# zbMATH — the first resource for mathematics

## Inverse Problems in Science and Engineering

 Short Title: Inverse Probl. Sci. Eng. Publisher: Taylor & Francis, Abingdon, Oxfordshire ISSN: 1741-5977; 1741-5985/e Online: http://www.tandfonline.com/loi/gipe20 Predecessor: Inverse Problems in Engineering
 Documents Indexed: 1,016 Publications (since 2005) References Indexed: 970 Publications with 27,167 References.
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#### Authors

 24 Lesnic, Daniel 22 Orlande, Helcio Rangel Barreto 19 Colaço, Marcelo J. 14 Liu, Chein-Shan 11 Johansson, B. Tomas 10 Dulikravich, George Stevo 10 Fu, Chuli 9 Hasanoǧlu, Alemdar 9 Yagola, Anatoliĭ Grigor’evich 7 Hamdi, Adel 7 Karageorghis, Andreas 7 Slodička, Marián 7 Wang, Yanfei 6 Carasso, Alfred S. 6 Cheng, Xiaoliang 6 Divo, Eduardo A. 6 Kassab, Alain J. 6 Qian, Zhi 6 Silva Neto, Antônio José 6 Wei, Ting 6 Yang, Chuanfu 5 Artioukhine, Eugene 5 Banks, Harvey Thomas 5 de Sousa, Fabiano Luis 5 Gaikovich, Konstantin P. 5 Han, Weimin 5 Loulou, Tahar 5 Marin, Liviu 5 Moaveni, S. 5 Russell, Kevin 5 Sebu, Cristiana 5 Stepanova, I. È. 4 Ameur, Hend Ben 4 Autrique, Laurent 4 Bardsley, Johnathan M. 4 Białecki, Ryszard A. 4 Chapko, Roman 4 Chavent, Guy 4 Chen, Wen 4 Chu, Jinkui 4 Gong, Rongfang 4 Guimarães, Gilmar 4 Han, Bo 4 Inglese, Gabriele 4 Kourehli, Seyed Sina 4 Koyunbakan, Hikmet 4 Li, Gongsheng 4 Liu, Jie 4 Liu, Tao 4 Meng, Zehong 4 Nguyen Huy Tuan 4 Pektas, Burhan 4 Petit, Daniel 4 Sixou, Bruno 4 Sun, Jianwei 4 Trivailo, Pavel M. 4 Weber, Gerhard-Wilhelm 4 Xiong, Xiangtuan 4 Yamamoto, Masahiro 4 Yang, Fan 4 Zhang, Ye 4 Zhao, Zhenyu 3 Alifanov, Oleg M. 3 Alves, Carlos J. S. 3 Amiri, Gholamreza Ghodrati 3 Ashrafizadeh, Ali 3 Battaglia, Jean-Luc 3 Berntsson, Fredrik 3 Chang, Chih-Wen 3 Chang, Jiang-ren 3 Chen, Hantaw 3 Clément, François 3 de Campos Velho, Haroldo Fraga 3 Đinh Nho Hào 3 Eksteen, J. J. A. 3 Esfandiari, Akbar 3 Feng, Xiaoli 3 Fox, Colin D. 3 Frankel, Jay I. 3 Fulginei, Francesco Riganti 3 Grebénnikov, Alexandre Ivanovich 3 Gulliksson, Mårten E. 3 Han, Xu 3 Herskovits, Jose Norman 3 Heyns, P. Stephan 3 Huang, Cheng-Hung 3 Ingham, Derek Binns 3 Jarny, Yvon 3 Jiang, Chao 3 Jolly, Jean-Claude 3 Kaipio, Jari P. 3 Khoa, Vo Anh 3 Klibanov, Michael V. 3 Kolodziej, Jan Adam 3 Kozlov, Vladimir A. 3 Lahmer, Tom 3 Lee, Wen-Tzong 3 Leem, Koung Hee 3 Leitão, Antonio 3 Leonov, Aleksandr Sergeevich ...and 1,831 more Authors
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#### Fields

 558 Numerical analysis (65-XX) 283 Partial differential equations (35-XX) 209 Mechanics of deformable solids (74-XX) 157 Classical thermodynamics, heat transfer (80-XX) 119 Biology and other natural sciences (92-XX) 107 Fluid mechanics (76-XX) 99 Optics, electromagnetic theory (78-XX) 62 Geophysics (86-XX) 60 Ordinary differential equations (34-XX) 53 Statistics (62-XX) 46 Operations research, mathematical programming (90-XX) 44 Systems theory; control (93-XX) 43 Integral equations (45-XX) 38 Computer science (68-XX) 33 Information and communication theory, circuits (94-XX) 31 Calculus of variations and optimal control; optimization (49-XX) 29 Operator theory (47-XX) 29 Mechanics of particles and systems (70-XX) 22 General and overarching topics; collections (00-XX) 18 Integral transforms, operational calculus (44-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 9 Probability theory and stochastic processes (60-XX) 6 Potential theory (31-XX) 5 Special functions (33-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Approximations and expansions (41-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Astronomy and astrophysics (85-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Combinatorics (05-XX) 2 Functional analysis (46-XX) 2 Quantum theory (81-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH Open

557 Publications have been cited 2,283 times in 1,663 Documents Cited by Year
A survey of applications of the MFS to inverse problems. Zbl 1220.65157
Karageorghis, A.; Lesnic, D.; Marin, L.
2011
The method of fundamental solutions for the backward heat conduction problem. Zbl 1194.80107
Mera, N. S.
2005
A coupled method for inverse source problem of spatial fractional anomalous diffusion equations. Zbl 1204.65116
Wei, Hui; Chen, Wen; Sun, Hongguang; Li, Xicheng
2010
Fourier regularization method for solving a Cauchy problem for the Laplace equation. Zbl 1258.65094
Fu, C.-L.; Li, H.-F.; Qian, Z.; Xiong, X.-T.
2008
Generalized finite difference method for solving two-dimensional inverse Cauchy problems. Zbl 1329.65257
Fan, Chia-Ming; Li, Po-Wei; Yeih, Weichung
2015
A simple projection method for solving the multiple-sets split feasibility problem. Zbl 1285.65038
Zhao, Jinling; Yang, Qingzhi
2013
A uniqueness theorem for the boundary value problems with non-linear dependence on the spectral parameter in the boundary conditions. Zbl 1187.34016
Chernozhukova, A.; Freiling, G.
2009
CMARS: A new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization. Zbl 1254.65020
Weber, Gerhard-Wilhelm; Batmaz, İNci; Köksal, Gülser; Taylan, Pakize; Yerlikaya-Özkurt, Fatma
2012
Stable numerical evaluation of Grünwald-Letnikov fractional derivatives applied to a fractional IHCP. Zbl 1159.65313
Murio, Diego A.
2009
Detection of cavities using the method of fundamental solutions. Zbl 1175.65130
Karageorghis, A.; Lesnic, D.
2009
The inverse problem of finding the time-dependent diffusion coefficient of the heat equation from integral overdetermination data. Zbl 1259.65142
Kanca, Fatma; Ismailov, Mansur I.
2012
Reconstruction of a moving boundary from Cauchy data in one-dimensional heat equation. Zbl 1165.65387
Wei, T.; Yamamoto, M.
2009
Inverse problems for discontinuous Sturm-Liouville operators with mixed spectral data. Zbl 1326.34034
Wang, Yu Ping
2015
Identifying an unknown source term in a heat equation. Zbl 1183.65116
Dou, Fang-Fang; Fu, Chu-Li; Yang, Fan
2009
A numerical method for solving the inverse heat conduction problem without initial value. Zbl 1193.35254
Wang, Y. B.; Cheng, J.; Nakagawa, J.; Yamamoto, M.
2010
Uniqueness of positive solutions for boundary value problems of singular fractional differential equations. Zbl 1259.34010
Sun, Shurong; Zhao, Yige; Han, Zhenlai; Xu, Meirong
2012
Ritz-Galerkin method for solving an inverse heat conduction problem with a nonlinear source term via Bernstein multi-scaling functions and cubic B-spline functions. Zbl 1281.65124
Dehghan, Mehdi; Yousefi, Sohrab Ali; Rashedi, Kamal
2013
Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem. Zbl 1186.65132
Slodička, M.; Lesnic, D.; Onyango, T. T. M.
2010
The method of fundamental solutions for the inverse conductivity problem. Zbl 1194.65139
Karageorghis, A.; Lesnic, D.
2010
Inverse source identification for Poisson equation. Zbl 1194.65130
Ling, Leevan; Hon, Y. C.; Yamamoto, M.
2005
Numerical solution of two-dimensional inverse force function in the wave equation with nonlocal boundary conditions. Zbl 1398.65237
2017
Recovering the source term in a linear diffusion problem by the method of fundamental solutions. Zbl 1159.65354
Alves, Carlos J. S.; Colaço, Marcelo J.; Leitão, Vitor M. A.; Martins, Nuno F. M.; Orlande, Helcio R. B.; Roberty, Nilson C.
2008
Inverse nodal problems for Sturm-Liouville equation with polynomially dependent on the eigenparameter. Zbl 1248.34013
Yang, Chuan-Fu; Yang, Xiao-Ping
2011
An alternating iterative procedure for the Cauchy problem for the Helmholtz equation. Zbl 1321.35010
Berntsson, F.; Kozlov, V. A.; Mpinganzima, L.; Turesson, B. O.
2014
The method of fundamental solutions for solving a Cauchy problem of Laplace’s equation in a multi-connected domain. Zbl 1258.65102
Zhou, Dayong; Wei, Ting
2008
Projected Barzilai-Borwein method for large-scale nonnegative image restoration. Zbl 1202.94077
Wang, Yanfei; Ma, Shiqian
2007
A numerical method for solving a nonlinear inverse parabolic problem. Zbl 1207.65116
Pourgholi, R.; Rostamian, M.; Emamjome, M.
2010
A regularization for a Riesz-Feller space-fractional backward diffusion problem. Zbl 1329.65208
Cheng, Hao; Fu, Chu-Li; Zheng, Guang-Hui; Gao, Jie
2014
The inverse source problem for time-fractional diffusion equation: stability analysis and regularization. Zbl 1329.35357
Yang, Fan; Fu, Chu-Li; Li, Xiao-Xiao
2015
Determination of space-time-dependent heat source in a parabolic inverse problem via the Ritz-Galerkin technique. Zbl 1321.65146
Rashedi, Kamal; Adibi, Hojatollah; Dehghan, Mehdi
2014
Regularization methods for ill-conditioned system of the integral equation of the first kind with the logarithmic kernel. Zbl 1321.65194
Chen, Jeng-Tzong; Han, Houde; Kuo, Shyh-Rong; Kao, Shing-Kai
2014
Boundary particle method for Cauchy inhomogeneous potential problems. Zbl 1242.65227
Fu, Zhuojia; Chen, Wen; Zhang, Chuanzeng
2012
Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters. Zbl 1258.74087
Gockenbach, M. S.; Jadamba, B.; Khan, A. A.
2008
Optimal modified method for a fractional-diffusion inverse heat conduction problem. Zbl 1195.65125
Qian, Zhi
2010
On a final value problem for the time-fractional diffusion equation with inhomogeneous source. Zbl 1398.65240
Tuan, Nguyen Huy; Long, Le Dinh; Nguyen, Van Thinh; Tran, Thanh
2017
Inversion of weighted Radon transforms via finite Fourier series weight approximations. Zbl 1329.65326
Guillement, J.-P.; Novikov, R. G.
2014
Recovery of a space-dependent vector source in thermoelastic systems. Zbl 1329.65214
Van Bockstal, K.; Slodička, M.
2015
Numerical approximation of the one-dimensional inverse Cauchy-Stefan problem using a method of fundamental solutions. Zbl 1254.65101
Johansson, B. Tomas; Lesnic, Daniel; Reeve, Thomas
2011
Level set reconstruction of conductivity and permittivity from boundary electrical measurements using experimental data. Zbl 1194.78011
Soleimani, M.; Lionheart, W. R. B.; Dorn, O.
2006
Determining magnitude of groundwater pollution sources by data compatibility analysis. Zbl 1194.76269
Li, G. S.; Tan, Y. J.; Cheng, J.; Wang, X. Q.
2006
On the half inverse spectral problem for an integro-differential operator. Zbl 1390.45022
Buterin, S. A.; Sat, M.
2017
Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations. Zbl 1391.35417
Garde, Henrik
2018
An inverse problem of identifying the source coefficient in a degenerate heat equation. Zbl 1326.35419
Deng, Zui-Cha; Qian, Kun; Rao, Xiao-Bo; Yang, Liu; Luo, Guan-Wei
2015
Inverse heat conduction problems with boundary and final time measured output data. Zbl 1241.35218
Hasanov, Alemdar; Otelbaev, Muhtarbay; Akpayev, Bakytzhan
2011
A modified method for determining the surface heat flux of IHCP. Zbl 1202.80017
Qian, Z.; Fu, C.-L.; Xiong, X.-T.
2007
Semi-analytic inversion method for the determination of elastoplastic properties of power hardening materials from limited torsional experiment. Zbl 1422.74101
Hasanov, Alemdar; Tatar, Salih
2010
A homotopy method for the inversion of a two-dimensional acoustic wave equation. Zbl 1194.76262
Han, B.; Fu, H. S.; Li, Z.
2005
A modified quasi-boundary value method for regularizing of a backward problem with time-dependent coefficient. Zbl 1227.65089
Quan, Pham Hoang; Trong, Dang Duc; Triet, Le Minh; Tuan, Nguyen Huy
2011
A local meshless method for Cauchy problem of elliptic PDEs in annulus domains. Zbl 1342.65209
2016
A meshless method for an inverse two-phase one-dimensional linear Stefan problem. Zbl 1267.80011
Johansson, B. Tomas; Lesnic, Daniel; Reeve, Thomas
2013
Identification of point sources in two-dimensional advection-diffusion-reaction equation: application to pollution sources in a river. Stationary case. Zbl 1258.76151
2007
Solving ill-conditioned linear algebraic systems by the dynamical systems method. Zbl 1258.65036
Hoang, N. S.; Ramm, A. G.
2008
Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques. Zbl 1190.65147
Helsing, Johan; Johansson, B. Tomas
2010
Approximation of the likelihood function in the Bayesian technique for the solution of inverse problems. Zbl 1154.65006
Orlande, Helcio R. B.; Colaço, Marcelo J.; Dulikravich, George S.
2008
Simultaneous determination of a time-dependent heat source and the initial temperature in an inverse heat conduction problem. Zbl 1281.65126
Wen, Jin; Yamamoto, Masahiro; Wei, Ting
2013
A nonlinear integral equation method for the inverse scattering problem by sound-soft rough surfaces. Zbl 1326.65182
Li, Jianliang; Sun, Guanying
2015
A modified Tikhonov regularization method for a backward heat equation. Zbl 1244.65136
Zhao, Zhenyu; Meng, Zehong
2011
A parallel radial bisection algorithm for inverse scattering problems. Zbl 1269.65116
Liu, Keji; Xu, Yongzhi; Zou, Jun
2013
Regularization of an ill-posed problem in corneal topography. Zbl 1308.35326
Płociniczak, Ł.; Okrasiński, W.
2013
Tikhonov regularized Poisson likelihood estimation: theoretical justification and a computational method. Zbl 1258.35206
Bardsley, Johnathan M.; Laobeul, N’djekornom
2008
Finding a control parameter in a one-dimensional parabolic inverse problem by using the Bernstein Galerkin method. Zbl 1175.65109
Yousefi, S. A.
2009
A spectral method for an axisymmetric backward heat equation. Zbl 1186.65130
Cheng, Wei; Fu, Chu-Li
2009
Reconstruction formula for the potential function of Sturm-Liouville problem with eigenparameter boundary condition. Zbl 1187.34017
Panakhov, Etibar S.; Koyunbakan, Hikmet; Ic, Unal
2010
Solving inverse heat conduction problems using trained POD-RBF network inverse method. Zbl 1158.35433
Ostrowski, Z.; Białecki, R. A.; Kassab, A. J.
2008
Robin coefficient identification for a time-fractional diffusion equation. Zbl 1342.65210
Wei, T.; Zhang, Z. Q.
2016
On the identification of star-shape sources from boundary measurements using a reciprocity functional. Zbl 1166.65392
Roberty, N. C.; Alves, C. J. S.
2009
Circular integrating detectors in photo and thermoacoustic tomography. Zbl 1156.92027
Zangerl, Gerhard; Scherzer, Otmar; Haltmeier, Markus
2009
Traces of Sturm-Liouville operators with discontinuities. Zbl 1329.34057
Yang, Chuan-Fu
2014
An evolution of the back and forth nudging for geophysical data assimilation: application to Burgers equation and comparisons. Zbl 1281.35093
Auroux, Didier; Bansart, Patrick; Blum, Jacques
2013
A new improved regularization method for dynamic load identification. Zbl 1321.65196
Sun, Xingsheng; Liu, Jie; Han, Xu; Jiang, Chao; Chen, Rui
2014
Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method. Zbl 1300.92047
Hoang, K. C.; Khoo, B. C.; Liu, G. R.; Nguyen, N. C.; Patera, A. T.
2013
Regularization of an autoconvolution problem in ultrashort laser pulse characterization. Zbl 1304.47013
Gerth, Daniel; Hofmann, Bernd; Birkholz, Simon; Koke, Sebastian; Steinmeyer, Günter
2014
Image restoration using $$L_1$$ norm penalty function. Zbl 1258.94013
Agarwal, Vivek; Gribok, Andrei V.; Abidi, Mongi A.
2007
A semi-inverse problem of flows of fluids with pressure-dependent viscosities. Zbl 1258.76080
Rajagopal, K. R.
2008
Inverse scattering for an impedance cylinder buried in a dielectric cylinder. Zbl 1172.78005
Kress, Rainer; Yaman, Fatih; Yapar, Ali; Akduman, Ibrahim
2009
Reconstruction of part of a boundary for the Laplace equation by using a regularized method of fundamental solutions. Zbl 1178.65134
Yang, F. L.; Yan, L.; Wei, T.
2009
Identifying an unknown source term in radial heat conduction. Zbl 1258.65085
Cheng, Wei; Ma, Yun-Jie; Fu, Chu-Li
2012
Stable explicit time marching in well-posed or ill-posed nonlinear parabolic equations. Zbl 1348.65128
Carasso, Alfred S.
2016
Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions. Zbl 1348.65176
Movahedian, Bashir; Boroomand, Bijan
2016
A stable numerical scheme for a time fractional inverse parabolic equation. Zbl 1398.65239
Taghavi, A.; Babaei, A.; Mohammadpour, A.
2017
An inverse coefficient identification problem for the bio-heat equation. Zbl 1169.65092
Trucu, Dumitru; Ingham, Derek B.; Lesnic, Daniel
2009
Direct collocation method for identifying the initial conditions in the inverse wave problem using radial basis functions. Zbl 1428.65036
Wang, Lihua; Wang, Zhen; Qian, Zhihao; Gao, Yukui; Zhou, Yueting
2018
Application of the linear sampling method to identify cracks with impedance boundary conditions. Zbl 1267.78036
Ben Hassen, Fahmi; Boukari, Yosra; Haddar, Houssem
2013
Inverse problems for the Sturm-Liouville operator with discontinuity. Zbl 1318.34029
Yang, Chuan-Fu
2014
Inverse source problem in a one-dimensional evolution linear transport equation with spatially varying coefficients: application to surface water pollution. Zbl 1308.65158
2013
Identifying Lamé parameters from time-dependent elastic wave measurements. Zbl 1359.74034
Lechleiter, Armin; Schlasche, John W.
2017
Shape optimization for Navier-Stokes flow. Zbl 1258.76079
Gao, Z. M.; Ma, Y. C.; Zhuang, H. W.
2008
Newton’s method for optimal temperature-tracking of glass cooling processes. Zbl 1114.49301
Pinnau, René; Schulze, Alexander
2007
Numerical differentiation and its applications. Zbl 1359.65035
Cheng, J.; Jia, X. Z.; Wang, Y. B.
2007
Abel inversion using total variation regularization: applications. Zbl 1200.65115
Asaki, Thomas J.; Campbell, Patrick R.; Chartrand, Rick; Powell, Collin E.; Vixie, Kevin R.; Wohlberg, Brendt E.
2006
Identification of thermal conductivity and the shape of an inclusion using the boundary elements method and the particle swarm optimization algorithm. Zbl 1177.65142
2009
RTE-based bioluminescence tomography: A theoretical study. Zbl 1217.92061
Han, Weimin; Eichholz, Joseph A.; Huang, Jianguo; Lu, Jia
2011
Initial temperature reconstruction for nonlinear heat equation: application to a coupled radiative-conductive heat transfer problem. Zbl 1159.80003
Pereverzyev, S. S.; Pinnau, R.; Siedow, N.
2008
Solving the inverse Stefan design problem using genetic algorithms. Zbl 1154.65073
Słota, Damian
2008
A non-linear mathematical model for an undisturbed soil-column experiment and source parameter identification. Zbl 1351.80011
Li, Gongsheng; Tan, Yongji; Yao, De; Wang, Xiaoqin; Liu, Hongliang
2008
Inverse scattering with fixed observation angle data in 2D. Zbl 1390.35213
Fotopoulos, Georgios; Harju, Markus
2017
First-order and second-order adjoint methods for parameter identification problems with an application to the elasticity imaging inverse problem. Zbl 1387.92057
2017
Numerical methods for solving a boundary-value inverse heat conduction problem. Zbl 1329.65215
Yaparova, Natalia
2014
Determination of a differential operator with discontinuity from interior spectral data. Zbl 1329.34039
Neamaty, A.; Khalili, Y.
2014
An optimal tri-vector iterative algorithm for solving ill-posed linear inverse problems. Zbl 1281.65100
Liu, Chein-Shan
2013
Real-time reconstruction of moving point/dipole wave sources from boundary measurements. Zbl 07354229
Ohe, Takashi
2020
Identification of thermal conductivity for orthotropic FGMs by DT-DRBEM and L-m algorithm. Zbl 07354186
Zhou, Huan-Lin; Xiao, Xiong; Chen, Hao-Long; Yu, Bo
2020
Sensitivity analysis for the active manipulation of Helmholtz fields in 3D. Zbl 07354193
Egarguin, Neil Jerome A.; Onofrei, Daniel; Platt, Eric
2020
Trace formula and inverse nodal problem for a conformable fractional Sturm-Liouville problem. Zbl 1461.34010
Mortazaasl, H.; Akbarfam, A. Jodayree
2020
Accelerated alternating minimization algorithm for Poisson noisy image recovery. Zbl 1465.94015
2020
Constructive solution of the inverse spectral problem for the matrix Sturm-Liouville operator. Zbl 1461.65209
Bondarenko, Natalia P.
2020
The monotonicity method for the inverse crack scattering problem. Zbl 1466.74022
Daimon, Tomohiro; Furuya, Takashi; Saiin, Ryuji
2020
Damage detection in beam through change in measured frequency and undamaged curvature mode shape. Zbl 1464.74140
Dahak, Mustapha; Touat, Noureddine; Kharoubi, Mounir
2019
On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere. Zbl 1460.65022
Gerhards, Christian
2019
Damage assessment in plate-like structures using a two-stage method based on modal strain energy change and Jaya algorithm. Zbl 1464.74142
Dinh-Cong, D.; Vo-Duy, T.; Ho-Huu, V.; Nguyen-Thoi, T.
2019
Nonlinear Tikhonov regularization in Hilbert scales with balancing principle tuning parameter in statistical inverse problems. Zbl 1460.65061
2019
An adaptive quadrature-based factorization method for inverse acoustic scattering problems. Zbl 07348507
Leem, Koung Hee; Liu, Jun; Pelekanos, George
2019
Refinement indicators for estimating hydrogeologic parameters. Zbl 1460.86020
Riahi, M-H.; Ameur, H. Ben; Jaffré, J.; Bouhlila, R.
2019
Thermal imaging of time-varying longitudinal defects in the internal coating of a tube. Zbl 1464.80015
Inglese, G.; Olmi, R.
2019
Reconstruction for Sturm-Liouville equations with a constant delay with twin-dense nodal subsets. Zbl 1461.34036
Wang, Yu Ping; Shieh, Chung Tsun; Miao, Hong Yi
2019
An iterated IRS technique for cross-sectional damage modelling and identification in beams using limited sensors measurement. Zbl 1466.74037
Hosseinzadeh, Ali Zare; Razzaghi, Seyed Ali Seyed; Amiri, Gholamreza Ghodrati
2019
Limited-angle acousto-electrical tomography. Zbl 1466.92088
Hubmer, Simon; Knudsen, Kim; Li, Changyou; Sherina, Ekaterina
2019
Determination of thermal conductivity of inhomogeneous orthotropic materials from temperature measurements. Zbl 1465.65088
Cao, K.; Lesnic, D.; Colaco, M. J.
2019
Reconstruction of a time-dependent source term in a time-fractional diffusion-wave equation. Zbl 1465.65089
Gong, Xuhong; Wei, Ting
2019
Simultaneous determination of spatially varying thermal conductivity and specific heat using boundary temperature measurements. Zbl 1466.80007
Reddy, Sohail R.; Dulikravich, George S.
2019
Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations. Zbl 1391.35417
Garde, Henrik
2018
Direct collocation method for identifying the initial conditions in the inverse wave problem using radial basis functions. Zbl 1428.65036
Wang, Lihua; Wang, Zhen; Qian, Zhihao; Gao, Yukui; Zhou, Yueting
2018
Simultaneous reconstruction of the time-dependent Robin coefficient and heat flux in heat conduction problems. Zbl 1423.35431
Abdelhamid, Talaat; Elsheikh, A. H.; Elazab, Ahmed; Sharshir, S. W.; Selima, Ehab S.; Jiang, Daijun
2018
Landweber iteration regularization method for identifying unknown source on a columnar symmetric domain. Zbl 1409.65066
Yang, Fan; Ren, Yu-Peng; Li, Xiao-Xiao
2018
Inverse spectral problems for Sturm-Liouville operators with complex weights. Zbl 1428.34033
Yurko, Vjacheslav
2018
Structural damage detection using improved particle swarm optimization. Zbl 1409.74041
Wei, Zitian; Liu, Jike; Lu, Zhongrong
2018
Inclusion boundary reconstruction and sensitivity analysis in electrical impedance tomography. Zbl 1409.92136
Ren, Shangjie; Soleimani, Manuchehr; Xu, Yaoyuan; Dong, Feng
2018
A numerical method for determining a quasi solution of a backward time-fractional diffusion equation. Zbl 1409.65064
Salehi Shayegan, A. H.; Zakeri, A.
2018
A greedy MLPG method for identifying a control parameter in 2D parabolic PDEs. Zbl 1428.65034
2018
A meshless method for solving 1D time-dependent heat source problem. Zbl 1398.65281
Rostamian, Malihe; Shahrezaee, Alimardan
2018
Identification of diffusion parameters in a non-linear convection-diffusion equation using adaptive homotopy perturbation method. Zbl 1388.76260
Liu, Tao; Liu, Songshu
2018
Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case. Zbl 1398.65361
D&rsquo;Amore, Luisa; Mele, Valeria; Campagna, Rosanna
2018
A new generalized Tikhonov method based on filtering idea for stable analytic continuation. Zbl 1398.65116
Qian, Zhi
2018
Direct regularization for system of integral-algebraic equations of index-1. Zbl 1454.65193
2018
A non-iterative method for identifying multiple unknown time-dependent sources compactly supported occurring in a 2D parabolic equation. Zbl 1409.65063
2018
Vascular blood flow reconstruction with contrast-enhanced computerized tomography. Zbl 1409.92139
Sixou, B.; Boussel, L.; Sigovan, M.
2018
The method of fundamental solution for the inverse source problem for the space-fractional diffusion equation. Zbl 1409.65065
Wen, Jin; Cheng, Jun-Feng
2018
Mathematical investigation of the error self-compensation mechanism in optical coating technology. Zbl 1409.74017
Tikhonravov, Alexander; Kochikov, Igor; Yagola, Anatoly
2018
Sensitivity-based damage identification method for structures exposed to ground excitation. Zbl 1423.86017
Vahedi, M.; Khoshnoudian, F.
2018
An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data. Zbl 1428.65037
Zhang, Y.; Forssén, P.; Fornstedt, T.; Gulliksson, M.; Dai, X.
2018
Inverse scattering problems of near-field subsurface pulse diagnostics. Zbl 1428.78018
Gaikovich, Konstantin P.; Maksimovitch, Yelena S.; Sumin, Mikhail I.
2018
Force identification based on a comprehensive approach combining Taylor formula and acceleration transmissibility. Zbl 1425.74205
Li, Xiaowang; Zhao, Haitao; Chen, Zheng; Wang, Quanbao; Chen, Ji-an; Duan, Dengping
2018
Multi cracks detection in Euler-Bernoulli beam subjected to a moving mass based on acceleration responses. Zbl 1425.74414
2018
First-order indicators for the estimation of discrete fractures in porous media. Zbl 1391.74226
Ameur, H. Ben; Chavent, G.; Cheikh, F.; Clément, F.; Martin, V.; Roberts, J. E.
2018
A model for the interaction of phytoplankton aggregates and the environment: approximation and parameter estimation. Zbl 1390.92155
Ackleh, Azmy S.; Miller, Robert L.
2018
Mathematical and statistical model misspecifications in modelling immune response in renal transplant recipients. Zbl 1390.92061
Banks, H. T.; Everett, R. A.; Hu, Shuhua; Murad, Neha; Tran, H. T.
2018
Bayesian model calibration and uncertainty quantification for an HIV model using adaptive Metropolis algorithms. Zbl 1390.92086
Wentworth, Mami T.; Smith, Ralph C.; Williams, Brian
2018
Application of inverse method to predict the breakthrough curve in fixed-bed adsorption. Zbl 1398.65236
Rahideh, H.; Mofarahi, M.; Malekzadeh, P.
2018
Characterization of elastic parameters for functionally graded material by a meshfree method combined with the NMS approach. Zbl 1388.74118
Chen, Bin; Chen, Wen; Wei, Xing
2018
Phase retrieval for sparse binary signal: uniqueness and algorithm. Zbl 1429.94038
Yuan, Ziyang; Wang, Hongxia
2018
The approximate solutions to source inverse problem of 1-D convection-diffusion equation by LS-SVM. Zbl 1409.74055
Yu, Jiaju; Li, Fule; Yu, Shuanghe; Wu, Ziku
2018
Numerical inversions for diffusion coefficients in two-dimensional space fractional diffusion equation. Zbl 1409.65062
Chi, Guangsheng; Li, Gongsheng
2018
Multivariate numerical derivative by solving an inverse heat source problem. Zbl 07039163
Qiu, Shufang; Wang, Zewen; Xie, Anlai
2018
On efficient reconstruction of boundary data with optimal placement of the source points in the MFS: application to inverse Stefan problems. Zbl 1428.65053
Reddy, G. M. M.; Vynnycky, M.; Cuminato, J. A.
2018
A high-order Lie groups scheme for solving the recovery of external force in nonlinear system. Zbl 1425.93098
Liu, Yu-Chen; Chen, Yung-Wei; Wang, Yu-Ting; Chang, Jiang-Ren
2018
Numerical solution of two-dimensional inverse force function in the wave equation with nonlocal boundary conditions. Zbl 1398.65237
2017
On a final value problem for the time-fractional diffusion equation with inhomogeneous source. Zbl 1398.65240
Tuan, Nguyen Huy; Long, Le Dinh; Nguyen, Van Thinh; Tran, Thanh
2017
On the half inverse spectral problem for an integro-differential operator. Zbl 1390.45022
Buterin, S. A.; Sat, M.
2017
A stable numerical scheme for a time fractional inverse parabolic equation. Zbl 1398.65239
Taghavi, A.; Babaei, A.; Mohammadpour, A.
2017
Identifying Lamé parameters from time-dependent elastic wave measurements. Zbl 1359.74034
Lechleiter, Armin; Schlasche, John W.
2017
Inverse scattering with fixed observation angle data in 2D. Zbl 1390.35213
Fotopoulos, Georgios; Harju, Markus
2017
First-order and second-order adjoint methods for parameter identification problems with an application to the elasticity imaging inverse problem. Zbl 1387.92057
2017
Simultaneous inversion for the diffusion and source coefficients in the multi-term TFDE. Zbl 1398.65238
Sun, Chunlong; Li, Gongsheng; Jia, Xianzheng
2017
Stabilized Richardson leapfrog scheme in explicit stepwise computation of forward or backward nonlinear parabolic equations. Zbl 1398.65205
Carasso, Alfred S.
2017
A self-regularized approach for rank-deficient systems in the BEM of 2D Laplace problems. Zbl 1359.74460
Chen, Jeng-Tzong; Lee, Ying-Te; Chang, Yu-Lung; Jian, Jie
2017
Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation. Zbl 1359.92056
Babaniyi, Olalekan A.; Oberai, Assad A.; Barbone, Paul E.
2017
Determining the initial distribution in space-fractional diffusion by a negative exponential regularization method. Zbl 1369.65137
Zheng, Guang-Hui; Zhang, Quan-Guo
2017
Determination of the initial condition in parabolic equations from integral observations. Zbl 1369.65116
Hào, Dinh Nho; Oanh, Nguyen Thi Ngoc
2017
Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations. Zbl 1397.65174
Asiri, Sharefa; Laleg-Kirati, Taous-Meriem
2017
A novel Trefftz method of the inverse Cauchy problem for 3D modified Helmholtz equation. Zbl 1398.65276
Liu, Chein-Shan; Qu, Wenzhen; Chen, Wen; Lin, Ji
2017
A posteriori error estimates for numerical solutions to inverse problems of elastography. Zbl 1359.74421
Leonov, A. S.; Sharov, A. N.; Yagola, A. G.
2017
Improved artificial bee colony algorithm for crack identification in beam using natural frequencies only. Zbl 1359.74203
Ding, Zhenghao; Lu, Zhongrong; Huang, Min; Liu, Jike
2017
Model-based identification of damage from sparse sensor measurements using Neumann series expansion. Zbl 1359.74361
Hosseinzadeh, Ali Zare; Amiri, Gholamreza Ghodrati; Razzaghi, Seyed Ali Seyed
2017
Identification of separable sources for advection-diffusion equations with variable diffusion coefficient from boundary measured data. Zbl 1362.80005
Kulbay, M.; Mukanova, B.; Sebu, C.
2017
Detection and identification of multiple unknown time-dependent point sources occurring in 1D evolution transport equations. Zbl 1359.65177
2017
Recovery of a time-dependent heat source in one-dimensional thermoelasticity of type-III. Zbl 1369.74023
Van Bockstal, K.; Slodička, M.
2017
Numerical solution of inverse nodal problem with an eigenvalue in the boundary condition. Zbl 1371.65066
Neamaty, A.; Akbarpoor, Sh.
2017
An adjoint method in inverse problems of chromatography. Zbl 1369.65119
Zhang, Y.; Lin, G.; Gulliksson, M.; Forssén, P.; Fornstedt, T.; Cheng, X.
2017
An inverse problem for a family of time fractional diffusion equations. Zbl 1398.65232
2017
Distributed dynamic load identification based on shape function method and polynomial selection technique. Zbl 1398.65177
Li, Kun; Liu, Jie; Han, Xu; Jiang, Chao; Zhang, Dequan
2017
Detection-identification of multiple unknown time-dependent point sources in a $$2D$$ transport equation: application to accidental pollution. Zbl 1398.65234
2017
Identification of injection and extraction wells from overspecified boundary data. Zbl 1369.65133
Mansouri, Wafa; Baranger, Thouraya Nouri; Ameur, Hend Ben; Tlatli, Nejla Hariga
2017
Iterative computational identification of a space-wise dependent source in parabolic equation. Zbl 1369.65118
Vabishchevich, P. N.
2017
A new hybrid real-coded genetic algorithm and its application to parameters identification of soils. Zbl 1390.74138
Jin, Yin-Fu; Yin, Zhen-Yu; Shen, Shui-Long; Zhang, Dong-Mei
2017
Convergence study of $$2D$$ forward problem of electrical impedance tomography with high-order finite elements. Zbl 1398.65295
Crabb, M. G.
2017
A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography. Zbl 1398.65363
Tepe, Jens; Schuster, Thomas; Littau, Benjamin
2017
Inverse problem of fracture mechanics for a circular disc under mixed boundary conditions. Zbl 1390.74168
Mirsalimov, Vagif M.; Hasanov, Shahin H.
2017
Optimal parameters identification and sensitivity study for abrasive waterjet milling model. Zbl 1444.35161
Auroux, D.; Groza, V.
2017
A numerical reconstruction method in inverse elastic scattering. Zbl 1390.74030
Bazán, F. S. V.; Francisco, J. B.; Leem, K. H.; Pelekanos, G.; Sevroglou, V.
2017
Dynamic moving load identification of laminated composite beams using a hybrid FE-TMDQ-GAs method. Zbl 1386.74081
Vosoughi, Ali R.; Anjabin, Nozar
2017
New “improved” Compton scatter tomography modality for investigative imaging of one-sided large objects. Zbl 1387.92055
Cebeiro, J.; Nguyen, M. K.; Morvidone, M. A.; Noumowé, A.
2017
Multifrequency near-field acoustic tomography and holography of 3D subbottom inhomogeneities. Zbl 1391.76691
Gaikovich, Konstantin P.; Gaikovich, Petr K.; Khilko, Alexander I.
2017
Inverse estimation of thermal properties using Bayesian inference and three different sampling techniques. Zbl 1359.74059
Somasundharam, S.; Reddy, K. S.
2017
Numerical solution of two backward parabolic problems using method of fundamental solutions. Zbl 1359.65238
2017
Crack identification of beam structures using homotopy continuation algorithm. Zbl 1359.74211
Hu, L.; Huang, L.; Lu, Z. R.
2017
Regularizing inversion of susceptibility with projection onto convex set using full tensor magnetic gradient data. Zbl 1362.78010
Ji, Shuangxi; Wang, Yanfei; Zou, Anqi
2017
Proper generalized decomposition model reduction in the Bayesian framework for solving inverse heat transfer problems. Zbl 1362.80003
Berger, Julien; Orlande, Helcio R. B.; Mendes, Nathan
2017
Taguchi-based design of experiments in training POD-RBF surrogate model for inverse material modelling using nanoindentation. Zbl 1359.74410
Hamim, Salah U.; Singh, Raman P.
2017
Inverse problem in the hyperthermia therapy of cancer with laser heating and plasmonic nanoparticles. Zbl 1359.92050
Lamien, Bernard; Orlande, Helcio Rangel Barreto; Eliçabe, Guillermo Enrique
2017
Robust inversion methods for aerosol spectroscopy. Zbl 1372.78014
Kyrion, Tobias; Alldredge, Graham
2017
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#### Cited by 2,398 Authors

 49 Lesnic, Daniel 37 Liu, Chein-Shan 27 Yang, Fan 25 Fu, Chuli 25 Johansson, B. Tomas 22 Wei, Ting 21 Li, Xiaoxiao 21 Nguyen Huy Tuan 20 Karageorghis, Andreas 18 Marin, Liviu 18 Yang, Chuanfu 15 Chen, Wen 15 Gu, Yan 15 Khan, Akhtar Ali 14 Bondarenko, Natalia P. 14 Xiong, Xiangtuan 13 Klibanov, Michael V. 13 Shivanian, Elyas 13 Slodička, Marián 13 Wang, Yuping 12 Jadamba, Baasansuren 12 Kanca, Fatma 12 Weber, Gerhard-Wilhelm 11 Chapko, Roman 11 Fan, Chia-Ming 11 Liu, Jijun 10 Buterin, Sergey Alexandrovich 10 Harrach, Bastian 10 Li, Gongsheng 9 Cheng, Xiaoliang 9 Han, Bo 9 Liu, Tao 9 Sama, Miguel 9 Shieh, Chung-Tsun 9 Sun, Shurong 9 Tatar, Salih 9 Wang, Yanfei 8 Baglan, Irem Sakinc 8 Bin-Mohsin, Bandar 8 Đinh Nho Hào 8 Frankel, Jay I. 8 Han, Weimin 8 Hon, Yiu-Chung 8 Orlande, Helcio Rangel Barreto 8 Qian, Zhi 8 Rashedi, Kamal 8 Trong, Dang Duc 8 van Bockstal, Karel 8 Wang, Jungang 8 Zhang, Ye 7 Gong, Rongfang 7 Grabski, Jakub Krzysztof 7 Hamdi, Adel 7 Jafarabadi, Ahmad 7 Kamynin, Vitaly L. 7 Khanh, Tra Quoc 7 Kolodziej, Jan Adam 7 Koyunbakan, Hikmet 7 Liu, Songshu 7 Reeve, Thomas 7 Šarler, Božidar 7 Wang, Fajie 7 Yagola, Anatoliĭ Grigor’evich 6 Abbasbandy, Saeid 6 Băleanu, Dumitru I. 6 Chen, Jeng-Tzong 6 Cheng, Hao 6 Cheng, Wei 6 Dehghan Takht Fooladi, Mehdi 6 Dou, Fangfang 6 Fu, Zhuojia 6 Gao, Zhiming 6 Hai, Dinh Nguyen Duy 6 Han, Zhenlai 6 Jia, Xianzheng 6 Keyhani, Majid 6 Li, Po-Wei 6 Lv, Xiaoguang 6 Ma, Yichen 6 Ma, Yunjie 6 Özmen, Ayşe 6 Pourgholi, Reza 6 Qiu, Shufang 6 Sun, Yao 6 Wang, Lihua 6 Wang, Zewen 6 Xu, Yongzhi S. 6 Zhang, Chuanzeng 6 Zheng, Guanghui 5 Adibi, Hojatollah 5 Alves, Carlos J. S. 5 Colaço, Marcelo J. 5 Corsato, Chiara 5 De Cezaro, Adriano 5 Feng, Xiaoli 5 Gutiérrez, Sergio 5 Haddar, Houssem 5 Hofmann, Bernd 5 Keskin, Baki 5 Kim, Sin-Bom ...and 2,298 more Authors
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#### Cited in 249 Journals

 319 Inverse Problems in Science and Engineering 121 Engineering Analysis with Boundary Elements 63 Journal of Inverse and Ill-Posed Problems 62 Computers & Mathematics with Applications 59 Journal of Computational and Applied Mathematics 52 Inverse Problems 49 Applied Mathematics and Computation 46 Applied Mathematical Modelling 31 Applicable Analysis 29 Applied Numerical Mathematics 28 Mathematical Problems in Engineering 24 International Journal of Heat and Mass Transfer 22 Journal of Computational Physics 21 Computer Methods in Applied Mechanics and Engineering 19 Numerical Algorithms 18 Boundary Value Problems 18 Inverse Problems and Imaging 16 Mathematical Methods in the Applied Sciences 15 Applied Mathematics Letters 15 International Journal of Computational Methods 14 Computational and Applied Mathematics 13 Optimization 13 SIAM Journal on Applied Mathematics 13 Advances in Difference Equations 12 Journal of Mathematical Analysis and Applications 12 SIAM Journal on Imaging Sciences 11 Journal of Engineering Mathematics 10 Journal of Differential Equations 10 International Journal of Computer Mathematics 10 SIAM Journal on Scientific Computing 10 Abstract and Applied Analysis 9 Mathematics and Computers in Simulation 9 Numerical Methods for Partial Differential Equations 9 Journal of Scientific Computing 9 Advances in Computational Mathematics 8 International Journal for Numerical Methods in Engineering 8 Numerical Functional Analysis and Optimization 8 Computational Mathematics and Mathematical Physics 8 Journal of Inequalities and Applications 8 Advances in Mathematical Physics 7 Computational Geosciences 6 Computational Mechanics 6 SIAM Journal on Mathematical Analysis 6 Computational Optimization and Applications 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Journal of Applied Mathematics and Computing 5 Computers and Fluids 5 Wave Motion 5 BIT 5 Results in Mathematics 5 Journal of Global Optimization 5 International Journal of Numerical Methods for Heat & Fluid Flow 5 Communications in Nonlinear Science and Numerical Simulation 5 Differential Equations 5 Journal of Applied Mathematics 5 Analysis and Mathematical Physics 4 Acta Mechanica 4 International Journal of Engineering Science 4 Journal of Optimization Theory and Applications 4 Numerische Mathematik 4 Quarterly of Applied Mathematics 4 Acta Applicandae Mathematicae 4 Journal of Mathematical Imaging and Vision 4 Cybernetics and Systems Analysis 4 Applied Mathematics. Series B (English Edition) 4 Filomat 4 European Journal of Mechanics. A. Solids 4 International Journal of Applied Mathematics and Computer Science 4 International Journal of Applied and Computational Mathematics 4 Journal of Applied Mathematics and Computational Mechanics 3 International Journal of Solids and Structures 3 Journal of Mathematical Physics 3 Ukrainian Mathematical Journal 3 Automatica 3 Mathematical and Computer Modelling 3 Journal of Integral Equations and Applications 3 Japan Journal of Industrial and Applied Mathematics 3 Turkish Journal of Mathematics 3 Mathematics and Mechanics of Solids 3 Optimization Methods & Software 3 Acta Mathematica Sinica. English Series 3 CEJOR. Central European Journal of Operations Research 3 Archives of Computational Methods in Engineering 3 Iranian Journal of Science and Technology. Transaction A: Science 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Structural and Multidisciplinary Optimization 3 Fixed Point Theory and Applications 3 Journal of Industrial and Management Optimization 3 Journal of Fixed Point Theory and Applications 3 Computational & Mathematical Methods in Medicine 3 Asian-European Journal of Mathematics 3 Mathematical Sciences 3 Journal of Mathematics 3 Journal of Function Spaces 3 Computational Methods for Differential Equations 2 Computer Physics Communications 2 Journal of Fluid Mechanics 2 Journal of the Franklin Institute 2 Linear and Multilinear Algebra 2 Bulletin of Mathematical Biology ...and 149 more Journals
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#### Cited in 41 Fields

 957 Numerical analysis (65-XX) 722 Partial differential equations (35-XX) 208 Mechanics of deformable solids (74-XX) 193 Classical thermodynamics, heat transfer (80-XX) 153 Operator theory (47-XX) 142 Ordinary differential equations (34-XX) 129 Fluid mechanics (76-XX) 94 Biology and other natural sciences (92-XX) 87 Operations research, mathematical programming (90-XX) 86 Calculus of variations and optimal control; optimization (49-XX) 85 Optics, electromagnetic theory (78-XX) 71 Integral equations (45-XX) 57 Statistics (62-XX) 56 Geophysics (86-XX) 56 Information and communication theory, circuits (94-XX) 49 Systems theory; control (93-XX) 35 Integral transforms, operational calculus (44-XX) 34 Computer science (68-XX) 27 Real functions (26-XX) 19 Probability theory and stochastic processes (60-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 16 Mechanics of particles and systems (70-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 11 Approximations and expansions (41-XX) 10 Potential theory (31-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Astronomy and astrophysics (85-XX) 6 Special functions (33-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Functional analysis (46-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Functions of a complex variable (30-XX) 4 Differential geometry (53-XX) 4 General topology (54-XX) 4 Quantum theory (81-XX) 3 History and biography (01-XX) 3 Difference and functional equations (39-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Mathematics education (97-XX)