The Complex Geometry of the Mandelbrot Set

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

Topological Entropy of Quadratic Polynomials and Dimension of Sections of the Mandelbrot Set

A fundamental theme in holomorphic dynamics is that the local geometry of parameter space (e.g. the Mandelbrot set) near a parameter reflects the geometry of the Julia set, hence ultimately the dynamical properties, of the corresponding dynamical system. We establish a new instance of this phenomenon in terms of entropy. Indeed, we prove an “entropy formula” relating the entropy of a polynomial...

Turbulent Flow in 2-D Domains with Complex Geometry-Finite Elelment Method

Using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-D domains with complex geometry. The Petrov-Galerkin finite element formulation is adopted to avoid numerical oscillations. Turbulence is modeled using the two equation k-ω model. The discretized equations are written in the form o...

Turbulent Flow in 2-D Domains with Complex Geometry-Finite Elelment Method

Using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-D domains with complex geometry. The Petrov-Galerkin finite element formulation is adopted to avoid numerical oscillations. Turbulence is modeled using the two equation k-ω model. The discretized equations are written in the form o...

Basis Set Effects in Density Functional Calculations and BSSEcorrected on the Molybdate-Phosphonic acid Complex

In this research, this possibility was investigated the relative stablilty geometry and bindingenergies of the hydrogen bonds of Molybdate-Phosphonic Acid (MPA) complex in gas phase onthe basis of result of ab initio and DFT calculations. Three DFT methods have been applied forcalculations are B3LYP, BP86 and B3PW91 that have been studied in two series of basis sets:D95** and 6-31+G(d,p) for hy...