Edit Profile (opens in new tab) Tanaka, Taka-aki Co-Author Distance Author ID: tanaka.taka-aki Published as: Tanaka, Taka-aki; Tanaka, Taka-Aki External Links: MGP Documents Indexed: 47 Publications since 1991, including 1 Additional arXiv Preprint Co-Authors: 12 Co-Authors with 12 Joint Publications 76 Co-Co-Authors all top 5 Co-Authors 21 single-authored 4 Kurosawa, Takeshi 4 Tachiya, Yohei 3 Nishioka, Kumiko 2 Ide, Haruki 2 Kajishima, Takeo 2 Potthoff, Michael 2 Wen, Zhi-Ying 1 Barry, J. H. 1 Duverney, Daniel 1 Erizal 1 Goto, Akinari 1 Ichinose, Kenichi 1 Kaneko, Hajime 1 Kanoko, Tomoaki 1 Kunihiro, Teiji 1 Muttalib, K. A. 1 Satofuka, Nobuyuki 1 Siddiquee, M. S. A. 1 Tanuma, Yusuke 1 Tatsuoka, Fuminori 1 Tokunaga, Hiroshi 1 Toshimitsu, Takeshi 1 Toyama, Kento 1 Yamada, Shuuji all top 5 Serials 3 Journal of Number Theory 3 Tokyo Journal of Mathematics 3 Tsukuba Journal of Mathematics 3 RIMS Kokyuroku 2 Journal of Electromagnetic Waves and Applications 2 Acta Arithmetica 2 Monatshefte für Mathematik 2 Osaka Journal of Mathematics 1 Astrophysics and Space Science 1 Computers and Fluids 1 International Journal of Multiphase Flow 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 International Journal of Theoretical Physics 1 Journal of Computational Physics 1 Journal of Fluid Mechanics 1 Physica A 1 Physics Letters. A 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Archiv der Mathematik 1 Mathematische Nachrichten 1 Results in Mathematics 1 IEEE Transactions on Signal Processing 1 Indagationes Mathematicae. New Series 1 Keio Science and Technology Reports 1 International Journal of Number Theory 1 The European Physical Journal B. Condensed Matter and Complex Systems 1 Journal of Physics A: Mathematical and Theoretical 1 Annales Mathematicae et Informaticae all top 5 Fields 29 Number theory (11-XX) 6 Fluid mechanics (76-XX) 2 Numerical analysis (65-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 2 Information and communication theory, circuits (94-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 27 Publications have been cited 55 times in 29 Documents Cited by ▼ Year ▼ Large-eddy simulation of turbulent gas-particle flow in a vertical channel: Effect of considering inter-particle collisions. Zbl 1004.76513 Yamamoto, Y.; Potthoff, M.; Tanaka, T.; Kajishima, T.; Tsuji, Y. 54 2001 Finite volume TVD scheme on an unstructured grid system for three- dimensional MHD simulation of inhomogeneous systems including strong background potential fields. Zbl 0797.76061 Tanaka, T. 21 1994 Algebraic independence results related to linear recurrences. Zbl 0946.11015 Tanaka, Taka-aki 9 1999 Transcendence of certain reciprocal sums of linear recurrences. Zbl 1012.11062 Duverney, Daniel; Kanoko, Tomoaki; Tanaka, Taka-aki 7 2002 Algebraic independence of the values of power series generated by linear recurrences. Zbl 0876.11036 Tanaka, Taka-aki 6 1996 Algebraic independence of infinite products generated by Fibonacci numbers. Zbl 1218.11071 Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-aki 5 2010 Algebraic relations with the infinite products generated by Fibonacci numbers. Zbl 1274.11113 Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-aki 4 2013 Algebraic independence of sums of reciprocals of the Fibonacci numbers. Zbl 0939.11028 Nishioka, Kumiko; Tanaka, Taka-aki; Toshimitsu, Takeshi 3 1999 Algebraic independence properties related to certain infinite products. Zbl 1284.11103 Tanaka, Taka-aki 3 2011 Algebraic independence results for the values of certain Mahler functions and their application to infinite products. Zbl 1311.11066 Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-aki 3 2014 Tracing the equilibrium path by dynamic relaxation in materially nonlinear problems. Zbl 0835.73057 Siddiquee, M. S. A.; Tanaka, T.; Tatsuoka, F. 2 1995 Algebraic independence of certain numbers defined by linear recurrences. Zbl 0923.11108 Tanaka, Taka-aki 2 1994 Substitution in two symbols and transcendence. Zbl 0940.11015 Nishioka, Kumiko; Tanaka, Taka-aki; Wen, Zhi-Ying 2 1999 Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers. Zbl 1331.11057 Kaneko, Hajime; Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-Aki 2 2015 Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences. Zbl 1119.11041 Tanaka, Taka-aki 2 2005 Transcendence of the values of certain series with Hadamard’s gaps. Zbl 0998.11037 Tanaka, Taka-aki 2 2002 Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers. Zbl 1445.11068 Tanaka, Taka-aki; Tanuma, Yusuke 1 2018 Image reconstruction of two-dimensional impenetrable objects using genetic algorithm. Zbl 0938.68087 Meng, Z. Q.; Takenaka, T.; Tanaka, T. 1 1999 Algebraic independence of power series generated by linearly independent positive numbers. Zbl 1074.11037 Tanaka, Taka-aki 1 2004 A direct design of oversampled perfect reconstruction FIR filter banks. Zbl 1373.94711 Tanaka, T. 1 2006 Algebraic independence of the values of functions satisfying Mahler type functional equations under the transformation represented by a power relatively prime to the characteristic of the base field. Zbl 1420.11106 Goto, Akinari; Tanaka, Taka-aki 1 2018 Algebraic independence of Fibonacci reciprocal sums associated with Newton’s method. Zbl 1057.11036 Tanaka, Taka-aki 1 2003 Modern numerical schemes for solving magnetohydrodynamic equations. Zbl 0915.76059 Murawski, K.; Tanaka, T. 1 1997 Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion. Zbl 1051.11040 Tanaka, Taka-aki 1 2004 Experiments on the unsteady drag and wake of a sphere at high Reynolds numbers. Zbl 1134.76689 Tsuji, Y.; Kato, N.; Tanaka, T. 1 1991 Mean field theory of communication. Zbl 1189.94012 Tanaka, T.; Nakamura, K. 1 2008 Ionic conductivity in a quantum lattice gas model with three-particle interactions. Zbl 1257.82012 Barry, J. H.; Muttalib, K. A.; Tanaka, T. 1 2012 Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers. Zbl 1445.11068 Tanaka, Taka-aki; Tanuma, Yusuke 1 2018 Algebraic independence of the values of functions satisfying Mahler type functional equations under the transformation represented by a power relatively prime to the characteristic of the base field. Zbl 1420.11106 Goto, Akinari; Tanaka, Taka-aki 1 2018 Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers. Zbl 1331.11057 Kaneko, Hajime; Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-Aki 2 2015 Algebraic independence results for the values of certain Mahler functions and their application to infinite products. Zbl 1311.11066 Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-aki 3 2014 Algebraic relations with the infinite products generated by Fibonacci numbers. Zbl 1274.11113 Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-aki 4 2013 Ionic conductivity in a quantum lattice gas model with three-particle interactions. Zbl 1257.82012 Barry, J. H.; Muttalib, K. A.; Tanaka, T. 1 2012 Algebraic independence properties related to certain infinite products. Zbl 1284.11103 Tanaka, Taka-aki 3 2011 Algebraic independence of infinite products generated by Fibonacci numbers. Zbl 1218.11071 Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-aki 5 2010 Mean field theory of communication. Zbl 1189.94012 Tanaka, T.; Nakamura, K. 1 2008 A direct design of oversampled perfect reconstruction FIR filter banks. Zbl 1373.94711 Tanaka, T. 1 2006 Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences. Zbl 1119.11041 Tanaka, Taka-aki 2 2005 Algebraic independence of power series generated by linearly independent positive numbers. Zbl 1074.11037 Tanaka, Taka-aki 1 2004 Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion. Zbl 1051.11040 Tanaka, Taka-aki 1 2004 Algebraic independence of Fibonacci reciprocal sums associated with Newton’s method. Zbl 1057.11036 Tanaka, Taka-aki 1 2003 Transcendence of certain reciprocal sums of linear recurrences. Zbl 1012.11062 Duverney, Daniel; Kanoko, Tomoaki; Tanaka, Taka-aki 7 2002 Transcendence of the values of certain series with Hadamard’s gaps. Zbl 0998.11037 Tanaka, Taka-aki 2 2002 Large-eddy simulation of turbulent gas-particle flow in a vertical channel: Effect of considering inter-particle collisions. Zbl 1004.76513 Yamamoto, Y.; Potthoff, M.; Tanaka, T.; Kajishima, T.; Tsuji, Y. 54 2001 Algebraic independence results related to linear recurrences. Zbl 0946.11015 Tanaka, Taka-aki 9 1999 Algebraic independence of sums of reciprocals of the Fibonacci numbers. Zbl 0939.11028 Nishioka, Kumiko; Tanaka, Taka-aki; Toshimitsu, Takeshi 3 1999 Substitution in two symbols and transcendence. Zbl 0940.11015 Nishioka, Kumiko; Tanaka, Taka-aki; Wen, Zhi-Ying 2 1999 Image reconstruction of two-dimensional impenetrable objects using genetic algorithm. Zbl 0938.68087 Meng, Z. Q.; Takenaka, T.; Tanaka, T. 1 1999 Modern numerical schemes for solving magnetohydrodynamic equations. Zbl 0915.76059 Murawski, K.; Tanaka, T. 1 1997 Algebraic independence of the values of power series generated by linear recurrences. Zbl 0876.11036 Tanaka, Taka-aki 6 1996 Tracing the equilibrium path by dynamic relaxation in materially nonlinear problems. Zbl 0835.73057 Siddiquee, M. S. A.; Tanaka, T.; Tatsuoka, F. 2 1995 Finite volume TVD scheme on an unstructured grid system for three- dimensional MHD simulation of inhomogeneous systems including strong background potential fields. Zbl 0797.76061 Tanaka, T. 21 1994 Algebraic independence of certain numbers defined by linear recurrences. Zbl 0923.11108 Tanaka, Taka-aki 2 1994 Experiments on the unsteady drag and wake of a sphere at high Reynolds numbers. Zbl 1134.76689 Tsuji, Y.; Kato, N.; Tanaka, T. 1 1991 all cited Publications top 5 cited Publications all top 5 Cited by 23 Authors 9 Tanaka, Taka-aki 7 Kurosawa, Takeshi 4 Duverney, Daniel 4 Ide, Haruki 4 Tachiya, Yohei 2 Bundschuh, Peter 2 Kaneko, Hajime 2 Shiokawa, Iekata 2 Väänänen, Keijo O. 1 Allouche, Jean-Paul Simon 1 Ara, Pere 1 Bell, Jason P. 1 Catarino, Paula Maria Machado Cruz 1 Chyzak, Frédéric 1 Claramunt, Joan 1 Coons, Michael 1 de Almeida, Regina 1 Dumas, Philippe 1 Goto, Akinari 1 Kanoko, Tomoaki 1 Rhouma, Mohamed Ben Hadj 1 Tanuma, Yusuke 1 Toyama, Kento all top 5 Cited in 18 Serials 6 Journal of Number Theory 2 Acta Arithmetica 2 Functiones et Approximatio. Commentarii Mathematici 2 Monatshefte für Mathematik 2 Tokyo Journal of Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 Research in Number Theory 1 Journal of Mathematical Analysis and Applications 1 Osaka Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Combinatorics 1 Journal of the Australian Mathematical Society 1 Mediterranean Journal of Mathematics 1 Algebra & Number Theory 1 Moscow Journal of Combinatorics and Number Theory all top 5 Cited in 10 Fields 27 Number theory (11-XX) 3 Difference and functional equations (39-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) Citations by Year