**
1.
Evidence of Noisy Chaotic Dynamics in the Returns
of Four Dow Jones Stock Indices**
Full text (PDF)

**John Francis T. Diaz**

**
Pages: 1-1**5

**
Abstract:
** This
research finds evidence of noisy chaotic properties in the returns of
four Dow Jones indices, based on three tests of non-linearity and chaos.
The study uses an average of 24,815 data points to correctly simulate
chaos in financial time-series. The data consists of the Dow Jones
Industrial Average (29,229 observations); Dow Jones Transportation
Average (29,121 observations); Dow Jones Utility Average (21,150
observations) and the Dow Jones Composite Average (19,906 observations).
The a) Brock, Dechert, and Scheinkman (BDS) test indicates that most of
the Dow Jones indices are not
iid
series, except
for the filtered residuals from the GARCH of the Dow Jones Utility
Average. The b) rescaled range analysis shows that after scrambling the
data, all Hurst exponents are above 0.5, and a trend-reinforcing
property, which helps in the conclusion of having a chaotic process.
Lastly, the c) correlation dimension analysis complements the initial findings and concludes the presence of a high dimensional noisy chaotic
structure in the four Dow Jones indices.

**2. **
**Dynamic Behaviour of a Unified Two-Point Fourth Order Family of
Iterative Methods****
Full
text (PDF)**

**D. K. R. Babajee and S. K. Khratti**

**
Pages: **
**15-29**

**
Abstract:
**Many variants of
existing multipoint methods have been developed. Recently, Khratti et
al. (2011) developed a unifying family of two-point fourth order methods
which contains the well-known Ostrowski method. The authors also
obtained some new methods which are variants of Ostrowski’s
method. However, it is difficult to compare the methods with the same of
the order of convergence. The dynamic behaviour of the methods can be
used as a tool for comparison.
In this
work, we study the dynamic of six members of the unifying family for
some quadratic and cubic polynomials. By means of computer generated
plots, we draw their polynomiographs for the polynomials
f(z)
= z2−1
and f(z)
= z3−1
and explain their respective dynamic behaviour by analyzing the free
critical and additional fixed points. Our results show that the methods
exhibit different fractal behaviour and the most efficient method based
on the size of its basins of attractions was found to the well-known
Ostrowski method. This shows that these fourth order variants of
Ostrowski’s
method are inefficient.

**3. **
**A Common Fixed Point Theorem of Presic Type for Three Maps in
Fuzzy Metric Space**
**
Full text (PDF)**

**P. P. Murthy, Rashmi****
**
**
**

**
Pages:
30-36**

**
Abstract:
** The
present paper deals with a common fixed point theorem in Fuzzy metric
space by implementing the concept of Presic fixed point theorem [16]. In
this paper
we have proved a unique common fixed point theorem of Presic type for
three maps
in a Fuzzy metric space. Also we have obtained the main theorem of R.
George
[Some
fixed point results in dislocated fuzzy metric spaces, Journal of
Advanced
Studies in Topology, (2012), 3(4), 41-52] as a corollary by employing
the conditions
of our theorem
for dislocated spaces.

**4****. **
**Analysis of Dual Functions **
** **Full text (PDF)

** ****Farid
Messelmi**

**
Pages: 37-55**

**
Abstract:
** The
purpose of this paper is to develop a theory, inspired from complex
analysis,
of dual functions. In detail, we introduce the notion of holomorphic
dual functions and we establish a general representation of holomorphic
dual functions. As an
application, we generalize some usual real functions to the dual plane.
Finally, we will define the integral trough curves of any dual functions
as well as the dual
primitive.

**5.
**
**Chaotic Dynamical Behavior of Recurrent Neural Network**** **Full text (PDF)

** ****A.
Zerroug, L. Terrissa, A. Faure**

**
Pages:
55-66**

**
Abstract:
** On
account of their role played in the fundamental biological rhythms and
by
considering their potential use in information processing, the dynamical
properties
of an artificial neural network are particularly interesting to
investigate. In order to reduce the degree of complexity of this work,
we have considered in this paper
a fully connected neural network of two discrete neurons. We have
proceeded to a qualitative and quantitative study of their state
evolution by means of numerical
simulation. The first aim was to find the possible equilibrium states.
Other authors have already shown that some oscillating state can occur.
So, the second aim was
to analyze the dynamical properties of each of them. We have computed
the value of the Lyapunov’s
exponents and the fractal dimension. The sensitivity of the
dynamical characteristics to parameters such as the
weights of the connections
nd the shape of the activation function has been
studied.

**
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