# zbMATH — the first resource for mathematics

## Inverse Problems

 Short Title: Inverse Probl. Publisher: IOP Publishing, Bristol ISSN: 0266-5611 Online: http://iopscience.iop.org/0266-5611 Comments: Indexed cover-to-cover
 Documents Indexed: 4,427 Publications (since 1985) References Indexed: 860 Publications with 33,006 References.
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#### Authors

 72 Yamamoto, Masahiro 39 Ikehata, Masaru 39 Klibanov, Michael V. 36 Bertero, Mario 35 Somersalo, Erkki 32 Ramlau, Ronny 31 Burger, Martin 31 Colton, David Lem 30 Borcea, Liliana 30 Kaltenbacher, Barbara 30 Scherzer, Otmar 29 Cakoni, Fioralba 29 Cheney, Margaret 28 Hofmann, Bernd 27 Bal, Guillaume 27 Haddar, Houssem 27 Papanicolaou, George C. 26 Aktosun, Tuncay 26 Kaipio, Jari P. 26 Kirsch, Andreas 26 Kress, Rainer 26 Nakamura, Gen 26 Ramm, Alexander G. 24 Arridge, Simon R. 23 Louis, Alfred Karl 23 Monk, Peter B. 23 Siltanen, Samuli 23 Uhlmann, Gunther Alberto 22 Piana, Michele 21 Hu, Guanghui 21 Jin, Bangti 21 Rundell, William 21 Zou, Jun 20 Calvetti, Daniela 20 Hohage, Thorsten 20 Lesselier, Dominique 20 Seo, Jin Keun 19 Fokas, Athanassios S. 19 Isakov, Victor M. 19 Jin, Qinian 19 Schuster, Thomas 18 Boccacci, Patrizia 18 de Hoop, Maarten V. 18 Haltmeier, Markus 18 Lassas, Matti 18 Liu, Xiaodong 18 Novikov, Roman G. 17 Bao, Gang 17 Boiti, Marco 17 Cheng, Jin 17 Garnier, Josselin 17 Haber, Eldad 17 Kunyansky, Leonid A. 17 Liu, Hongyu 17 Pempinelli, Flora 17 Pike, E. R. 17 Potthast, Roland W. E. 17 Zhang, Bo 16 El Badia, Abdellatif 16 Hyvönen, Nuutti 16 Lionheart, William Robert Breckon 15 Defrise, Michel 15 Li, Peijun 15 McLaughlin, Joyce Rogers 15 Sabatier, Pierre C. 14 Đinh Nho Hào 14 Dorn, Oliver 14 Grünbaum, Francisco Alberto 14 Kang, Hyeonbae 14 Maass, Peter 14 Schönlieb, Carola-Bibiane 14 Shen, Chao-Liang 14 Sun, Jiguang 14 Symes, William W. 14 Yagle, Andrew E. 13 Akduman, Ibrahim 13 Engl, Heinz W. 13 Harrach, Bastian 13 Imanuvilov, Oleg Yu. 13 Lechleiter, Armin 13 Pereverzev, Sergei V. 13 Schotland, John C. 13 Stefanov, Plamen D. 13 Tsogka, Chrysoula 13 van den Berg, Peter M. 12 Abubakar, Aria 12 Bellassoued, Mourad 12 Borden, Brett 12 Han, Bo 12 Herman, Gabor T. 12 Hettlich, Frank 12 Kolehmainen, Ville 12 Mathé, Peter 12 Palamodov, Victor Pavlovitch 12 Rieder, Andreas 12 Sini, Mourad 12 Stuart, Andrew M. 12 Tautenhahn, Ulrich 12 Vauhkonen, Marko 12 Wang, Jenn-Nan ...and 4,496 more Authors
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#### Fields

 2,395 Partial differential equations (35-XX) 1,764 Numerical analysis (65-XX) 835 Optics, electromagnetic theory (78-XX) 566 Biology and other natural sciences (92-XX) 353 Operator theory (47-XX) 343 Information and communication theory, circuits (94-XX) 324 Integral transforms, operational calculus (44-XX) 283 Statistics (62-XX) 263 Geophysics (86-XX) 262 Ordinary differential equations (34-XX) 260 Fluid mechanics (76-XX) 255 Mechanics of deformable solids (74-XX) 232 Integral equations (45-XX) 197 Dynamical systems and ergodic theory (37-XX) 176 Calculus of variations and optimal control; optimization (49-XX) 147 Operations research, mathematical programming (90-XX) 143 Computer science (68-XX) 136 Quantum theory (81-XX) 82 Probability theory and stochastic processes (60-XX) 78 Harmonic analysis on Euclidean spaces (42-XX) 78 Systems theory; control (93-XX) 68 Global analysis, analysis on manifolds (58-XX) 54 Linear and multilinear algebra; matrix theory (15-XX) 49 Differential geometry (53-XX) 49 Statistical mechanics, structure of matter (82-XX) 41 Classical thermodynamics, heat transfer (80-XX) 40 Astronomy and astrophysics (85-XX) 38 Potential theory (31-XX) 33 Mechanics of particles and systems (70-XX) 29 Functional analysis (46-XX) 27 Functions of a complex variable (30-XX) 24 Difference and functional equations (39-XX) 23 Special functions (33-XX) 21 General and overarching topics; collections (00-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Approximations and expansions (41-XX) 11 Abstract harmonic analysis (43-XX) 11 Relativity and gravitational theory (83-XX) 10 Real functions (26-XX) 7 Combinatorics (05-XX) 6 Algebraic topology (55-XX) 4 History and biography (01-XX) 4 Topological groups, Lie groups (22-XX) 4 Sequences, series, summability (40-XX) 4 Convex and discrete geometry (52-XX) 3 General topology (54-XX) 2 Nonassociative rings and algebras (17-XX) 2 Measure and integration (28-XX) 2 Geometry (51-XX) 1 Number theory (11-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Manifolds and cell complexes (57-XX)

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3,511 Publications have been cited 37,878 times in 14,495 Documents Cited by Year
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Iterative oblique projection onto convex sets and the split feasibility problem. Zbl 0996.65048
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2002
The multiple-sets split feasibility problem and its applications for inverse problems. Zbl 1089.65046
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2005
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Optical tomography in medical imaging. Zbl 0926.35155
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The relaxed CQ algorithm solving the split feasibility problem. Zbl 1066.65047
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Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Zbl 1213.65085
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2010
Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044
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Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems. Zbl 0695.65037
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1989
A simple method for solving inverse scattering problems in the resonance region. Zbl 0859.35133
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A note on the $$CQ$$ algorithm for the split feasibility problem. Zbl 1080.65033
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2005
The split common fixed-point problem for demicontractive mappings. Zbl 1219.90185
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Inverse problems and Carleman estimates. Zbl 0755.35151
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Solving the split feasibility problem without prior knowledge of matrix norms. Zbl 1262.90193
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Multi-peakon solutions of the Degasperis-Procesi equation. Zbl 1041.35090
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Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation. Zbl 1181.35322
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2009
Multi-peakons and a theorem of Stieltjes. Zbl 0923.35154
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1999
A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Zbl 1131.65046
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Geometry of linear ill-posed problems in variable Hilbert spaces. Zbl 1026.65040
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Electrical impedance tomography. Zbl 1031.35147
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Electrical impedance tomography and Calderón’s problem. Zbl 1181.35339
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Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Zbl 0919.35147
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A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems. Zbl 0873.65057
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The stability for the Cauchy problem for elliptic equations. Zbl 1190.35228
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2009
Carleman estimates for parabolic equations and applications. Zbl 1194.35512
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2009
Several solution methods for the split feasibility problem. Zbl 1080.65035
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2005
Convergence rates of convex variational regularization. Zbl 1068.65085
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2004
A tutorial on inverse problems for anomalous diffusion processes. Zbl 1323.34027
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2015
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1987
Inverse problems in elasticity. Zbl 1070.35118
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2005
Lipschitz stability in inverse parabolic problems by the Carleman estimate. Zbl 0992.35110
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1998
Sparsity and incoherence in compressive sampling. Zbl 1120.94005
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2007
Structural identification of an unknown source term in a heat equation. Zbl 0917.35156
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1998
Restricted isometry properties and nonconvex compressive sensing. Zbl 1143.94004
Chartrand, Rick; Staneva, Valentina
2008
Prolate spheroidal wavefunctions, quadrature and interpolation. Zbl 0991.65024
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2001
Exponential instability in an inverse problem for the Schrödinger equation. Zbl 0985.35110
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2001
Global Lipschitz stability in an inverse hyperbolic problem by interior observations. Zbl 0983.35151
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2001
Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Zbl 0916.35132
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1998
The domain derivative and two applications in inverse scattering theory. Zbl 0773.35085
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Tensor completion and low-$$n$$-rank tensor recovery via convex optimization. Zbl 1211.15036
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2011
The strong convergence of a KM-CQ-like algorithm for a split feasibility problem. Zbl 1211.65065
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2011
Krasnoselski–Mann iteration for hierarchical fixed-point problems. Zbl 1128.47060
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2007
Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014
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2003
Analysis versus synthesis in signal priors. Zbl 1138.93055
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2007
Inverse source problem for a fractional diffusion equation. Zbl 1211.35280
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2011
Boundary control in reconstruction of manifolds and metrics (the BC method). Zbl 0990.35135
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1997
A survey on sampling and probe methods for inverse problems. Zbl 1094.35144
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2006
Thermoacoustic tomography with variable sound speed. Zbl 1177.35256
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2009
Uniqueness and stability in an inverse problem for the Schrödinger equation. Zbl 1023.35091
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2002
Solutions of inverse nodal problems. Zbl 0667.34020
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1989
Level set methods for inverse scattering. Zbl 1191.35272
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2006
A finite-difference solution to an inverse problem for determining a control function in a parabolic partial differential equation. Zbl 0683.65106
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1989
Proximity algorithms for image models: denoising. Zbl 1216.94015
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2011
Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method. Zbl 0822.35154
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1995
An inverse problem for a one-dimensional time-fractional diffusion problem. Zbl 1247.35203
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2012
Simultaneous reconstruction of the initial temperature and heat radiative coefficient. Zbl 0987.35166
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2001
Logarithmic convergence rates of the iteratively regularized Gauss-Newton method for an inverse potential and an inverse scattering problem. Zbl 0895.35109
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1997
A simple method using Morozov’s discrepancy principle for solving inverse scattering problems. Zbl 0902.35123
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1997
Edge-preserving and scale-dependent properties of total variation regularization. Zbl 1043.94512
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2003
On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions. Zbl 0617.35119
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1986
Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets. Zbl 0938.35190
Bouchouev, Ilia; Isakov, Victor
1999
One new strategy for a priori choice of regularizing parameters in Tikhonov’s regularization. Zbl 0957.65052
Cheng, J.; Yamamoto, M.
2000
Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates. Zbl 1205.65194
Egger, Herbert; Engl, Heinz W.
2005
Level-set function approach to an inverse interface problem. Zbl 0986.35130
Ito, Kazufumi; Kunisch, Karl; Li, Zhilin
2001
An inverse problem in corrosion detection. Zbl 0882.35133
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1997
Explicit inversion formulae for the spherical mean Radon transform. Zbl 1127.44003
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2007
Recent progress in the boundary control method. Zbl 1126.35089
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2007
Nonlinear integral equations and the iterative solution for an inverse boundary value problem. Zbl 1086.35139
Kress, Rainer; Rundell, William
2005
Inverse spectral problems for Sturm-Liouville operators on graphs. Zbl 1089.34009
Yurko, V.
2005
Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation. Zbl 1281.65125
Li, Gongsheng; Zhang, Dali; Jia, Xianzheng; Yamamoto, Masahiro
2013
A scaled gradient projection method for constrained image deblurring. Zbl 1155.94011
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2009
Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations. Zbl 0805.65133
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1994
Nonlinear evolution equations, rescalings, model PDEs and their integrability. I. Zbl 0645.35087
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1987
Solving Cauchy problems by minimizing an energy-like functional. Zbl 1089.35084
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2006
Nonparametric statistical inverse problems. Zbl 1137.62323
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2008
Inverse nodal problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions. Zbl 0860.34007
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1996
On the method of Lavrentiev regularization for nonlinear ill-posed problems. Zbl 1005.65058
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2002
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media. Zbl 1180.35563
Hristova, Yulia; Kuchment, Peter; Nguyen, Linh
2008
Generalized KM theorems and their applications. Zbl 1117.65081
Yang, Qingzhi; Zhao, Jinling
2006
Optical tomography: forward and inverse problems. Zbl 1188.35197
Arridge, Simon R.; Schotland, John C.
2009
Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography. Zbl 1044.78513
Kaipio, Jari P.; Kolehmainen, Ville; Somersalo, Erkki; Vauhkonen, Marko
2000
Linear spectral problems, nonlinear equations and the $${\bar \partial}$$- method. Zbl 0685.35080
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1989
An implementation of the reconstruction algorithm of A. Nachman for the 2D inverse conductivity problem. Zbl 0962.35193
Siltanen, Samuli; Mueller, Jennifer; Isaacson, David
2000
Prolongation algebras and Hamiltonian operators for peakon equations. Zbl 1020.35096
Hone, Andrew N. W.; Wang, Jing Ping
2003
On a global estimate in a linear inverse hyperbolic problem. Zbl 0862.35141
Puel, Jean-Pierre; Yamamoto, Masahiro
1996
Multisoliton solutions of the Degasperis-Procesi equation and their peakon limit. Zbl 1086.35095
Matsuno, Yoshimasa
2005
Identification of Robin coefficients by the means of boundary measurements. Zbl 0943.35100
Chaabane, Slim; Jaoua, Mohamed
1999
Fréchet derivatives in inverse obstacle scattering. Zbl 0821.35147
Hettlich, Frank
1995
An iterative regularization method for the solution of the split feasibility problem in Banach spaces. Zbl 1153.46308
Schöpfer, F.; Schuster, T.; Louis, A. K.
2008
An inverse source problem in potential analysis. Zbl 0963.35194
2000
Uniqueness in inverse obstacle scattering. Zbl 0787.35119
Kirsch, Andreas; Kress, Rainer
1993
Identifying the volatility of underlying assets from option prices. Zbl 0997.91024
Jiang, Lishang; Tao, Youshan
2001
Identification of planar cracks by complete overdetermined data: Inversion formulae. Zbl 0858.35131
Andrieux, Stéphane; Ben Abda, Amel
1996
Numerical identification of parameters in parabolic systems. Zbl 0894.35127
Keung, Yee Lo; Zou, Jun
1998
Cloaking via change of variables in electric impedance tomography. Zbl 1153.35406
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2008
Fréchet differentiability of boundary integral operators in inverse acoustic scattering. Zbl 0805.35157
Potthast, Roland
1994
Determination of a coefficient in an acoustic equation with a single measurement. Zbl 1020.35117
Imanuvilov, Oleg Yu.; Yamamoto, Masahiro
2003
Construction of dKP and BKP equations with self-consistent sources. Zbl 1105.37043
Hu, Xing-Biao; Wang, Hong-Yan
2006
Approximate solution of a Cauchy problem for the Helmholtz equation. Zbl 1099.35160
Regińska, Teresa; Regiński, Kazimierz
2006
Monotonicity principle in tomography of nonlinear conducting materials. Zbl 1462.78012
Corbo Esposito, Antonio; Faella, Luisa; Piscitelli, Gianpaolo; Prakash, Ravi; Tamburrino, Antonello
2021
A projected Bouligand-Landweber iteration for non-smooth ill-posed problems. Zbl 07323231
Fu, Zhenwu; Chen, Yong; Han, Bo
2021
Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems. Zbl 1456.35192
Diao, Huaian; Liu, Hongyu; Zhang, Long; Zou, Jun
2021
Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation. Zbl 1462.35469
Sun, L. L.; Li, Y. S.; Zhang, Y.
2021
A deterministic-statistical approach to reconstruct moving sources using sparse partial data. Zbl 1466.35369
Liu, Yanfang; Guo, Yukun; Sun, Jiguang
2021
3D Compton scattering imaging with multiple scattering: analysis by FIO and contour reconstruction. Zbl 1466.35372
Rigaud, Gaël
2021
Recovery of coefficients for a weighted $$p$$-Laplacian perturbed by a linear second order term. Zbl 1460.35386
Cârstea, Cătălin I.; Kar, Manas
2021
Recovering a quasilinear conductivity from boundary measurements. Zbl 1457.65172
Shankar, Ravi
2021
A direct method for solving inverse Sturm-Liouville problems. Zbl 07305940
Kravchenko, Vladislav V.; Torba, Sergii M.
2021
Unique determination for an inverse problem from the vortex dynamics. Zbl 1462.34041
Lai, Ru-Yu; Zhou, Hanming
2021
An inverse potential problem for subdiffusion: stability and reconstruction. Zbl 1458.35477
Jin, Bangti; Zhou, Zhi
2021
The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy. Zbl 1434.65082
Denoyelle, Quentin; Duval, Vincent; Peyré, Gabriel; Soubies, Emmanuel
2020
Convergence analysis of (statistical) inverse problems under conditional stability estimates. Zbl 07153871
Werner, Frank; Hofmann, Bernd
2020
Uniqueness in inverse cavity scattering problems with phaseless near-field data. Zbl 1460.35246
Zhang, Deyue; Wang, Yinglin; Guo, Yukun; Li, Jingzhi
2020
NETT: solving inverse problems with deep neural networks. Zbl 1456.65038
Li, Housen; Schwab, Johannes; Antholzer, Stephan; Haltmeier, Markus
2020
Convexification and experimental data for a 3D inverse scattering problem with the moving point source. Zbl 1446.35265
Khoa, Vo Anh; Bidney, Grant W.; Klibanov, Michael V.; Nguyen, Loc H.; Nguyen, Lam H.; Sullivan, Anders J.; Astratov, Vasily N.
2020
The Calderón problem for the fractional magnetic operator. Zbl 1443.35194
Li, Li
2020
Preconditioning inverse problems for hyperbolic equations with applications to photoacoustic tomography. Zbl 07153865
Beigl, Alexander; Scherzer, Otmar; Sogn, Jarle; Zulehner, Walter
2020
Compton scattering tomography in translational geometries. Zbl 1466.44002
Webber, James; Miller, Eric L.
2020
Persistent homology detects curvature. Zbl 07161824
Bubenik, Peter; Hull, Michael; Patel, Dhruv; Whittle, Benjamin
2020
Fast acoustic source imaging using multi-frequency sparse data. Zbl 1448.35566
Alzaalig, Ala; Hu, Guanghui; Liu, Xiaodong; Sun, Jiguang
2020
Sparse reconstructions from few noisy data: analysis of hierarchical Bayesian models with generalized gamma hyperpriors. Zbl 1464.62365
Calvetti, Daniela; Pragliola, Monica; Somersalo, Erkki; Strang, Alexander
2020
Inverse problems for nonlinear quasi-hemivariational inequalities with application to mixed boundary value problems. Zbl 1433.35462
Migórski, Stanisław; Khan, Akhtar A.; Zeng, Shengda
2020
Half-inverse Sturm-Liouville problem on a time scale. Zbl 1433.93084
2020
An inverse acoustic-elastic interaction problem with phased or phaseless far-field data. Zbl 1437.35702
Dong, Heping; Lai, Jun; Li, Peijun
2020
Recovering piecewise constant refractive indices by a single far-field pattern. Zbl 1446.35262
Blåsten, Emilia; Liu, Hongyu
2020
Monotonicity in inverse obstacle scattering on unbounded domains. Zbl 1458.35469
Albicker, Annalena; Griesmaier, Roland
2020
The inverse problem of reconstructing reaction-diffusion systems. Zbl 1444.65055
Kaltenbacher, Barbara; Rundell, William
2020
Convergence rates of Tikhonov regularizations for elliptic and parabolic inverse radiativity problems. Zbl 07220290
Chen, De-Han; Jiang, Daijun; Zou, Jun
2020
Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves. Zbl 07220297
Chen, Bo; Guo, Yukun; Ma, Fuming; Sun, Yao
2020
A new temporal control approach for SCAO systems. Zbl 1440.93131
Pöttinger, Markus; Ramlau, Ronny; Auzinger, Günter
2020
Determining both the source of a wave and its speed in a medium from boundary measurements. Zbl 1458.35480
2020
Analysis of shape optimization problems for unsteady fluid-structure interaction. Zbl 1440.49044
Haubner, Johannes; Ulbrich, Michael; Ulbrich, Stefan
2020
Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations. Zbl 1453.35197
Sunseri, Isaac; Hart, Joseph; van Bloemen Waanders, Bart; Alexanderian, Alen
2020
Hölder-logarithmic stability in Fourier synthesis. Zbl 1453.42008
Isaev, Mikhail; Novikov, Roman G.
2020
Bayesian approach to inverse time-harmonic acoustic scattering with phaseless far-field data. Zbl 1443.76205
Yang, Zhipeng; Gui, Xinping; Ming, Ju; Hu, Guanghui
2020
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs. Zbl 1443.62213
Koval, Karina; Alexanderian, Alen; Stadler, Georg
2020
Semiclassical inverse spectral problem for seismic surface waves in isotropic media. I: Love waves. Zbl 1442.86003
de Hoop, Maarten V.; Iantchenko, Alexei; van der Hilst, Robert D.; Zhai, Jian
2020
A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium. Zbl 1433.78016
Fujiwara, Hiroshi; Sadiq, Kamran; Tamasan, Alexandru
2020
Reconstruction of the principal coefficient in the damped wave equation from Dirichlet-to-Neumann operator. Zbl 1457.35094
2020
Inverse transport problem in fluorescence ultrasound modulated optical tomography with angularly averaged measurements. Zbl 1466.35370
Li, Wei; Yang, Yang; Zhong, Yimin
2020
Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes. Zbl 07161831
Moscovich, Amit; Halevi, Amit; Andén, Joakim; Singer, Amit
2020
Sharp stability estimate for the geodesic ray transform. Zbl 1450.44003
Assylbekov, Yernat M.; Stefanov, Plamen
2020
Recovery of singularities for the weighted cone transform appearing in Compton camera imaging. Zbl 1442.44003
Zhang, Yang
2020
The ML-EM algorithm in continuum: sparse measure solutions. Zbl 1436.62392
Pouchol, Camille; Verdier, Olivier
2020
Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media. Zbl 1436.35328
Wei, Zhaoying; Wei, Guangsheng
2020
On the inverse spectral stability for the transmission eigenvalue problem with finite data. Zbl 07239311
Xu, Xiao-Chuan; Yang, Chuan-Fu
2020
Convexification for an inverse parabolic problem. Zbl 1445.35333
Klibanov, Michael V.; Li, Jingzhi; Zhang, Wenlong
2020
Stable determination of polygonal inclusions in Calderón’s problem by a single partial boundary measurement. Zbl 1445.35334
Liu, Hongyu; Tsou, Chun-Hsiang
2020
On a regularization approach to the inverse transmission eigenvalue problem. Zbl 1454.34036
Buterin, S. A.; Choque-Rivero, A. E.; Kuznetsova, M. A.
2020
A joint reconstruction and lambda tomography regularization technique for energy-resolved x-ray imaging. Zbl 07236582
Webber, James W.; Quinto, Eric Todd; Miller, Eric L.
2020
Semiclassical inverse spectral problem for seismic surface waves in isotropic media. II: Rayleigh waves. Zbl 1440.86007
de Hoop, Maarten V.; Iantchenko, Alexei; van der Hilst, Robert D.; Zhai, Jian
2020
Backward problems in time for fractional diffusion-wave equation. Zbl 1456.35205
Floridia, Giuseppe; Yamamoto, Masahiro
2020
A globally convergent algorithm for a class of gradient compounded non-Lipschitz models applied to non-additive noise removal. Zbl 1461.94030
Zheng, Zhe; Ng, Michael; Wu, Chunlin
2020
Well-conditioned ptychograpic imaging via lost subspace completion. Zbl 1458.94029
Forstner, Anton; Krahmer, Felix; Melnyk, Oleh; Sissouno, Nada
2020
Numerical solution of inverse problems by weak adversarial networks. Zbl 1452.65308
Bao, Gang; Ye, Xiaojing; Zang, Yaohua; Zhou, Haomin
2020
The conical Radon transform with vertices on triple line segments. Zbl 1451.81404
Moon, Sunghwan; Haltmeier, Markus
2020
Classification of stroke using neural networks in electrical impedance tomography. Zbl 1451.92178
Agnelli, J. P.; Çöl, A.; Lassas, Matti; Murthy, Rashmi; Santacesaria, Matteo; Siltanen, Samuli
2020
Recovering a potential in damped wave equation from Neumann-to-Dirichlet operator. Zbl 1452.35260
2020
Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data. Zbl 1452.35259
Li, Zhiyuan; Zhang, Zhidong
2020
An unbiased approach to compressed sensing. Zbl 1458.94080
Carlsson, Marcus; Gerosa, Daniele; Olsson, Carl
2020
TV-based reconstruction of periodic functions. Zbl 1458.94087
Fageot, Julien; Simeoni, Matthieu
2020
Stability for inverse source problems by Carleman estimates. Zbl 1459.35393
Huang, X.; Yu Imanuvilov, Oleg; Yamamoto, M.
2020
Radiative transport model for coherent acousto-optic tomography. Zbl 1442.65453
Chung, Francis J.; Hoskins, Jeremy G.; Schotland, John C.
2020
The bound-state soliton solutions of the complex modified KdV equation. Zbl 1447.35290
Zhang, Yongshuai; Tao, Xiangxing; Xu, Shuwei
2020
A parameter choice rule for Tikhonov regularization based on predictive risk. Zbl 07211714
Benvenuto, Federico; Jin, Bangti
2020
A note on the minimization of a Tikhonov functional with $$\ell^1$$-penalty. Zbl 1455.65086
Hinterer, Fabian; Hubmer, Simon; Ramlau, Ronny
2020
Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction. Zbl 1444.65062
Cueva, Evelyn; Courdurier, Matias; Osses, Axel; Castañeda, Victor; Palacios, Benjamin; Härtel, Steffen
2020
Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed. Zbl 1448.34156
Bugarija, Sophia; Gibson, Peter C.; Hu, Guanghui; Li, Peijun; Zhao, Yue
2020
A revisit on Landweber iteration. Zbl 1460.65062
Real, Rommel; Jin, Qinian
2020
Uniqueness of an inverse source problem in experimental aeroacoustics. Zbl 1464.76186
Hohage, Thorsten; Raumer, Hans-Georg; Spehr, Carsten
2020
Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity. Zbl 1439.35564
Jin, Bangti; Xu, Yifeng
2020
Quasi-best approximation in optimization with PDE constraints. Zbl 1457.49022
Gaspoz, Fernando; Kreuzer, Christian; Veeser, Andreas; Wollner, Winnifried
2020
Image reconstruction through metamorphosis. Zbl 1447.94005
Gris, Barbara; Chen, Chong; Öktem, Ozan
2020
Preface to special issue on joint reconstruction and multi-modality/multi-spectral imaging. Zbl 1429.00023
Arridge, Simon R.; Burger, Martin; Ehrhardt, Matthias J.
2020
Factorization of the translation kernel for fast rigid image alignment. Zbl 07161829
Rangan, Aaditya; Spivak, Marina; Andén, Joakim; Barnett, Alex
2020
Sparsity and level set regularization for near-field electromagnetic imaging in 3D. Zbl 1433.78033
Hiles, Alex J.; Dorn, Oliver
2020
A Nash game based variational model for joint image intensity correction and registration to deal with varying illumination. Zbl 1452.94009
Theljani, Anis; Chen, Ke
2020
Explicit power laws in analytic continuation problems via reproducing kernel Hilbert spaces. Zbl 1455.65089
Grabovsky, Yury; Hovsepyan, Narek
2020
Solving inverse bioheat problems of skin tumour identification by dynamic thermography. Zbl 1435.80011
Iljaž, Jurij; Wrobel, L. C.; Gomboc, T.; Hriberšek, M.; Marn, J.
2020
Electro-magnetoencephalography for a spherical multiple-shell model: novel integral operators with singular-value decompositions. Zbl 07180441
Leweke, S.; Michel, V.; Fokas, A. S.
2020
The fixed angle scattering problem and wave equation inverse problems with two measurements. Zbl 1439.35569
Rakesh; Salo, Mikko
2020
Uniqueness of solution of an inverse source problem for ultrahyperbolic equations. Zbl 1446.45010
Gölgeleyen, Fikret; Yamamoto, Masahiro
2020
Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains. Zbl 1445.35147
Behrndt, Jussi; Rohleder, Jonathan
2020
Applications of kinetic tools to inverse transport problems. Zbl 1452.65211
Li, Qin; Sun, Weiran
2020
Nachman’s reconstruction method for the Calderón problem with discontinuous conductivities. Zbl 1437.35356
Lytle, George; Perry, Peter; Siltanen, Samuli
2020
Modulus-based iterative methods for constrained $$\ell_p$$-$$\ell_q$$ minimization. Zbl 1451.65072
Buccini, A.; Pasha, M.; Reichel, L.
2020
Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem. Zbl 1445.35330
Giordano, Matteo; Nickl, Richard
2020
On diffusive scaling in acousto-optic imaging. Zbl 1445.35327
Chung, Francis J.; Lai, Ru-Yu; Li, Qin
2020
Microlocally accurate solution of the inverse source problem of thermoacoustic tomography. Zbl 1448.92110
Eller, M.; Hoskins, P.; Kunyansky, L.
2020
The D-bar method for electrical impedance tomography – demystified. Zbl 1453.78007
Mueller, J. L.; Siltanen, Samuli
2020
A frame decomposition of the atmospheric tomography operator. Zbl 1448.78011
Hubmer, Simon; Ramlau, Ronny
2020
Geometry of the phase retrieval problem. Zbl 1451.49037
Barnett, Alexander H.; Epstein, Charles L.; Greengard, Leslie F.; Magland, Jeremy F.
2020
Computed tomography reconstruction using deep image prior and learned reconstruction methods. Zbl 1460.68093
Baguer, Daniel Otero; Leuschner, Johannes; Schmidt, Maximilian
2020
A projective averaged Kaczmarz iteration for nonlinear ill-posed problems. Zbl 1451.65068
Tong, Shanshan; Han, Bo; Tang, Jinping
2020
Generalized V-line transforms in 2D vector tomography. Zbl 1461.44001
2020
Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data. Zbl 1450.35286
Arens, Tilo; Ji, Xia; Liu, Xiaodong
2020
Hyper-molecules: on the representation and recovery of dynamical structures for applications in flexible macro-molecules in cryo-EM. Zbl 1467.92076
Lederman, Roy R.; Andén, Joakim; Singer, Amit
2020
Consistency of a phase field regularisation for an inverse problem governed by a quasilinear Maxwell system. Zbl 07371357
Lam, Kei Fong; Yousept, Irwin
2020
The quadratic Wasserstein metric for inverse data matching. Zbl 1465.49029
Engquist, Björn; Ren, Kui; Yang, Yunan
2020
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#### Cited by 13,485 Authors

 128 Yamamoto, Masahiro 78 Fu, Chuli 77 Uhlmann, Gunther Alberto 74 Klibanov, Michael V. 73 Ammari, Habib M. 67 Nguyen Huy Tuan 67 Yang, Chuanfu 66 Lesnic, Daniel 61 Yurko, Vjacheslav Anatoljevich 56 Dehghan Takht Fooladi, Mehdi 56 Scherzer, Otmar 55 Hofmann, Bernd 55 Yao, Yonghong 52 Ma, Wen-Xiu 52 Ramm, Alexander G. 51 Liu, Jijun 50 Yin, Zhaoyang 49 Lassas, Matti 49 Wei, Ting 49 Yao, Jen-Chih 48 Ceng, Lu-Chuan 48 Xiong, Xiangtuan 45 Hu, Guanghui 45 Liou, Yeongcheng 44 Shehu, Yekini 43 Banks, Harvey Thomas 43 Kaltenbacher, Barbara 43 Nakamura, Gen 41 de Hoop, Maarten V. 41 Jin, Bangti 39 Liu, Hongyu 38 Geng, Xianguo 38 Han, Bo 38 Zou, Jun 37 Bellassoued, Mourad 37 Cakoni, Fioralba 37 Haddar, Houssem 37 Hasanoǧlu, Alemdar 37 Kress, Rainer 36 Fokas, Athanassios S. 35 Fan, Engui 35 Kian, Yavar 35 Pereverzev, Sergei V. 35 Reichel, Lothar 35 Sakhnovich, Alexander L. 34 Bal, Guillaume 34 Garnier, Josselin 34 Lu, Shuai 33 Salo, Mikko 33 Stuart, Andrew M. 33 Vessella, Sergio 32 Bondarenko, Natalia P. 32 Burger, Martin 32 Chang, Shih-Sen 32 Hon, Yiu-Chung 32 Liu, Chein-Shan 32 Marin, Liviu 32 Van der Mee, Cornelis Victor Maria 31 Cheng, Jin 31 George, Santhosh 31 Haltmeier, Markus 31 Huang, Ting-Zhu 31 Mathé, Peter 31 Yang, Fan 30 Kang, Hyeonbae 30 Ramlau, Ronny 30 Wei, Guangsheng 29 Bao, Gang 29 Novikov, Roman G. 29 Park, Won-Kwang 29 Sini, Mourad 29 Stefanov, Plamen D. 29 Xu, Hong-Kun 28 Belishev, Mikhail Igorevitch 28 Censor, Yair 28 Choulli, Mourad 28 Hyvönen, Nuutti 28 Jin, Qinian 28 Korotyaev, Evgeny L. 28 Kunisch, Karl 28 Ma, Fuming 28 Wen, Chingfeng 28 Yan, Guozheng 27 Aktosun, Tuncay 27 Cho, Yeol Je 27 Li, Jingzhi 27 Oksanen, Lauri 27 Trong, Dang Duc 26 Buterin, Sergey Alexandrovich 26 Cheng, Xiaoliang 26 Colton, David Lem 26 Hu, Xingbiao 26 Kumam, Poom 26 Novotny, Antonio André 26 Romanov, Vladimir Gavrilovich 26 Rundell, William 26 Wang, Jenn-Nan 26 Zhang, Bo 25 Đinh Nho Hào 25 Han, Weimin ...and 13,385 more Authors
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#### Cited in 737 Journals

 678 Inverse Problems 462 Journal of Mathematical Physics 438 Inverse Problems in Science and Engineering 400 Journal of Inverse and Ill-Posed Problems 391 Journal of Computational and Applied Mathematics 386 Applied Mathematics and Computation 349 Journal of Mathematical Analysis and Applications 327 Applicable Analysis 297 Inverse Problems and Imaging 272 Journal of Computational Physics 223 Computers & Mathematics with Applications 181 Journal of Differential Equations 175 SIAM Journal on Imaging Sciences 162 Numerical Algorithms 157 Mathematical Methods in the Applied Sciences 153 Applied Mathematics Letters 140 SIAM Journal on Scientific Computing 137 Journal of Nonlinear Mathematical Physics 133 Applied and Computational Harmonic Analysis 130 Computer Methods in Applied Mechanics and Engineering 129 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 128 Theoretical and Mathematical Physics 119 Applied Numerical Mathematics 118 Numerical Functional Analysis and Optimization 118 Linear Algebra and its Applications 117 Abstract and Applied Analysis 116 Journal of Scientific Computing 114 Fixed Point Theory and Applications 109 Mathematical Problems in Engineering 108 SIAM Journal on Applied Mathematics 108 SIAM Journal on Mathematical Analysis 103 Wave Motion 99 Optimization 97 Journal of Mathematical Imaging and Vision 96 Communications in Mathematical Physics 95 Applied Mathematical Modelling 94 Engineering Analysis with Boundary Elements 92 Journal of Optimization Theory and Applications 88 Communications in Partial Differential Equations 87 Journal of Inequalities and Applications 84 Numerische Mathematik 75 Computational Optimization and Applications 70 Journal of Functional Analysis 63 Journal of Integral Equations and Applications 63 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 62 International Journal of Computer Mathematics 59 Mathematics of Computation 58 Journal of Mathematical Sciences (New York) 57 Chaos, Solitons and Fractals 57 Advances in Computational Mathematics 57 SIAM/ASA Journal on Uncertainty Quantification 56 Journal de Mathématiques Pures et Appliquées. Neuvième Série 56 Computational Geosciences 55 Physica D 55 Journal of Applied Mathematics 55 Comptes Rendus. Mathématique. Académie des Sciences, Paris 53 Studies in Applied Mathematics 52 Mathematics and Computers in Simulation 52 Boundary Value Problems 51 Computational and Applied Mathematics 51 Nonlinear Analysis. Real World Applications 50 SIAM Journal on Numerical Analysis 50 The Journal of Fourier Analysis and Applications 50 Communications in Nonlinear Science and Numerical Simulation 48 Proceedings of the American Mathematical Society 48 Transactions of the American Mathematical Society 47 Journal of Geometry and Physics 47 Analysis and Mathematical Physics 46 Physics Letters. A 45 Mathematical and Computer Modelling 45 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 44 Journal of Nonlinear Science and Applications 43 Letters in Mathematical Physics 43 BIT 43 Results in Mathematics 43 Acta Applicandae Mathematicae 42 Archive for Rational Mechanics and Analysis 40 Acta Mathematicae Applicatae Sinica. English Series 39 The Annals of Statistics 39 Integral Equations and Operator Theory 39 Discrete and Continuous Dynamical Systems 36 International Journal for Numerical Methods in Engineering 36 SIAM Journal on Optimization 36 Differential Equations 36 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 36 Electronic Journal of Statistics 35 Quarterly of Applied Mathematics 34 Advances in Mathematics 33 Mathematical Notes 33 Foundations of Computational Mathematics 33 Advances in Mathematical Physics 32 Journal of Fixed Point Theory and Applications 31 Applied Mathematics and Optimization 31 The Journal of Geometric Analysis 30 Mathematical Programming. Series A. Series B 29 Reports on Mathematical Physics 29 Computational Mechanics 29 Journal of Global Optimization 29 GEM - International Journal on Geomathematics 28 Doklady Mathematics ...and 637 more Journals
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#### Cited in 61 Fields

 6,237 Partial differential equations (35-XX) 5,356 Numerical analysis (65-XX) 1,800 Operator theory (47-XX) 1,213 Dynamical systems and ergodic theory (37-XX) 1,183 Calculus of variations and optimal control; optimization (49-XX) 1,150 Optics, electromagnetic theory (78-XX) 1,050 Ordinary differential equations (34-XX) 1,046 Information and communication theory, circuits (94-XX) 1,001 Operations research, mathematical programming (90-XX) 878 Biology and other natural sciences (92-XX) 871 Mechanics of deformable solids (74-XX) 850 Statistics (62-XX) 749 Fluid mechanics (76-XX) 661 Computer science (68-XX) 513 Integral equations (45-XX) 475 Quantum theory (81-XX) 449 Integral transforms, operational calculus (44-XX) 415 Systems theory; control (93-XX) 389 Linear and multilinear algebra; matrix theory (15-XX) 381 Geophysics (86-XX) 376 Harmonic analysis on Euclidean spaces (42-XX) 355 Probability theory and stochastic processes (60-XX) 263 Classical thermodynamics, heat transfer (80-XX) 252 Global analysis, analysis on manifolds (58-XX) 209 Differential geometry (53-XX) 188 Functional analysis (46-XX) 184 Approximations and expansions (41-XX) 172 Special functions (33-XX) 171 Statistical mechanics, structure of matter (82-XX) 134 Mechanics of particles and systems (70-XX) 132 Potential theory (31-XX) 129 Difference and functional equations (39-XX) 126 Functions of a complex variable (30-XX) 121 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 111 Real functions (26-XX) 63 Combinatorics (05-XX) 63 Nonassociative rings and algebras (17-XX) 62 Algebraic geometry (14-XX) 48 General topology (54-XX) 44 Convex and discrete geometry (52-XX) 43 Astronomy and astrophysics (85-XX) 38 Abstract harmonic analysis (43-XX) 38 Algebraic topology (55-XX) 38 Relativity and gravitational theory (83-XX) 25 Measure and integration (28-XX) 24 General and overarching topics; collections (00-XX) 24 Topological groups, Lie groups (22-XX) 21 Several complex variables and analytic spaces (32-XX) 20 Number theory (11-XX) 17 Associative rings and algebras (16-XX) 16 Manifolds and cell complexes (57-XX) 14 History and biography (01-XX) 11 Geometry (51-XX) 8 Commutative algebra (13-XX) 7 Sequences, series, summability (40-XX) 6 Group theory and generalizations (20-XX) 6 Mathematics education (97-XX) 5 Field theory and polynomials (12-XX) 3 Category theory; homological algebra (18-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 1 Mathematical logic and foundations (03-XX)