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## Luchko, Yuri

Compute Distance To:
 Author ID: luchko.yuri Published as: Luchko, Yuri; Luchko, Yu.
 Documents Indexed: 44 Publications since 1997, including 3 Books Reviewing Activity: 25 Reviews
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#### Co-Authors

 13 single-authored 7 Gorenflo, Rudolf 6 Yamamoto, Masahiro 4 Mainardi, Francesco 3 Al-Refai, Mohammed 3 Boyadjiev, Lyubomir I. 2 Kiryakova, Virginia S. 2 Kochubeĭ, Anatoliĭ Naumovych 2 Li, Zhiyuan 2 Machado, José António Tenreiro 1 Alkandari, Maryam 1 Buckwar, Evelyn 1 Datsko, Bohdan 1 Diethelm, Kai 1 Hanna, Latif A.-M. 1 Hausser, Frank 1 Iskenderov, Asaf 1 Korbel, Jan 1 Loutchko, Joulia 1 Pagnini, Gianni 1 Povstenko, Yuriy Z. 1 Rundell, William 1 Stojanović, Mirjana N. 1 Zuo, Lihua
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#### Serials

 18 Fractional Calculus & Applied Analysis 3 Computers & Mathematics with Applications 2 Journal of Mathematical Physics 2 Integral Transforms and Special Functions 2 Mathematical Modelling of Natural Phenomena 2 Handbook of Fractional Calculus with Applications 1 Inverse Problems 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Chaos, Solitons and Fractals 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Mathematica Balkanica. New Series 1 Theory of Probability and Mathematical Statistics 1 Analysis (München) 1 Journal of Computational Analysis and Applications 1 Communications in Nonlinear Science and Numerical Simulation 1 Communications in Applied and Industrial Mathematics 1 Axioms 1 Mathematics
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#### Fields

 24 Partial differential equations (35-XX) 23 Real functions (26-XX) 19 Integral equations (45-XX) 13 Special functions (33-XX) 9 Integral transforms, operational calculus (44-XX) 6 Probability theory and stochastic processes (60-XX) 4 Ordinary differential equations (34-XX) 3 General and overarching topics; collections (00-XX) 3 Numerical analysis (65-XX) 2 Functions of a complex variable (30-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

39 Publications have been cited 1,522 times in 1,064 Documents Cited by Year
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
2001
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
1999
Computation of the Mittag-Leffler function $$E_{\alpha,\beta}(z)$$ and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
2002
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
1998
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
2015
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
2012
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
2013
Numerical solutions of linear multi-term initial value problems of fractional order. Zbl 1083.65064
Diethelm, Kai; Luchko, Yuri
2004
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
2000
Fractional wave equation and damped waves. Zbl 1302.35408
Luchko, Yuri
2013
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
1999
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations. Zbl 1312.35184
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
2014
Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation. Zbl 1273.65131
Luchko, Yuri; Rundell, William; Yamamoto, Masahiro; Zuo, Lihua
2013
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 06604016
Luchko, Yuri; Yamamoto, Masahiro
2016
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006
Al-Refai, Mohammed; Luchko, Yuri
2014
Fractional Schrödinger equation for a particle moving in a potential well. Zbl 1280.81044
Luchko, Yuri
2013
Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives. Zbl 1338.35457
Al-Refai, Mohammed; Luchko, Yuri
2015
The Mellin integral transform in fractional calculus. Zbl 1312.26016
Luchko, Yuri; Kiryakova, Virginia
2013
Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem. Zbl 1409.35221
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
2017
Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Zbl 1381.35226
Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy
2013
Wave-diffusion dualism of the neutral-fractional processes. Zbl 1349.35402
Luchko, Yuri
2015
On the maximum principle for a time-fractional diffusion equation. Zbl 1374.35426
Luchko, Yuri; Yamamoto, Masahiro
2017
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
1997
Modeling of financial processes with a space-time fractional diffusion equation of varying order. Zbl 1354.91178
Korbel, Jan; Luchko, Yuri
2016
On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. Zbl 06898705
Luchko, Yuri
2017
Multi-dimensional fractional wave equation and some properties of its fundamental solution. Zbl 1329.35335
Luchko, Yuri
2014
A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Zbl 1393.35280
Luchko, Yu.
2016
Multi-dimensional $$\alpha$$-fractional diffusion-wave equation and some properties of its fundamental solution. Zbl 1386.35427
2017
Analysis of fractional diffusion equations of distributed order: maximum principles and their applications. Zbl 1381.35208
Al-Refai, Mohammed; Luchko, Yuri
2016
Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Zbl 1275.26015
Datsko, Bohdan; Luchko, Yuri
2012
Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Zbl 1374.35419
2017
Entropy production rate of a one-dimensional alpha-fractional diffusion process. Zbl 1415.35283
Luchko, Yuri
2016
The neutral-fractional telegraph equation. Zbl 1398.35262
2017
Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives. Zbl 1441.34009
Hanna, Latif A-M.; Al-Kandari, Maryam; Luchko, Yuri
2020
Basic theory. Zbl 1410.26003
Kochubei, Anatoly (ed.); Luchko, Yuri (ed.)
2019
On the distribution of zeros of the Wright function. Zbl 1057.33014
Luchko, Yuri
2001
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 07268213
Luchko, Yuri
2020
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. Zbl 1461.35007
Luchko, Yu.
2019
Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives. Zbl 1441.34009
Hanna, Latif A-M.; Al-Kandari, Maryam; Luchko, Yuri
2020
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 07268213
Luchko, Yuri
2020
Basic theory. Zbl 1410.26003
Kochubei, Anatoly; Luchko, Yuri
2019
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. Zbl 1461.35007
Luchko, Yu.
2019
Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem. Zbl 1409.35221
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
2017
On the maximum principle for a time-fractional diffusion equation. Zbl 1374.35426
Luchko, Yuri; Yamamoto, Masahiro
2017
On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. Zbl 06898705
Luchko, Yuri
2017
Multi-dimensional $$\alpha$$-fractional diffusion-wave equation and some properties of its fundamental solution. Zbl 1386.35427
2017
Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Zbl 1374.35419
2017
The neutral-fractional telegraph equation. Zbl 1398.35262
2017
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 06604016
Luchko, Yuri; Yamamoto, Masahiro
2016
Modeling of financial processes with a space-time fractional diffusion equation of varying order. Zbl 1354.91178
Korbel, Jan; Luchko, Yuri
2016
A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Zbl 1393.35280
Luchko, Yu.
2016
Analysis of fractional diffusion equations of distributed order: maximum principles and their applications. Zbl 1381.35208
Al-Refai, Mohammed; Luchko, Yuri
2016
Entropy production rate of a one-dimensional alpha-fractional diffusion process. Zbl 1415.35283
Luchko, Yuri
2016
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
2015
Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives. Zbl 1338.35457
Al-Refai, Mohammed; Luchko, Yuri
2015
Wave-diffusion dualism of the neutral-fractional processes. Zbl 1349.35402
Luchko, Yuri
2015
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations. Zbl 1312.35184
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
2014
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006
Al-Refai, Mohammed; Luchko, Yuri
2014
Multi-dimensional fractional wave equation and some properties of its fundamental solution. Zbl 1329.35335
Luchko, Yuri
2014
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
2013
Fractional wave equation and damped waves. Zbl 1302.35408
Luchko, Yuri
2013
Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation. Zbl 1273.65131
Luchko, Yuri; Rundell, William; Yamamoto, Masahiro; Zuo, Lihua
2013
Fractional Schrödinger equation for a particle moving in a potential well. Zbl 1280.81044
Luchko, Yuri
2013
The Mellin integral transform in fractional calculus. Zbl 1312.26016
Luchko, Yuri; Kiryakova, Virginia
2013
Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Zbl 1381.35226
Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy
2013
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
2012
Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Zbl 1275.26015
Datsko, Bohdan; Luchko, Yuri
2012
Numerical solutions of linear multi-term initial value problems of fractional order. Zbl 1083.65064
Diethelm, Kai; Luchko, Yuri
2004
Computation of the Mittag-Leffler function $$E_{\alpha,\beta}(z)$$ and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
2002
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
2001
On the distribution of zeros of the Wright function. Zbl 1057.33014
Luchko, Yuri
2001
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
2000
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
1999
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
1999
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
1998
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
1997
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#### Cited by 1,317 Authors

 32 Liu, Fawang 32 Mainardi, Francesco 22 Băleanu, Dumitru I. 21 Luchko, Yuri 20 Turner, Ian William 19 Pagnini, Gianni 18 Gorenflo, Rudolf 17 Anh, Vo V. 17 Povstenko, Yuriy Z. 17 Yamamoto, Masahiro 14 Nguyen Huy Tuan 13 Wang, Jinrong 12 Garrappa, Roberto 12 Luchko, Yurii F. 12 Sun, Zhizhong 11 Li, Zhiyuan 11 Saxena, Ram Kishore 10 Wang, Hong 10 Zheng, Xiangcheng 9 Jin, Bangti 9 Odibat, Zaid M. 9 Sandev, Trifce 9 Stynes, Martin 8 Al-Refai, Mohammed 8 Kirane, Mokhtar 8 Roscani, Sabrina D. 8 Singla, Komal 8 Tomovski, Živorad 7 Bazhlekova, Emilia G. 7 Ford, Neville J. 7 Kiryakova, Virginia S. 7 Machado, José António Tenreiro 7 Mathai, Arakaparampli Mathai 7 Momani, Shaher M. 7 O’Regan, Donal 7 Tang, Yifa 7 Zaky, Mahmoud A. 7 Zhou, Zhi 6 Abdeljawad, Thabet 6 Ansari, Alireza 6 Bhalekar, Sachin 6 Bu, Weiping 6 de Oliveira, Edmundo Capelas 6 Chechkin, Aleksei V. 6 Gao, Guanghua 6 Gupta, Rajesh Kumar 6 Haubold, Hans Joachim 6 Hofmann, Bernd 6 Kaminski Lenzi, Ervin 6 Lazarov, Raytcho D. 6 Li, Gongsheng 6 Lizama, Carlos 6 Meerschaert, Mark Marvin 6 Płociniczak, Łukasz 6 Popolizio, Marina 6 Sin, Chung-Sik 5 Chen, Yangquan 5 D’Ovidio, Mirko 5 Duan, Junsheng 5 Gómez-Aguilar, José Francisco 5 Hai, Dinh Nguyen Duy 5 Jarad, Fahd 5 Jia, Junxiong 5 Jiang, Xiaoyun 5 Keyantuo, Valentin 5 Kienle, Alwin 5 Liemert, André 5 Polito, Federico 5 Sahadevan, Ramajayam 5 Sun, Chunlong 5 Tarzia, Domingo Alberto 5 Trong, Dang Duc 5 Trujillo, Juan J. 5 Umarov, Sabir R. 5 Wang, Gangwei 5 Xu, Mingyu 5 Yang, Xiao-Jun 5 Yang, Xuehua 5 Zhang, Haixiang 4 Al-saedi, Ahmed Eid Salem 4 Arshad, Muhammad Sarmad 4 Atanackovic, Teodor M. 4 Atangana, Abdon 4 Beghin, Luisa 4 Bhrawy, Ali Hassan 4 Boyadjiev, Lyubomir I. 4 Brandibur, Oana 4 Chen, Wen 4 Demir, Ali 4 El-Sayed, Ahmed Mohamed Ahmed 4 Esmaeili, Shahrokh 4 Feng, Libo 4 Ferreira, Milton 4 Garra, Roberto 4 Hanna, Latif A.-M. 4 Janno, Jaan 4 Kaslik, Eva 4 Khaliq, Abdul Q. M. 4 Kiliçman, Adem 4 Kolokoltsov, Vassili N. ...and 1,217 more Authors
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#### Cited in 228 Serials

 131 Fractional Calculus & Applied Analysis 52 Applied Mathematics and Computation 50 Computers & Mathematics with Applications 49 Journal of Computational and Applied Mathematics 28 Journal of Mathematical Physics 26 Journal of Computational Physics 25 Communications in Nonlinear Science and Numerical Simulation 24 Advances in Difference Equations 21 Journal of Mathematical Analysis and Applications 20 Journal of Scientific Computing 20 Nonlinear Dynamics 19 Chaos, Solitons and Fractals 19 Applied Numerical Mathematics 18 Inverse Problems 16 Journal of Applied Mathematics and Computing 15 Integral Transforms and Special Functions 13 Computational and Applied Mathematics 13 Abstract and Applied Analysis 12 Applied Mathematics Letters 12 Numerical Algorithms 12 Mathematical Problems in Engineering 11 Mathematics 10 Physica A 10 International Journal of Differential Equations 9 Journal of Inverse and Ill-Posed Problems 8 Applied Mathematical Modelling 8 Advances in Mathematical Physics 7 Applicable Analysis 7 Journal of Differential Equations 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Stochastic Processes and their Applications 7 Lobachevskii Journal of Mathematics 7 Inverse Problems in Science and Engineering 6 Mathematical Methods in the Applied Sciences 6 SIAM Journal on Numerical Analysis 6 Boundary Value Problems 6 Journal of Nonlinear Science and Applications 5 BIT 5 Journal of Evolution Equations 5 Mathematical Modelling of Natural Phenomena 5 Journal of Function Spaces 4 Computer Methods in Applied Mechanics and Engineering 4 Journal of Statistical Physics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Journal of Functional Analysis 4 Acta Mathematicae Applicatae Sinica. English Series 4 International Journal of Computer Mathematics 4 Engineering Analysis with Boundary Elements 4 Nonlinear Analysis. Modelling and Control 4 Journal of Applied Mathematics 4 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 4 Ufimskiĭ Matematicheskiĭ Zhurnal 4 Axioms 4 Journal of Mathematics 3 Acta Mechanica 3 Advances in Applied Probability 3 International Journal of Theoretical Physics 3 Lithuanian Mathematical Journal 3 Mathematics of Computation 3 Mathematics and Computers in Simulation 3 Meccanica 3 Semigroup Forum 3 Zeitschrift für Analysis und ihre Anwendungen 3 Physica D 3 Russian Mathematics 3 Journal of Mathematical Chemistry 3 Journal of Inequalities and Applications 3 Discrete and Continuous Dynamical Systems. Series B 3 Computational Methods in Applied Mathematics 3 International Journal of Geometric Methods in Modern Physics 3 Inverse Problems and Imaging 3 Tbilisi Mathematical Journal 3 Symmetry 3 Fractional Differential Calculus 3 Evolution Equations and Control Theory 3 East Asian Journal on Applied Mathematics 2 Mathematical Notes 2 Nonlinearity 2 Reports on Mathematical Physics 2 Theoretical and Mathematical Physics 2 Journal of Geometry and Physics 2 Calcolo 2 Journal of Optimization Theory and Applications 2 Monatshefte für Mathematik 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Quarterly of Applied Mathematics 2 Applied Mathematics and Mechanics. (English Edition) 2 Journal of Integral Equations and Applications 2 Signal Processing 2 SIAM Journal on Mathematical Analysis 2 SIAM Journal on Scientific Computing 2 Journal of Mathematical Sciences (New York) 2 International Journal of Numerical Methods for Heat & Fluid Flow 2 Journal of the Egyptian Mathematical Society 2 Fractals 2 Advances in Computational Mathematics 2 Journal of Vibration and Control 2 Taiwanese Journal of Mathematics 2 Mathematical Inequalities & Applications ...and 128 more Serials
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#### Cited in 49 Fields

 640 Partial differential equations (35-XX) 339 Real functions (26-XX) 323 Numerical analysis (65-XX) 194 Ordinary differential equations (34-XX) 160 Special functions (33-XX) 118 Probability theory and stochastic processes (60-XX) 114 Integral equations (45-XX) 66 Operator theory (47-XX) 60 Integral transforms, operational calculus (44-XX) 48 Fluid mechanics (76-XX) 36 Statistical mechanics, structure of matter (82-XX) 34 Mechanics of deformable solids (74-XX) 33 Classical thermodynamics, heat transfer (80-XX) 28 Quantum theory (81-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 19 Harmonic analysis on Euclidean spaces (42-XX) 19 Systems theory; control (93-XX) 17 Functions of a complex variable (30-XX) 16 Biology and other natural sciences (92-XX) 14 Dynamical systems and ergodic theory (37-XX) 11 Functional analysis (46-XX) 11 Statistics (62-XX) 10 Approximations and expansions (41-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Mechanics of particles and systems (70-XX) 8 Information and communication theory, circuits (94-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Optics, electromagnetic theory (78-XX) 6 Topological groups, Lie groups (22-XX) 4 History and biography (01-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Measure and integration (28-XX) 4 Sequences, series, summability (40-XX) 3 Potential theory (31-XX) 3 Geophysics (86-XX) 2 Combinatorics (05-XX) 2 Group theory and generalizations (20-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX)