Tricorns and Multicorns ofS-Iteration Scheme

Multicorns are not path connected

The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z 7! z2 + c. We prove that the tricorn is not locally connected and not even pathwise connected, confirming an observation of John Milnor from 1992. We extend this discussion more generally for antiholomorphic unicritical polynomials of degrees d 2 and their connectedness loci, known as multicorns.

Strong Convergence for Hybrid S-Iteration Scheme

A Cyclic Douglas-Rachford Iteration Scheme

In this paper we present two Douglas–Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our metho...

Wbb 5 - 1 Ofs ' 88

The passive resonator approach to fiber opt sensing has benefitted from recent advances in fiber High performance couplers, spliceless resonators' ic rotation components. , and long coherence length laser diodes have been described. Polarization maintaining components and 1.3 & 1.55 urn wavelength components are being made, and one company is selling high finesse resonators commercially2. This ...

Superior Multibrots for Multicorns for Positive Values

The Multibrots for Multicorns is a modification of the classic Mandelbrot and Julia sets and it is given by the complex function where and is a constant. The Multibrot fractal type is particularly interesting, with beautiful shapes and lots of spirals. In this paper we have presented different characteristics of Multibrot function for Multicorns using superior iterates. Further, different prope...