A Note on Diophantine Fractals for Α–lüroth Systems

Self-similar fractals and arithmetic dynamics

‎The concept of self-similarity on subsets of algebraic varieties‎ ‎is defined by considering algebraic endomorphisms of the variety‎ ‎as `similarity' maps‎. ‎Self-similar fractals are subsets of algebraic varieties‎ ‎which can be written as a finite and disjoint union of‎ ‎`similar' copies‎. ‎Fractals provide a framework in which‎, ‎one can‎ ‎unite some results and conjectures in Diophantine g...

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

The Set of Badly Approximable Vectors Is Strongly C Incompressible

We prove that the countable intersection of C1-diffeomorphic images of certain Diophantine sets has full Hausdorff dimension. For example, we show this for the set of badly approximable vectors in Rd, improving earlier results of Schmidt and Dani. To prove this, inspired by ideas of McMullen, we define a new variant of Schmidt’s (α, β)-game and show that our sets are hyperplane absolute winning...

Antenna Miniaturization Using Fractals (RESEARCH NOTE)

Antenna Miniaturization Using Fractals Richa Garg, AP ECE Deptt., [email protected], J.C.D.C.O.E., Sirsa ABSTRACTThe use of fractal geometry in designing antenna has been a resent topic of interest. Fractal shape has their own unique characteristics that the improved antenna performance can be achieved without degrading the antenna properties. Modern telecommunication system requires antenn...

Percolation Dimension of Fractals

“Percolation dimension” is introduced in this note. It characterizes certain fractals and its definition is based on the Hausdorff dimension. It is shown that percolation dimension and “boundary dimension” are in a sense independent from the Hausdorff dimension and, therefore, provide an additional tool for classification of fractals. A unifying concept of fractal was introduced by Mandelbrot t...