We construct a linear extension operator, Π, which extends a function u in the energy domain of the fractal Koch curve S to a larger domain Ω ⊆ R. The operator Π is the limit of a sequence of operators Πn and satisfies the estimate ∥Πu∥H1(Ω) ≤ C √ E[u] + ∥u∥2L2(S,μ) where C is a numerical constant independent of u. Our approach is different and more constructive than the standard approach and e...

In this paper, we study the fractal characteristics of the futures market. We take the empirical study on London Gold Futures yield by Rescaled Range Analysis, analyzing the fractal characteristics of the futures market. We further determine fractal characteristics and the structure of the nonlinear time series through random disturb the original time series observation sequence. The result of ...

Fractal compression is a technique for encoding images compactly. It is built on local self similarities within the images. Image blocks are seen as rescaled and intensity transformed approximate the copies of blocks found elsewhere in the image. In this paper the Fractal image compression technique using fixed level of scaling is proposed in which the time of encoding process is considerably r...

While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is a certain splitting of the total Hilbert space and its recursive iterations to further iterated subdivisions. This paper explores some implications for asso...

We have shown within quasistatic approximation that the giant fluctuations of a local electromagnetic field in random fractal aggregates of silver nanospheres are strongly correlated with a local anisotropy factor S which is defined in this paper. The latter is a purely geometrical parameter which characterizes the deviation of local environment of a given nanosphere in an aggregate from spheri...

Fractals can model many classes of time-seri" data. The fractal dimension is an important actertsfic of ftaqo& that coniai, c information . out their geometrical structure at multiple Ntod re a b g ms i l d h ti BC m h d t c s, : s a ass of CJJ4 ent proac ox-coun n ( } et over 1 g c es, e.g., o , o estimate the fractal-dimension. Jr. this paper, the d rential box-counting (DBC) approach, origin...

  Background & Objectives: Cancer is a serious problem for human being and is becoming a serious problem day-by-day .A prerequisite for any therapeutic modality is early diagnosis. Automated cancer diagnosis by automatic image feature extraction procedures can be used as a feature extraction in the field of fractal dimension. The aim of this survey was to introduce a quantitative and objective...