On the “mandelbrot Set” for a Pair of Linear Maps and Complex Bernoulli Convolutions

Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces

This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$

Spacings and Pair Correlations for Finite Bernoulli Convolutions

We consider finite Bernoulli convolutions with a parameter 1/2 < λ < 1 supported on a discrete point set, generically of size 2 . These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure νλ, as N → ∞. Numerical evidence suggests that for a generic λ, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some parti...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Quasi-Mandelbrot sets for perturbed complex analytic maps: visual patterns

We consider perturbations of the complex quadratic map $ z \to z^2 +c$ and corresponding changes in their quasi-Mandelbrot sets. Depending on particular perturbation, visual forms of quasi-Mandelbrot set changes either sharply (when the perturbation reaches some critical value) or continuously. In the latter case we have a smooth transition from the classical form of the set to some forms, cons...

Bernoulli Vacation Policy for a Bulk Retrial Queue with Fuzzy Parameters

In this paper, we investigate the fuzzy logic based system characteristics of MX/G/1 retrial queuing system with Bernoulli vacation schedule. The service time and vacation time are assumed to be generally distributed. It is found in many practical situations that the queuing models with fuzzy parameters are much more realistic than the classical crisp parameters based queuing models. We have...