منابع مشابه
The Natural Logarithm on Time Scales
We define an appropriate logarithm function on time scales and present its main properties. This gives answer to a question posed by M. Bohner in [J. Difference Equ. Appl. 11 (2005), no. 15, 1305–1306].
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Rodriguez Villegas expressed the Mahler measure of a polynomial in terms of an infinite series. Lück’s combinatorial L-torsion leads to similar series expressions for the Gromov norm of a knot complement. In this note we show that those formulae yield interesting power series expansions for the logarithm function. This generalizes an infinite series of Lehmer for the natural logarithm of 4. 1 T...
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In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.
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In this paper, we develop the theory of hybrid differential equations on time scales. An existence theorem for hybrid differential equations on time scales is given under Lipschitz conditions. Some fundamental fractional differential inequalities are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the compa...
متن کاملTorus Knot complements: A natural series for the natural logarithm
Lück expressed the Gromov norm of a knot complement in terms of an infinite series that can be computed from a presentation of the fundamental group of the knot complement. In this note we show that Lück’s formula, applied to torus knots, yields surprising power series expansions for the logarithm function. This generalizes an infinite series of Lehmer for the natural logarithm of 4. 1 Backgrou...
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ژورنال
عنوان ژورنال: Journal of Dynamical Systems and Geometric Theories
سال: 2009
ISSN: 1726-037X,2169-0057
DOI: 10.1080/1726037x.2009.10698561