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A nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets
strong law of large numbers nonconventional ergodic averages
2011/1/21
We provide conditions which yield a strong law of large num-bers for expressions of the form 1/N PN n=1 FX(q1(n)), · · · ,X(qℓ(n)) where X(n), n 0’s is a sufficiently fast mixing ve...
A Fractal Example of a Continuous Monotone Function with Vanishing Derivatives on a Dense Set and Infinite Derivatives on Another Dense Set
Sierpinki Gasket harmonic function
2011/6/2
Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on an...
The Fractional Derives of a Fractal Function
Weierstrass function fractional derivatives dimensions of graphs of functions
2007/12/12
The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of ...