2011, 2011(Special): 302-311. doi: 10.3934/proc.2011.2011.302

Some implications of a new approach to exponential functions on time scales

1. 

Uniwersytet w Białymstoku, Wydział Fizyki, ul. Lipowa 41, 15-424 Białystok, Poland

Received  August 2010 Revised  March 2011 Published  October 2011

We present a new approach to exponential functions on time scales and to timescale analogues of ordinary di erential equations. We describe in detail the Cayley-exponential function and associated trigonometric and hyperbolic functions. We show that the Cayley-exponential is related to implicit midpoint and trapezoidal rules, similarly as delta and nabla exponential functions are related to Euler numerical schemes. Extending these results on any Padé approximants, we obtain Pade-exponential functions. Moreover, the exact exponential function on time scales is de fined. Finally, we present applications of the Cayley-exponential function in the $q$-calculus and suggest a general approach to dynamic systems on Lie groups.
Citation: Jan L. Cieśliński. Some implications of a new approach to exponential functions on time scales. Conference Publications, 2011, 2011 (Special) : 302-311. doi: 10.3934/proc.2011.2011.302
[1]

Bahaaeldin Abdalla, Thabet Abdeljawad. Oscillation criteria for kernel function dependent fractional dynamic equations. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020443

[2]

Meenakshi Rana, Shruti Sharma. Combinatorics of some fifth and sixth order mock theta functions. Electronic Research Archive, 2021, 29 (1) : 1803-1818. doi: 10.3934/era.2020092

[3]

Tomasz Szostok. Inequalities of Hermite-Hadamard type for higher order convex functions, revisited. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020296

[4]

Peter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur Hafstein. Computing complete Lyapunov functions for discrete-time dynamical systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 299-336. doi: 10.3934/dcdsb.2020331

[5]

Yifan Chen, Thomas Y. Hou. Function approximation via the subsampled Poincaré inequality. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 169-199. doi: 10.3934/dcds.2020296

[6]

Guoliang Zhang, Shaoqin Zheng, Tao Xiong. A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations. Electronic Research Archive, 2021, 29 (1) : 1819-1839. doi: 10.3934/era.2020093

[7]

Bimal Mandal, Aditi Kar Gangopadhyay. A note on generalization of bent boolean functions. Advances in Mathematics of Communications, 2021, 15 (2) : 329-346. doi: 10.3934/amc.2020069

[8]

Andreas Koutsogiannis. Multiple ergodic averages for tempered functions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1177-1205. doi: 10.3934/dcds.2020314

[9]

Mark F. Demers. Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 217-256. doi: 10.3934/dcds.2020217

[10]

Huu-Quang Nguyen, Ya-Chi Chu, Ruey-Lin Sheu. On the convexity for the range set of two quadratic functions. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020169

[11]

Xinpeng Wang, Bingo Wing-Kuen Ling, Wei-Chao Kuang, Zhijing Yang. Orthogonal intrinsic mode functions via optimization approach. Journal of Industrial & Management Optimization, 2021, 17 (1) : 51-66. doi: 10.3934/jimo.2019098

[12]

Lars Grüne. Computing Lyapunov functions using deep neural networks. Journal of Computational Dynamics, 2020  doi: 10.3934/jcd.2021006

[13]

Peter Giesl, Sigurdur Hafstein. System specific triangulations for the construction of CPA Lyapunov functions. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020378

[14]

Thabet Abdeljawad, Mohammad Esmael Samei. Applying quantum calculus for the existence of solution of $ q $-integro-differential equations with three criteria. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020440

[15]

Gervy Marie Angeles, Gilbert Peralta. Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020108

[16]

Yu Zhou, Xinfeng Dong, Yongzhuang Wei, Fengrong Zhang. A note on the Signal-to-noise ratio of $ (n, m) $-functions. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020117

[17]

Djamel Aaid, Amel Noui, Özen Özer. Piecewise quadratic bounding functions for finding real roots of polynomials. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 63-73. doi: 10.3934/naco.2020015

[18]

Tahir Aliyev Azeroğlu, Bülent Nafi Örnek, Timur Düzenli. Some results on the behaviour of transfer functions at the right half plane. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020106

[19]

Kalikinkar Mandal, Guang Gong. On ideal $ t $-tuple distribution of orthogonal functions in filtering de bruijn generators. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020125

[20]

Jong Yoon Hyun, Boran Kim, Minwon Na. Construction of minimal linear codes from multi-variable functions. Advances in Mathematics of Communications, 2021, 15 (2) : 227-240. doi: 10.3934/amc.2020055

 Impact Factor: 

Metrics

  • PDF downloads (23)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]