## Welfert, Bruno D.

Compute Distance To:
 Author ID: welfert.bruno-d Published as: Welfert, Bruno D.; Welfert, B. D.; Welfert, B.; Welfert, Bruno External Links: MGP
 Documents Indexed: 46 Publications since 1990 Co-Authors: 24 Co-Authors with 40 Joint Publications 623 Co-Co-Authors
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### Co-Authors

 6 single-authored 13 Jackiewicz, Zdzislaw 9 Yalim, Jason 4 Bank, Randolph E. 4 Burrage, Kevin 4 Wu, Ke 3 Rahman, M. Mahbubur 2 Cardone, Angelamaria 2 Grayer, Hezekiah II 2 in ’t Hout, Karel J. 2 Kojouharov, Hristo V. 2 Owren, Brynjulf 2 Tracogna, S. 1 Braś, Michał 1 Buchta, M. Ryan 1 Hertono, G. 1 Jones, John William 1 Kitsios, Kyriakos 1 Mead, Jodi L. 1 Renaut, Rosemary Anne 1 Spanias, Andreas S. 1 Spijker, Marc N. 1 Verner, James H. 1 Yserentant, Harry 1 Zubik-Kowal, Barbara
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### Serials

 11 Journal of Fluid Mechanics 7 Applied Numerical Mathematics 4 BIT 3 Computer Methods in Applied Mechanics and Engineering 3 Applied Mathematics and Computation 3 Journal of Scientific Computing 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Numerical Analysis 1 Computers & Mathematics with Applications 1 Journal of Computational Physics 1 Mathematics of Computation 1 Numerische Mathematik 1 Signal Processing 1 Linear Algebra and its Applications 1 Advances in Computational Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics
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### Fields

 31 Numerical analysis (65-XX) 15 Fluid mechanics (76-XX) 10 Ordinary differential equations (34-XX) 9 Partial differential equations (35-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Integral equations (45-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Approximations and expansions (41-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 2 Geophysics (86-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

41 Publications have been cited 500 times in 416 Documents Cited by Year
A class of iterative methods for solving saddle point problems. Zbl 0684.65031
Bank, Randolph E.; Welfert, Bruno D.; Yserentant, Harry
1990
A posteriori error estimates for the Stokes problem. Zbl 0731.76040
Bank, Randolph E.; Welfert, Bruno D.
1991
Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms. Zbl 1161.65073
in ’t Hout, K. J.; Welfert, B. D.
2009
Generation of pseudospectral differentiation matrices. I. Zbl 0889.65013
Welfert, Bruno D.
1997
Stability of ADI schemes applied to convection–diffusion equations with mixed derivative terms. Zbl 1175.65104
in ’t Hout, K. J.; Welfert, B. D.
2007
A posteriori error estimates for the Stokes equations: A comparison. Zbl 0725.65106
Bank, Randolph E.; Welfert, Bruno D.
1990
Two-step Runge-Kutta: Theory and practice. Zbl 0979.65062
Tracogna, S.; Welfert, B.
2000
A comparison between the mini-element and the Petrov-Galerkin formulations for the generalized Stokes problem. Zbl 0732.65100
Bank, Randolph E.; Welfert, Bruno D.
1990
The Newton iteration on Lie groups. Zbl 0957.65054
Owren, B.; Welfert, B.
2000
Numerical solution of a Fredholm integro-differential equation modelling neural networks. Zbl 1089.65136
Jackiewicz, Z.; Rahman, M. Mahbubur; Welfert, B. D.
2006
Numerical solution of a Fredholm integro-differential equation modelling $$\dot \theta$$-neural networks. Zbl 1132.65116
Jackiewicz, Z.; Rahman, M. Mahbubur; Welfert, B. D.
2008
About the sharpness of the stability estimates in the Kreiss matrix theorem. Zbl 1019.15016
Spijker, M. N.; Tracogna, S.; Welfert, B. D.
2003
Order conditions for general linear methods. Zbl 1330.65103
Cardone, Angelamaria; Jackiewicz, Zdzisław; Verner, James H.; Welfert, Bruno
2015
Parametrically forced stably stratified cavity flow: complicated nonlinear dynamics near the onset of instability. Zbl 1419.76203
Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2019
Spectral versus pseudospectral solutions of the wave equation by waveform relaxation methods. Zbl 1047.65092
Jackiewicz, Z.; Welfert, B. D.; Zubik-Kowal, B.
2004
A nonstandard Euler scheme for $$y''+g(y)y'+f(y)y=0$$. Zbl 1018.65091
Kojouharov, H.; Welfert, B.
2003
Vertically forced stably stratified cavity flow: instabilities of the basic state. Zbl 1415.76113
Yalim, Jason; Lopez, Juan M.; Welfert, Bruno D.
2018
Complex dynamics in a stratified lid-driven square cavity flow. Zbl 1415.76216
Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.
2018
Precessing cube: resonant excitation of modes and triadic resonance. Zbl 1460.76904
Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.
2020
Pseudospectra of wave from relaxation operators. Zbl 0932.65080
Jackiewicz, Z.; Owren, B.; Welfert, B.
1998
Stochastic approximations of perturbed Fredholm Volterra integro-differential equation arising in mathematical neurosciences. Zbl 1117.65014
Rahman, M. Mahbubur; Jackiewicz, Z.; Welfert, B. D.
2007
Spectral approximation of time windows in the solution of dissipative linear differential equations. Zbl 1195.65091
Burrage, K.; Jackiewicz, Z.; Welfert, B. D.
2009
On the eigenvalues of second-order pseudospectral differentiation operators. Zbl 0824.65083
Welfert, Bruno D.
1994
Dynamics in a stably stratified tilted square cavity. Zbl 1430.76184
Grayer, Hezekiah; Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2020
Parametrically forced stably stratified flow in a three-dimensional rectangular container. Zbl 1460.76285
Yalim, Jason; Lopez, Juan M.; Welfert, Bruno D.
2020
Librational forcing of a rapidly rotating fluid-filled cube. Zbl 1421.76260
Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.
2018
Order reduction phenomenon for general linear methods. Zbl 1368.65111
Braś, Michał; Cardone, Angelamaria; Jackiewicz, Zdzisław; Welfert, Bruno
2017
Reflections and focusing of inertial waves in a librating cube with the rotation axis oblique to its faces. Zbl 1460.76905
Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.
2020
Absorbing boundary conditions of the second order for the pseudospectral Chebyshev methods for wave propagation. Zbl 0999.65108
Gelb, A.; Jackiewicz, Z.; Welfert, B. D.
2002
Stability of Gauss-Radau pseudospectral approximations of the one-dimensional wave equation. Zbl 1024.65094
Jackiewicz, Z.; Welfert, B. D.
2003
Stability of a pivoting strategy for parallel Gaussian elimination. Zbl 0991.65030
Mead, J. L.; Renaut, R. A.; Welfert, B. D.
2001
Welfert, B. D.
2010
Welfert, B. D.
2010
Analysis of iterated ADI-FDTD schemes for Maxwell curl equations. Zbl 1129.78025
Welfert, B. D.
2007
Evaluation of closure strategies for a periodically-forced Duffing oscillator with slowly modulated frequency subject to Gaussian white noise. Zbl 1462.60099
Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2017
Stably stratified square cavity subjected to horizontal oscillations: responses to small amplitude forcing. Zbl 1461.76150
Grayer, Hezekiah II; Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2021
Acceleration of convergence of static and dynamic iterations. Zbl 0992.65077
Burrage, K.; Hertono, G.; Jackiewicz, Z.; Welfert, B. D.
2001
On quadrature formulae based on derivative collocation. Zbl 1185.65047
Welfert, B. D.
2008
Zero-free regions for a rational function with applications. Zbl 0833.65016
Jones, John W.; Welfert, Bruno D.
1995
QX factorization of centrosymmetric matrices. Zbl 1400.15016
Steele, A.; Yalim, J.; Welfert, B.
2018
Parametric instabilities of a stratified shear layer. Zbl 07355123
Buchta, M. Ryan; Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2021
Stably stratified square cavity subjected to horizontal oscillations: responses to small amplitude forcing. Zbl 1461.76150
Grayer, Hezekiah II; Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2021
Parametric instabilities of a stratified shear layer. Zbl 07355123
Buchta, M. Ryan; Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2021
Precessing cube: resonant excitation of modes and triadic resonance. Zbl 1460.76904
Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.
2020
Dynamics in a stably stratified tilted square cavity. Zbl 1430.76184
Grayer, Hezekiah; Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2020
Parametrically forced stably stratified flow in a three-dimensional rectangular container. Zbl 1460.76285
Yalim, Jason; Lopez, Juan M.; Welfert, Bruno D.
2020
Reflections and focusing of inertial waves in a librating cube with the rotation axis oblique to its faces. Zbl 1460.76905
Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.
2020
Parametrically forced stably stratified cavity flow: complicated nonlinear dynamics near the onset of instability. Zbl 1419.76203
Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2019
Vertically forced stably stratified cavity flow: instabilities of the basic state. Zbl 1415.76113
Yalim, Jason; Lopez, Juan M.; Welfert, Bruno D.
2018
Complex dynamics in a stratified lid-driven square cavity flow. Zbl 1415.76216
Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.
2018
Librational forcing of a rapidly rotating fluid-filled cube. Zbl 1421.76260
Wu, Ke; Welfert, Bruno D.; Lopez, Juan M.
2018
QX factorization of centrosymmetric matrices. Zbl 1400.15016
Steele, A.; Yalim, J.; Welfert, B.
2018
Order reduction phenomenon for general linear methods. Zbl 1368.65111
Braś, Michał; Cardone, Angelamaria; Jackiewicz, Zdzisław; Welfert, Bruno
2017
Evaluation of closure strategies for a periodically-forced Duffing oscillator with slowly modulated frequency subject to Gaussian white noise. Zbl 1462.60099
Yalim, Jason; Welfert, Bruno D.; Lopez, Juan M.
2017
Order conditions for general linear methods. Zbl 1330.65103
Cardone, Angelamaria; Jackiewicz, Zdzisław; Verner, James H.; Welfert, Bruno
2015
Welfert, B. D.
2010
Welfert, B. D.
2010
Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms. Zbl 1161.65073
in &rsquo;t Hout, K. J.; Welfert, B. D.
2009
Spectral approximation of time windows in the solution of dissipative linear differential equations. Zbl 1195.65091
Burrage, K.; Jackiewicz, Z.; Welfert, B. D.
2009
Numerical solution of a Fredholm integro-differential equation modelling $$\dot \theta$$-neural networks. Zbl 1132.65116
Jackiewicz, Z.; Rahman, M. Mahbubur; Welfert, B. D.
2008
On quadrature formulae based on derivative collocation. Zbl 1185.65047
Welfert, B. D.
2008
Stability of ADI schemes applied to convection–diffusion equations with mixed derivative terms. Zbl 1175.65104
in &rsquo;t Hout, K. J.; Welfert, B. D.
2007
Stochastic approximations of perturbed Fredholm Volterra integro-differential equation arising in mathematical neurosciences. Zbl 1117.65014
Rahman, M. Mahbubur; Jackiewicz, Z.; Welfert, B. D.
2007
Analysis of iterated ADI-FDTD schemes for Maxwell curl equations. Zbl 1129.78025
Welfert, B. D.
2007
Numerical solution of a Fredholm integro-differential equation modelling neural networks. Zbl 1089.65136
Jackiewicz, Z.; Rahman, M. Mahbubur; Welfert, B. D.
2006
Spectral versus pseudospectral solutions of the wave equation by waveform relaxation methods. Zbl 1047.65092
Jackiewicz, Z.; Welfert, B. D.; Zubik-Kowal, B.
2004
About the sharpness of the stability estimates in the Kreiss matrix theorem. Zbl 1019.15016
Spijker, M. N.; Tracogna, S.; Welfert, B. D.
2003
A nonstandard Euler scheme for $$y''+g(y)y'+f(y)y=0$$. Zbl 1018.65091
Kojouharov, H.; Welfert, B.
2003
Stability of Gauss-Radau pseudospectral approximations of the one-dimensional wave equation. Zbl 1024.65094
Jackiewicz, Z.; Welfert, B. D.
2003
Absorbing boundary conditions of the second order for the pseudospectral Chebyshev methods for wave propagation. Zbl 0999.65108
Gelb, A.; Jackiewicz, Z.; Welfert, B. D.
2002
Stability of a pivoting strategy for parallel Gaussian elimination. Zbl 0991.65030
Mead, J. L.; Renaut, R. A.; Welfert, B. D.
2001
Acceleration of convergence of static and dynamic iterations. Zbl 0992.65077
Burrage, K.; Hertono, G.; Jackiewicz, Z.; Welfert, B. D.
2001
Two-step Runge-Kutta: Theory and practice. Zbl 0979.65062
Tracogna, S.; Welfert, B.
2000
The Newton iteration on Lie groups. Zbl 0957.65054
Owren, B.; Welfert, B.
2000
Pseudospectra of wave from relaxation operators. Zbl 0932.65080
Jackiewicz, Z.; Owren, B.; Welfert, B.
1998
Generation of pseudospectral differentiation matrices. I. Zbl 0889.65013
Welfert, Bruno D.
1997
Zero-free regions for a rational function with applications. Zbl 0833.65016
Jones, John W.; Welfert, Bruno D.
1995
On the eigenvalues of second-order pseudospectral differentiation operators. Zbl 0824.65083
Welfert, Bruno D.
1994
A posteriori error estimates for the Stokes problem. Zbl 0731.76040
Bank, Randolph E.; Welfert, Bruno D.
1991
A class of iterative methods for solving saddle point problems. Zbl 0684.65031
Bank, Randolph E.; Welfert, Bruno D.; Yserentant, Harry
1990
A posteriori error estimates for the Stokes equations: A comparison. Zbl 0725.65106
Bank, Randolph E.; Welfert, Bruno D.
1990
A comparison between the mini-element and the Petrov-Galerkin formulations for the generalized Stokes problem. Zbl 0732.65100
Bank, Randolph E.; Welfert, Bruno D.
1990
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### Cited by 609 Authors

 23 Jackiewicz, Zdzislaw 18 Welfert, Bruno D. 14 in ’t Hout, Karel J. 10 Dehghan Takht Fooladi, Mehdi 8 González-Pinto, Severiano 8 Hernandez-Abreu, Domingo 7 Huang, Na 7 Itkin, Andrey 6 Arrarás, Andres 6 Cardone, Angelamaria 6 Ma, Changfeng 6 Portero, Laura 6 Yalim, Jason 5 Bhowmik, Samir Kumar 5 Braś, Michał 5 D’Ambrosio, Raffaele 5 Franca, Leopoldo Luis Cabo Penna 5 Pérez Rodríguez, S. 5 Wang, Jinhua 4 Bartoszewski, Zbigniew 4 Calo, Victor Manuel 4 Cheng, Xiaoliang 4 Günther, Michael 4 He, Yinnian 4 Hendricks, Christian 4 Izzo, Giuseppe 4 Javidi, Mohammad 4 Jorge, Juan Carlos 4 Mishra, Chittaranjan 4 Olshanskii, Maxim A. 4 Repin, Sergeĭ Igorevich 4 Taleei, Ameneh 4 Verner, James H. 3 Agouzal, Abdellatif 3 Araya, Rodolfo A. 3 Bank, Randolph E. 3 Cao, Jun 3 Cao, Zhihao 3 Conte, Dajana 3 Düring, Bertram 3 Esmaeili, Shahrokh 3 Ghosh, Abhijit 3 Golbabai, Ahmad 3 Haentjens, Tinne 3 Heuer, Christof 3 Huang, Ting-Zhu 3 Konguetsof, Avrilia 3 Li, Chong 3 Lin, Yiqin 3 Muga, Ignacio 3 Paternoster, Beatrice 3 Patidar, Kailash C. 3 Reusken, Arnold 3 Rojas, Sergio 3 Sandu, Adrian 3 Vitse, Pascale 3 Wang, Lilian 3 Wei, Yimin 3 Wu, Ke 3 Wyns, Maarten 3 Zubik-Kowal, Barbara 2 Achchab, Boujemaa 2 Ainsworth, Mark 2 Alipanah, Amjad 2 Amiraliyev, Gabil M. 2 Argyros, Ioannis Konstantinos 2 Axelsson, Axel Owe Holger 2 Baltensperger, Richard 2 Barrenechea, Gabriel R. 2 Behiry, S. H. 2 Boen, Lynn 2 Borovykh, Natalia Alexandrovna 2 Bouihat, Khalid 2 Carstensen, Carsten 2 Chen, Long 2 de Frutos, Javier 2 Dedieu, Jean-Pierre 2 Driscoll, Tobin A. 2 Durán, Ricardo G. 2 Durmaz, Muhammet Enes 2 Eisner, Tanja 2 El Chami, Fida 2 Ervin, Vincent J. 2 Farzi, Javad 2 Feng, Xinlong 2 Foroozandeh, Zahra 2 García-Archilla, Bosco 2 Ge, Zhihao 2 Gilsinn, David E. 2 Grayer, Hezekiah II 2 Guglielmi, Nicola 2 Hairer, Ernst 2 Han, Weimin 2 He, Jinsu 2 Hu, Xiaozhe 2 Hundsdorfer, Willem H. 2 Khanamiryan, Marianna 2 Kim, Kwang Yeon 2 Layton, William J. 2 Liang, Dong ...and 509 more Authors
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### Cited in 107 Serials

 48 Journal of Computational and Applied Mathematics 36 Applied Numerical Mathematics 31 Applied Mathematics and Computation 29 Computer Methods in Applied Mechanics and Engineering 17 Computers & Mathematics with Applications 14 Journal of Scientific Computing 14 International Journal of Computer Mathematics 12 Journal of Fluid Mechanics 11 Mathematics of Computation 10 Journal of Computational Physics 10 Numerical Methods for Partial Differential Equations 8 SIAM Journal on Scientific Computing 7 Numerische Mathematik 7 Numerical Algorithms 4 Mathematical Methods in the Applied Sciences 4 Numerical Linear Algebra with Applications 4 Journal of Mathematical Chemistry 4 Abstract and Applied Analysis 3 Computers and Fluids 3 Computer Physics Communications 3 International Journal for Numerical Methods in Fluids 3 Journal of Mathematical Analysis and Applications 3 Chaos, Solitons and Fractals 3 BIT 3 International Journal for Numerical Methods in Engineering 3 Journal of Functional Analysis 3 Mathematics and Computers in Simulation 3 Applied Mathematics Letters 3 Journal of Mathematical Sciences (New York) 3 Advances in Computational Mathematics 3 Applied Mathematical Finance 3 Quantitative Finance 2 Linear and Multilinear Algebra 2 Calcolo 2 Computing 2 Journal of Optimization Theory and Applications 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 SIAM Journal on Numerical Analysis 2 Applied Mathematics and Mechanics. (English Edition) 2 Journal of Complexity 2 Mathematical and Computer Modelling 2 Communications in Numerical Methods in Engineering 2 St. Petersburg Mathematical Journal 2 Journal of Difference Equations and Applications 2 Communications in Nonlinear Science and Numerical Simulation 2 Mathematical Modelling and Analysis 2 Computational Methods in Applied Mathematics 2 Journal of Applied Mathematics 2 Mediterranean Journal of Mathematics 2 Advances in Difference Equations 2 Frontiers of Mathematics in China 2 Discrete and Continuous Dynamical Systems. Series S 2 East Asian Journal on Applied Mathematics 1 Applicable Analysis 1 Classical and Quantum Gravity 1 International Journal of Control 1 Journal of the Franklin Institute 1 Bulletin of Mathematical Biology 1 Automatica 1 Meccanica 1 Bulletin of the Korean Mathematical Society 1 Bulletin of the Iranian Mathematical Society 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Probability Theory and Related Fields 1 Computational Mechanics 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Integral Equations and Applications 1 Japan Journal of Industrial and Applied Mathematics 1 Applications of Mathematics 1 Journal of Global Optimization 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Applied Mathematical Modelling 1 Communications in Partial Differential Equations 1 Communications in Statistics. Theory and Methods 1 Mathematical Programming. Series A. Series B 1 Journal of Nonlinear Science 1 Computational Economics 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Computational and Applied Mathematics 1 Discrete and Continuous Dynamical Systems 1 Journal of Vibration and Control 1 Computing and Visualization in Science 1 Differential Equations and Dynamical Systems 1 Nonlinear Dynamics 1 Chaos 1 Revista Matemática Complutense 1 Discrete Dynamics in Nature and Society 1 International Journal of Theoretical and Applied Finance 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Computational Geosciences 1 The ANZIAM Journal 1 Nonlinear Analysis. Real World Applications 1 Journal of Numerical Mathematics 1 Journal of Applied Mathematics and Computing 1 Review of Derivatives Research 1 Boletim da Sociedade Paranaense de Matemática. Terceira Série 1 Fixed Point Theory and Applications 1 International Journal of Numerical Analysis and Modeling 1 Proyecciones 1 Journal of Zhejiang University. Science A ...and 7 more Serials
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### Cited in 35 Fields

 340 Numerical analysis (65-XX) 111 Fluid mechanics (76-XX) 100 Partial differential equations (35-XX) 41 Ordinary differential equations (34-XX) 40 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 31 Integral equations (45-XX) 16 Operator theory (47-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 16 Operations research, mathematical programming (90-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 12 Biology and other natural sciences (92-XX) 11 Probability theory and stochastic processes (60-XX) 11 Mechanics of deformable solids (74-XX) 8 Topological groups, Lie groups (22-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Approximations and expansions (41-XX) 5 Special functions (33-XX) 5 Optics, electromagnetic theory (78-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Quantum theory (81-XX) 4 Systems theory; control (93-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Mechanics of particles and systems (70-XX) 3 Information and communication theory, circuits (94-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Computer science (68-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)