The article mainly studies the contracting similarity fixed point and the structure of the general Sierpinski gasket. Firstly, the paper analyzes the importance of contracting similarity fixed point in fractal geometry. Based on a series of definitions, the article studies the contracting similarity fixed point. Then, the paper researches on the structure of the general Sierpinski gasket, and d...

Study on properties of Sierpinski-type fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. It is well know that studying fractal theory relies on in-depth observation and analysis to topological structures of fractals and their geometric constructions. But most works of simulating fractals are for graphical goal and often done by non-mathematical researchers....

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

We describe a method, based on vertex-labeling, to generate algorithms for manipulating the Hilbert space lling curve in the following ways: 1. Computing the image of a point in R. 2. Computing a pre-image of a point in R. 3. Drawing a nite approximation of the curve. 4. Finding neighbor cells in a decomposition ordered according to the curve. Our method is straightforward and exible, resulting...

N. Cagman, S. Karatas and S. Enginoglu, Soft topology, Comput. Math. Appl. 62 (2011), 351-358. D. Chen, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49 (2005) 757-763. F. Feng, Y. B. Jun, X. Z. Zhao, Soft semirings, Comput. Math. Appl. 57 (2009), 1547-1553. J. C. Kelly, Bitopological spaces, Proc. London Math. Soc. , 13 (1963), 71-81. P. K. Maji, R. Biswa...

We consider differential operators of type Au(x) = u(x) + (−1)t1 ∂ 2t1u(x) ∂x1 1 + (−1)t2 ∂ 2t2u(x) ∂x2 2 , x = (x1, x2) ∈ R2, and Sierpinski carpets Γ ⊂ R2. The aim of the paper is to investigate spectral properties of the fractal differential operator A−1 ◦ trΓ acting in the anisotropic Sobolev space W (t1,t2) 2 (R 2) where trΓ is closely related to the trace operator trΓ . Mathematics Subjec...

We introduce a class of stochastic processes in discrete time with finite state space by means of a simple matrix product. We show that this class coincides with that of the hidden Markov chains and provides a compact framework for it. We study a measure obtained by a projection on the real line of the uniform measure on the Sierpinski gasket, finding that the dimension of this measure fits wit...

The numerical analysis of highly iterated Sierpinski microstrip patch antennas by method of moments (MoM) involves many tiny subdomain basis functions, resulting in a very large number of unknowns. The Sierpinski pre-fractal can be defined by an iterated function system (IFS). As a consequence, the geometry has a multilevel structure with many equal subdomains. This property, together with a mu...

The lattice fractal Sierpinski carpet and the percolation theory are applied to develop a new random stock price for the financial market. Percolation theory is usually used to describe the behavior of connected clusters in a random graph, and Sierpinski carpet is an infinitely ramified fractal. In this paper, we consider percolation on the Sierpinski carpet lattice, and the corresponding finan...