Functions and Analysis

1203 Submissions

[8] viXra:1203.0078 [pdf] submitted on 2012-03-20 07:02:58

Apparent Measure and Relative Dimension

Authors: Faycal Ben Adda
Comments: 24 Pages. A short version of this paper was published in Journal Européen des Systèmes Automatisés, Fractional order systems, 42, p733-746, 2008.

In this paper, we introduce a concept of "apparent" measure in R^n and we define a concept of relative dimension (of real order) with it, which depends on the geometry of the object to measure and on the distance which separates it from an observer. At the end we discuss the relative dimension of the Cantor set. This measure enables us to provide a geometric interpretation of the Riemann-Liouville's integral of order alpha between 0 and 1.
Category: Functions and Analysis

[7] viXra:1203.0065 [pdf] submitted on 2012-03-16 20:48:14

On the Growth of Meromorphic Solutions of a type of Systems of Complex Algebraic Differential Equations

Authors: Xiao-meng Li, Xianfeng Su
Comments: 4 Pages.

This paper is concerned with the growth of meromorphic solutions of a class of systems of complex algebraic differentialequations. A general estimate the growth order of solutions of the systems of differential equation is obtained by Zalacman Lemma. We also take an example to show that the result is right.
Category: Functions and Analysis

[6] viXra:1203.0038 [pdf] submitted on 2012-03-11 08:37:50

The Finite Yang-Laplace Transform in Fractal Space

Authors: Guang-Sheng Chen
Comments: 4 Pages.

In this paper, we establish finte Yang-Laplace Transform on fractal space, considered some properties of finte Yang-Laplace Transform.
Category: Functions and Analysis

[5] viXra:1203.0037 [pdf] submitted on 2012-03-11 08:40:07

The Local Fractional Stieltjes Transform in Fractal Space

Authors: Guang-Sheng Chen
Comments: 4 Pages.

This paper deals with the theory of the local fractional Stieltjes transform. We derive the Stieltjes transform. This is followed by several examples and the basic operational properties of Stieltjes transforms.
Category: Functions and Analysis

[4] viXra:1203.0035 [pdf] replaced on 2012-03-12 15:27:40

Entropy and the Individual Iterations of the Logistic Map

Authors: S Halayka
Comments: 7 Pages. Changed title, reduced clutter, submitted to journal.

It is presumed a priori that there is an entropy-area relationship inherent to the iterations of the logistic map. Several interesting results are produced.
Category: Functions and Analysis

[3] viXra:1203.0030 [pdf] submitted on 2012-03-08 22:45:49

Local Fractional Mellin Transform in Fractal Space

Authors: Guang-Sheng Chen
Comments: 12 Pages.

This paper deals with the theory and applications of the local fractional Mellin transform of the real order α . We define the local fractional Mellin transform and its inverse transform. This is followed by several examples and the basic operational properties of local fractional Mellin transform. We discuss applications of local fractional Mellin transforms to local fractional boundary value problems.
Category: Functions and Analysis

[2] viXra:1203.0029 [pdf] submitted on 2012-03-08 22:49:14

Local Fractional Improper Integral in Fractal Space

Authors: Guang-Sheng Chen
Comments: 8 Pages.

In this paper we study Local fractional improper integrals on fractal space. By some mean value theorems for Local fractional integrals, we prove an analogue of the classical Dirichlet-Abel test for Local fractional improper integrals.
Category: Functions and Analysis

[1] viXra:1203.0023 [pdf] submitted on 2012-03-07 02:27:32

Quickly Identifying the Presence of the Golden Ratio in the Logistic Map

Authors: S Halayka
Comments: 2 Pages.

A brief visual demonstration of the presence of the golden ratio in the logistic map is given.
Category: Functions and Analysis