Jianfeng; Ortner, Christoph
2018
Convergence of phase-field free energy and boundary force for molecular solvation. Zbl 1384.35052
Dai, Shibin; Li, Bo; Lu, Jianfeng
2018
A quasi-nonlocal coupling method for nonlocal and local diffusion models. Zbl 06880667
Du, Qiang; Li, Xingjie Helen; Lu, Jianfeng; Tian, Xiaochuan
2018
Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: a mathematical justification of fewest switches surface hopping algorithms. Zbl 06869467
Lu, Jianfeng; Zhou, Zhennan
2018
Detecting localized eigenstates of linear operators. Zbl 1425.35128
Lu, Jianfeng; Steinerberger, Stefan
2018
PEXSI-$$\Sigma$$: a Green’s function embedding method for Kohn-Sham density functional theory. Zbl 1400.82023
Li, Xiantao; Lin, Lin; Lu, Jianfeng
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
Phase-space sketching for crystal image analysis based on synchrosqueezed transforms. Zbl 07097233
Lu, Jianfeng; Yang, Haizhao
2018
Stochastic dynamical low-rank approximation method. Zbl 1415.65015
Cao, Yu; Lu, Jianfeng
2018
Frozen Gaussian approximation for high frequency wave propagation in periodic media. Zbl 1417.35153
Delgadillo, Ricardo; Lu, Jianfeng; Yang, Xu
2018
Moderate deviation for random elliptic PDE with small noise. Zbl 1402.60032
Li, Xiaoou; Liu, Jingchen; Lu, Jianfeng; Zhou, Xiang
2018
A surface hopping Gaussian beam method for high-dimensional transport systems. Zbl 1398.81096
Cai, Zhenning; Lu, Jianfeng
2018
A concurrent global-local numerical method for multiscale PDEs. Zbl 1397.65232
Huang, Yufang; Lu, Jianfeng; Ming, Pingbing
2018
Point cloud discretization of Fokker-Planck operators for committor functions. Zbl 1431.65235
Lai, Rongjie; Lu, Jianfeng
2018
Nakayama automorphism and applications. Zbl 1396.16004
Lü, J.-F.; Mao, X.-F.; Zhang, J. J.
2017
A convergent method for linear half-space kinetic equations. Zbl 1380.35006
Li, Qin; Sun, Weiran; Lu, Jianfeng
2017
Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces. Zbl 1365.35174
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng
2017
Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime. Zbl 1377.35145
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng
2017
Validity and regularization of classical half-space equations. Zbl 1367.35176
Li, Qin; Lu, Jianfeng; Sun, Weiran
2017
Half-space kinetic equations with general boundary conditions. Zbl 1360.35131
Li, Qin; Lu, Jianfeng; Sun, Weiran
2017
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem. Zbl 1386.82053
Li, Lei; Liu, Jian-Guo; Lu, Jianfeng
2017
Quasi-nonlocal coupling of nonlocal diffusions. Zbl 1422.65166
Li, Xingjie Helen; Lu, Jianfeng
2017
The Nakayama automorphism of a class of graded algebras. Zbl 1376.16038
Lü, J.-F.; Mao, X.-F.; Zhang, J. J.
2017
Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature. Zbl 1357.81085
Watson, Alexander B.; Lu, Jianfeng; Weinstein, Michael I.
2017
Removal of canvas patterns in digital acquisitions of paintings. Zbl 1409.94095
Cornelis, Bruno; Yang, Haizhao; Goodfriend, Alex; Ocon, Noelle; Lu, Jianfeng; Daubechies, Ingrid
2017
Orbital minimization method with $$\ell^{1}$$ regularization. Zbl 1375.81099
Lu, Jianfeng; Thicke, Kyle
2017
Cubic scaling algorithms for RPA correlation using interpolative separable density fitting. Zbl 1375.81259
Lu, Jianfeng; Thicke, Kyle
2017
An asymptotic preserving method for transport equations with oscillatory scattering coefficients. Zbl 1395.65081
Li, Qin; Lu, Jianfeng
2017
Preconditioning orbital minimization method for planewave discretization. Zbl 1365.65273
Lu, Jianfeng; Yang, Haizhao
2017
Decay estimates of discretized Green’s functions for Schrödinger type operators. Zbl 1354.65218
Lin, Lin; Lu, Jianfeng
2016
Semi-supervised linear discriminant analysis for dimension reduction and classification. Zbl 1412.68195
Wang, Sheng; Lu, Jianfeng; Gu, Xingjian; Du, Haishun; Yang, Jingyu
2016
Localized density matrix minimization and linear-scaling algorithms. Zbl 1349.82007
Lai, Rongjie; Lu, Jianfeng
2016
Fast algorithm for periodic density fitting for Bloch waves. Zbl 1381.65098
Lu, Jianfeng; Ying, Lexing
2016
Gauge-invariant frozen Gaussian approximation method for the Schrödinger equation with periodic potentials. Zbl 1346.81043
Delgadillo, Ricardo; Lu, Jianfeng; Yang, Xu
2016
Analysis of the divide-and-conquer method for electronic structure calculations. Zbl 1344.65053
Chen, Jingrun; Lu, Jianfeng
2016
Sparsifying preconditioner for soliton calculations. Zbl 1349.65606
Lu, Jianfeng; Ying, Lexing
2016
Large eddy simulation of flow and mass exchange in an embayment with or without vegetation. Zbl 07162925
Lu, J.; Dai, H. C.
2016
Reactive trajectories and the transition path process. Zbl 1343.60074
Lu, Jianfeng; Nolen, James
2015
Density matrix minimization with $${\ell}_1$$ regularization. Zbl 1327.65110
Lai, Rongjie; Lu, Jianfeng; Osher, Stanley
2015
Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics. Zbl 1349.82096
Li, Qin; Lu, Jianfeng; Sun, Weiran
2015
Crystal image analysis using 2D synchrosqueezed transforms. Zbl 1336.74016
Yang, Haizhao; Lu, Jianfeng; Ying, Lexing
2015
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost. Zbl 1349.81020
Lu, Jianfeng; Ying, Lexing
2015
Strang splitting methods for a quasilinear Schrödinger equation: convergence, instability, and dynamics. Zbl 1326.35349
Lu, Jianfeng; Marzuola, Jeremy L.
2015
Efficient rare event simulation for failure problems in random media. Zbl 1320.65012
Liu, Jingchen; Lu, Jianfeng; Zhou, Xiang
2015
Orbital-free density functional theory of out-of-plane charge screening in graphene. Zbl 1343.82074
Lu, Jianfeng; Moroz, Vitaly; Muratov, Cyrill B.
2015
Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation. Zbl 1349.82056
Lu, Jianfeng; Mendl, Christian B.
2015
A variational perspective on cloaking by anomalous localized resonance. Zbl 1366.78002
Kohn, R. V.; Lu, J.; Schweizer, B.; Weinstein, M. I.
2014
Nonexistence of a minimizer for Thomas–Fermi–Dirac–von Weizsäcker model. Zbl 1301.49002
Lu, Jianfeng; Otto, Felix
2014
Multiple kernel clustering based on centered kernel alignment. Zbl 1373.68324
Lu, Yanting; Wang, Liantao; Lu, Jianfeng; Yang, Jingyu; Shen, Chunhua
2014
Stability of a force-based hybrid method with planar sharp interface. Zbl 1307.65148
Lu, Jianfeng; Ming, Pingbing
2014
Convergence of a force-based hybrid method in three dimensions. Zbl 1393.74166
Lu, Jianfeng; Ming, Pingbing
2013
The Kohn-Sham equation for deformed crystals. Zbl 1435.74001
E, Weinan; Lu, Jianfeng
2013
Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase. Zbl 1278.81084
E, Weinan; Lu, Jian-feng; Yang, Xu
2013
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation. Zbl 1251.82008
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
Convergence of frozen Gaussian approximation for high-frequency wave propagation. Zbl 1387.35400
Lu, Jianfeng; Yang, Xu
2012
Frozen Gaussian approximation for general linear strictly hyperbolic systems: formulation and Eulerian methods. Zbl 1447.81130
Lu, Jianfeng; Yang, Xu
2012
Optimized local basis set for Kohn-Sham density functional theory. Zbl 1250.82002
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model. Zbl 1278.82054
E, Weinan; Lu, Jianfeng
2012
Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Zbl 1213.42133
Daubechies, Ingrid; Lu, Jianfeng; Wu, Hau-Tieng
2011
Fast construction of hierarchical matrix representation from matrix-vector multiplication. Zbl 1218.65038
Lin, Lin; Lu, Jianfeng; Ying, Lexing
2011
SelInv – an algorithm for selected inversion of a sparse symmetric matrix. Zbl 1365.65069
Lin, Lin; Yang, Chao; Meza, Juan C.; Lu, Jianfeng; Ying, Lexing; E, Weinan
2011
Frozen Gaussian approximation for high frequency wave propagation. Zbl 1272.65075
Lu, Jianfeng; Yang, Xu
2011
The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born Rule. Zbl 1253.74025
E, Weinan; Lu, Jianfeng
2011
A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. Zbl 1230.65039
Lin, Lin; Yang, Chao; Lu, Jianfeng; Ying, Lexing; E, Weinan
2011
Effective Maxwell equations from time-dependent density functional theory. Zbl 1210.81030
Weinan, E.; Lu, Jianfeng; Yang, Xu
2011
Localized bases of eigensubspaces and operator compression. Zbl 1205.15017
E, Weinan; Li, Tiejun; Lu, Jianfeng
2010
Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model. Zbl 1277.81117
E, Weinan; Lu, Jianfeng
2010
Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Zbl 1182.65072
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Car, Roberto; E, Weinan
2009
Pole-based approximation of the Fermi-Dirac function. Zbl 1188.41007
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Weinan, E.
2009
Double delayed feedback control for the stabilization of unstable steady states in chaotic systems. Zbl 1221.37217
Lu, Jianfeng; Ma, Zhixin; Li, Lian
2009
Geometrical modeling of granular structures in two and three dimensions. Application to nanostructures. Zbl 1176.74051
Benabbou, A.; Borouchaki, H.; Laug, P.; Lu, J.
2009
Dynamical and thermal performance of molten salt pipe during filling process. Zbl 1167.80347
Lu, Jianfeng; Ding, Jing
2009
Generalized (complete, lag, anticipated) synchronization of discrete-time chaotic systems. Zbl 1221.37216
Lu, Jianfeng
2008
Adaptive synchronization of different chaotic systems with fully unknown parameters. Zbl 1203.93161
Chen, Xiaoyun; Lu, Jianfeng
2007
The elastic continuum limit of the tight binding model. Zbl 1136.74003
E, Weinan; Lu, Jianfeng
2007
A sub-linear scaling algorithm for computing the electronic structure of materials. Zbl 1133.35429
García-Cervera, Carlos J.; Lu, Jianfeng; E, Weinan
2007
Seamless multiscale modeling via dynamics on fiber bundles. Zbl 1133.65029
E, Weinan; Lu, Jianfeng
2007
Dynamic stress concentration around elliptic cavities in saturated poroelastic soil under harmonic plane waves. Zbl 1120.74521
Wang, J. H.; Zhou, X. L.; Lu, J. F.
2005
Quantum mechanics version of wavelet transform studied by virtue of IWOP technique. Zbl 1167.81462
Fan, Hong-Yi; Lü, Jian-Feng
2004
Feature fusion: Parallel strategy vs. serial strategy. Zbl 1028.68152
Yang, Jian; Yang, Jing-yu; Zhang, David; Lu, Jian-feng
2003
Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method. Zbl 1048.80009
Xu, B. Q.; Shen, Z. H.; Lu, J.; Ni, X. W.; Zhang, S. Y.
2003
Load share and finite element stress analysis for double circular-arc helical gears. Zbl 0835.73064
Lu, J.; Litvin, F. L.; Chen, J. S.
1995
Computerized design and generation of double circular-arc helical gears with low transmission errors. Zbl 0865.70002
Litvin, F. L.; Lu, J.
1995
Sound horizon of accretion onto a Kerr black hole. Zbl 0575.76126
Lu, J. F.
1986
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#### Cited by 924 Authors

 54 Lu, Jianfeng 22 Ying, Lexing 18 Lin, Lin 15 Li, Qin 15 Nguyen, Hoai-Minh 13 E, Weinan 13 Yang, Haizhao 12 Hou, Thomas Yizhao 12 Ortner, Christoph 11 Li, Hongjie 11 Liu, Hongyu 11 Yang, Xu 10 Liu, Jianguo 8 Shi, Zuoqiang 7 Steinerberger, Stefan 7 Wu, Hau-Tieng 6 Gao, Yuan 6 Knüpfer, Hans 6 Li, Yingzhou 6 Muratov, Cyrill B. 6 Topaloglu, Ihsan 6 Xia, Jianlin 5 Chen, Huajie 5 Choksi, Rustum 5 Chui, Charles Kam-tai 5 Damle, Anil 5 Fan, Yuwei 5 Frank, Rupert L. 5 Gavini, Vikram 5 Hu, Guanghui 5 Jin, Shi 5 Kang, Hyeonbae 5 Novaga, Matteo 5 Zhang, Lei 4 Alama, Stan 4 Ando, Kazunori 4 Bao, Gang 4 Bronsard, Lia 4 Chen, Jingrun 4 Huang, Hui 4 Liu, Di 4 Ming, Pingbing 4 Shapeev, Alexander V. 4 Sun, Weiran 4 Xu, Xiangsheng 4 Zepeda-Núñez, Leonardo 3 Bonacini, Marco 3 Borsche, Raul 3 Cancès, Eric 3 Chen, Ke 3 Daubechies, Ingrid Chantal 3 Delgadillo, Ricardo 3 Deng, Youjun 3 Du, Qiang 3 Ghattas, Omar N. 3 Ghysels, Pieter 3 Goldman, Michael 3 Ho, Kenneth L. 3 Klar, Axel 3 Lai, Rongjie 3 Levitt, Antoine 3 Li, Lei 3 Li, Wuchen 3 Li, Xiaoye Sherry 3 Li, Xingjie Helen 3 Lu, Xinyang 3 Motamarri, Phani 3 Pask, John Ernest 3 Phan Thành Nam 3 Rouet, François-Henry 3 Saad, Yousef 3 Schweizer, Ben 3 Thicke, Kyle 3 Watson, Alexander B. 3 Weinstein, Michael I. 3 Xing, Xin 3 Yu, SangHyeon 3 Zhang, James J. 3 Zhang, Pengchuan 3 Zhou, Hao-Min 3 Zhou, Xiang 2 Aghababa, Mohammad Pourmahmood 2 Al-Sawalha, Mohammed Mossa 2 Alger, Nick 2 Alizadeh, Ghasem 2 Altmann, Robert 2 Balakrishnan, Venkataramanan 2 Boukaram, Wajih-Halim 2 Braun, Julian 2 Bui-Thanh, Tan 2 Cai, Zhenning 2 Calo, Victor Manuel 2 Cao, Yu 2 Cauley, Stephen 2 Chai, Lihui 2 Chow, Edmond G. W. 2 Chung, Tsz Shun Eric 2 Cicone, Antonio 2 Crouseilles, Nicolas 2 Dalcín, Lisandro D. ...and 824 more Authors
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#### Cited in 152 Serials

 46 Journal of Computational Physics 36 Multiscale Modeling & Simulation 34 SIAM Journal on Scientific Computing 21 SIAM Journal on Mathematical Analysis 16 Archive for Rational Mechanics and Analysis 14 Applied and Computational Harmonic Analysis 11 Computer Methods in Applied Mechanics and Engineering 11 Communications in Nonlinear Science and Numerical Simulation 10 Journal of Mathematical Physics 9 Journal of Scientific Computing 9 SIAM Journal on Applied Mathematics 8 SIAM Journal on Numerical Analysis 7 Journal of Statistical Physics 7 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 7 Nonlinear Dynamics 7 Research in the Mathematical Sciences 6 Communications in Mathematical Physics 6 Mathematics of Computation 6 Calculus of Variations and Partial Differential Equations 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Science China. Mathematics 5 Journal of Mathematical Analysis and Applications 5 Journal of Algebra 5 Numerische Mathematik 5 SIAM Journal on Matrix Analysis and Applications 5 Pattern Recognition 5 Journal of Nonlinear Science 4 Information Sciences 4 Journal of Differential Equations 4 Transactions of the American Mathematical Society 4 Applied Mathematical Modelling 4 Mechanism and Machine Theory 4 Acta Numerica 3 Communications on Pure and Applied Mathematics 3 Inverse Problems 3 Mathematische Zeitschrift 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Circuits, Systems, and Signal Processing 3 Chinese Annals of Mathematics. Series B 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Advances in Computational Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Chaos 3 SIAM Journal on Applied Dynamical Systems 3 Analysis and Applications (Singapore) 3 SIAM Journal on Imaging Sciences 3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 International Journal of Modern Physics B 2 Computers & Mathematics with Applications 2 International Journal of Heat and Mass Transfer 2 Journal d’Analyse Mathématique 2 Journal of the Mechanics and Physics of Solids 2 Nonlinearity 2 Physica A 2 Wave Motion 2 Applied Mathematics and Computation 2 Fuzzy Sets and Systems 2 Indiana University Mathematics Journal 2 International Journal for Numerical Methods in Engineering 2 Journal of the American Statistical Association 2 Quarterly of Applied Mathematics 2 European Journal of Applied Mathematics 2 Numerical Algorithms 2 Communications in Partial Differential Equations 2 International Journal of Computer Mathematics 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Proceedings of the National Academy of Sciences of the United States of America 2 Numerical Linear Algebra with Applications 2 Discrete and Continuous Dynamical Systems 2 Mathematical Problems in Engineering 2 Abstract and Applied Analysis 2 Computational Methods in Applied Mathematics 2 Inverse Problems and Imaging 2 Algorithms 2 Advances in Mathematical Physics 2 GEM - International Journal on Geomathematics 2 Journal of the Operations Research Society of China 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Advances in Data Science and Adaptive Analysis 2 Pure and Applied Analysis 1 Astrophysics and Space Science 1 General Relativity and Gravitation 1 Journal of the Franklin Institute 1 Journal of Mathematical Biology 1 Letters in Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Acta Mathematica Vietnamica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Statistics 1 Canadian Journal of Mathematics 1 Glasgow Mathematical Journal 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Mathematics and Computers in Simulation 1 Meccanica 1 Mechanics Research Communications 1 Memoirs of the American Mathematical Society 1 Journal of Classification 1 Physica D 1 Applied Numerical Mathematics ...and 52 more Serials
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#### Cited in 47 Fields

 223 Numerical analysis (65-XX) 186 Partial differential equations (35-XX) 80 Statistical mechanics, structure of matter (82-XX) 61 Quantum theory (81-XX) 55 Mechanics of deformable solids (74-XX) 46 Calculus of variations and optimal control; optimization (49-XX) 45 Information and communication theory, circuits (94-XX) 38 Ordinary differential equations (34-XX) 38 Statistics (62-XX) 38 Optics, electromagnetic theory (78-XX) 31 Computer science (68-XX) 29 Probability theory and stochastic processes (60-XX) 29 Systems theory; control (93-XX) 23 Dynamical systems and ergodic theory (37-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 20 Operator theory (47-XX) 17 Mechanics of particles and systems (70-XX) 15 Fluid mechanics (76-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 14 Operations research, mathematical programming (90-XX) 13 Biology and other natural sciences (92-XX) 12 Associative rings and algebras (16-XX) 7 Integral equations (45-XX) 6 Integral transforms, operational calculus (44-XX) 5 Approximations and expansions (41-XX) 5 Functional analysis (46-XX) 5 Differential geometry (53-XX) 4 Potential theory (31-XX) 4 Convex and discrete geometry (52-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Astronomy and astrophysics (85-XX) 4 Geophysics (86-XX) 3 Real functions (26-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Relativity and gravitational theory (83-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 $$K$$-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 Mathematics education (97-XX)