INTERNATIONAL JOURNAL of

APPLIED MATHEMATICS and

APPLIED MATHEMATICS and

INFORMATICS

ISSN: 2074-1278

Editorial Board

Prof. Metin Demiralp (Turkey),

Prof. A.Kuri-Morales (Mexico),

Prof. V.Mladenov (Bulgaria),

Prof. G.Bognar (Hyngary),

Prof. Lotfi A. Zadeh (USA),

Prof. Leonid Kazovsky (USA),

Prof. T.Kaczorek (Poland),

Prof. L.Chua (USA),

Prof. O.Martin (Romania),

Prof. C.Udriste (Romania),

Prof. N.Mastorakis (Greece),

Prof. D.Bertsekas (USA),

Prof. R.Yager (USA),

Prof. Anping Xu (China),

Prof. M. A. Breuer (USA),

Prof. M.Wasfy (USA)

All aspects of classic and modern applied mathematics are covered including
algebra, differential equations, probability, statistics, operational research,
optimization, algorthms theory, computational complexity, control . It appears
quarterly. Special Issues are specially encouraged.

A Lyapunov Shortest-Path Characterization
for Markov Decision Processes

by Julio B. Clempner and Jesus Medel

Abstract:
In this paper we introduce a modeling paradigm
for developing decision process representation for shortest-path
problems. Whereas, in previous work attention was restricted to
tracking the net using Bellman?s equation as a utility function,
this work uses a Lyapunov-like function. In this sense, we are
changing the traditional cost function by a trajectory-tracking
function which is also an optimal cost-to-target function for tracking
the net. The main point of the Markov decision process is its
ability to represent the system-dynamic and trajectory-dynamic
properties of a decision process. Within the system-dynamic
properties framework we prove new notions of equilibrium
and stability. In the trajectory-dynamic properties framework,
we optimize the value of the trajectory-function used for path
planning via a Lyapunov-like function, obtaining as a result
new characterizations for final decision points (optimum points)
and stability. Moreover, we show that the system-dynamic and
Lyapunov trajectory-dynamic properties of equilibrium, stability
and final decision points (optimum points) meet under certain
restrictions.

__Keywords:__

Automatic generation, HTML frames, HTML framesets, web application, web components

Full Paper, pp.
1-4

A New Paradigm for the Computational Complexity Analysis of
Algorithms and Functions

by Ahmed Tarek

Abstract:
There exists a variety of techniques for the computational
complexity analysis of algorithms and functions. This analysis
is foundational to the algorithmic and the functional performance.
Asides from the big-oh complexity, there are other complexity
notations, such as ?, ?, small o and small ! notational complexities.
Complexity analysis is used to select an appropriate algorithm for
solving a given problem using computer. Unfortunately, most of the
prevailing approaches lack in simplicity, and consistency. Existing
techniques are complex, and rather hard to realize in practice. There
is a trend to exploit the notational complexities in the existing
literature by treating those as functions instead of sets. In this paper,
notational complexities and their applications paradigms are studied
from the new perspectives. Simplified and consistent approaches are
introduced that will make the analysis even simpler and easy to
understand. Abused notational complexities are analyzed through the
appropriate approach. Also, the paradigm introduced is extended to
algorithms and functions involving multiple input variables.

__Keywords:__

Time Complexity, Space Complexity, Complexity
Function, Notational Complexity, Complexity Paradigm, Algorithm
Analysis.

Full Paper, pp.
5-12

Modern mathematical model using mixed p-z
approach for the analyze of the switching power
circuits

by Jiri Klima

Abstract:
The mathematical method for the time-domain
analysis of power converters with periodic pulse width
modulation (PWM) is developed .The method is based on mixed
p-z description of linear periodically time-varying system. The
mathematical model uses the Laplace and modified Z transforms.
The solution is not dependent on the number of the pulses of the
PWM pattern. Instead of solution of algebraic equations the
change of switching instants is reflected in the solution only by a
change in two values mk and nk. All the results were visualized
from the derived equations by the programme Mathcad. The
derived equations are validated using a 3 kW three-phase inverter

__Keywords:__

Modified Z-transform, Laplace transform,
switching circuits

Full Paper, pp.
13-20

Probability of collisions in Soft Input
Decryption

by Nata?a ?ivi? and Christoph Ruland

Abstract:
In this work, probability of collision in Soft Input
Decryption has been analyzed and calculated. Collisions of
cryptographic check values cause wrong verification results.
Therefore, it is important to find an analytical form of a probability
of collisions, which can be used for estimation of an efficiency of
Soft Input Decryption. It is known, that shorter cryptographic check
values cause often collisions. For that reason, the number of
collisions for cryptographic check values has been tested and
compared with the theoretical results.

__Keywords:__

Collisions, Probability of Collisions, Probability of a
Match, Soft Input Decryption.

Full Paper, pp.
21-27

Just-in-Time Business Intelligence
and Real-Time DecisioningDecryption

by Zeljko Panian

Abstract:
Enterprise agility often may be the difference between
organizational success and failure. The changing conditions in which
businesses operate might be from customers, competitors, partners,
market forces, regulatory forces, or world events. In these
circumstances, decisioning is playing a critical role and must also be
made in real time. Real-time decisioning is an analytic approach that
allows organizations to automate the ?next best actions? based upon
their goals and objectives. It embeds real-time analytic capabilities
into business processes and substitutes traditional Business
Intelligence (BI) which is oriented dominantly towards analyzing
historical data coming from processes that are already accomplished.

__Keywords:__

Business agility, just-in-time business intelligence,
decision-making process, real-time decisioning.

Full Paper, pp.
28-35

Continuation of Nonsmooth Bifurcations in
Filippov Systems Using Singular Point Tracking

by Iv? Arango and John Alexander Taborda

Abstract:
In this paper, we propose a novel numerical method
for continuation of nonsmooth bifurcations in discontinuous
piecewise smooth systems or Filippov systems which we are
denominated Singular Point Tracking (SPT). We use the evaluation
of the vector fields on the discontinuity boundary (DB) to analyze the
dynamics of the systems without integration of the ODE sets or
integrating only in the points computed by the SPT algorithm. We
apply a classification of points and events on DB recently proposed.
Local and global nonsmooth bifurcations are detected using the SPT
method. Two principal advantages have the SPT method with other
numerical methods to continuation of bifurcations in nonsmooth
systems. First, the integration-free algorithms in the SPT avoid the
well know numerical problems of these algorithms. Second, when
the integration is unavoidable the SPT method computes the initial
condition of the simulation to reduce the compute time. A piecewise
smooth prey-predator model is used as illustrative example of the
SPT method.

__Keywords:__

Bifurcation theory, continuation techniques,
filippov systems, nonsmooth bifurcations.

Full Paper, pp.
36-49

A complete system of structural invariants for
regularizable singular systems

by M. Isabel Garcia-Planas, A. Diaz

Abstract:
Let (E; A;B;C) be a quadruple of matrices with E;A 2 Mn(C), B 2 Mn?m(C),
C 2 Mp?n(C) representing a singular time-invariant linear system, Ex? = Ax + Bu, y = Cx.
In this paper we present a collection of invariants for singular systems in terms of ranks of
certain matrices, that permit us to reduce the system in a canonical form in such a way that the
system is decomposed in following five independent subsystems: i) controllable and observable
system, ii) controllable non observable system, iii) observable non controllable system, iv) Jordan
system v) completely singular system.

__Keywords:__

Singular systems, proportional and derivative feedback, proportional and derivative
output injection, canonical forms.

Full Paper, pp.
97-102

Numerical simulations used to detect the
chaotic evolution of the exchange rate
described by a nonlinear determinist system

by Mirela-Catrinel Voicu

Abstract:
In this paper we present a study concerning the
exchange rate evolution governed by a third-order nonlinear
determinist discrete system. We present some results concerning the
unique fixed point of the system, its stability and its attraction
domain under certain values of parameters and we also present the
existence of period-two cycles. Given the nonlinear nature of the
system, its most complex type of behavior is the chaotic dynamics.
We cannot detect this type of behavior using only analytical tools.
For this reason, in order to detect the dynamics of the system, we will
use numerical simulations. It is known that the Lyapunov exponents
are a tool used to establish the type of behavior in nonlinear
dynamics. We will calculate their values, in order to establish the
type of dynamics. From our numerical simulations, we present a case
in which the system displays a chaotic behavior. For this particular
case we also consider a corresponding system of the second order.
From the images of the figures in this paper we can observe a
similarity between the images of attractors for each particular order
of the systems.

__Keywords:__

nonlinear system, numerical simulations, chaos,
attractors.

Full Paper, pp.
103-109

Adapting the teaching model to the new
generation with the use of the ICT

by Javier Bilbao, Eugenio Bravo, Olatz Garc?, Concepci? Varela, Miguel Rodr?uez, Ver?ica
Valdenebro, Gorka Garate, Izaskun Baro, Purificaci? Gonz?ez, and M. Emiliana Uranga

Abstract:
In the last century the pedagogical and psychoeducational
changes, advances and studies were the major figures in
the educational programmes and in the way of teaching. In the
century XXI, although these items continue with a great prominence,
new tools have emerging which are very useful for teachers by
means of Information and Communication Technologies (ICT).
Moreover, in Europe an small revolution in the educational system is
happening: the Bologna process. From our research group we are
developing and using different tools to obtain and to facilitate this
change of attitude: we have created some new and interactive
material, similar to videos, we use the Moodle platform, we have
created test for an auto-evaluation by students, etc. These new tools
are implemented on the one hand in our subjects of the Engineering
School of Bilbao and on the other hand in the subjects of the Spanish
Group 9 of Universities by means of its Virtual Campus.

__Keywords:__

Computer applications, E-learning, ICT, Knowledge
improvement, Teaching model.

Full Paper, pp.
110-114

The Design and Implementation of Database
Encryption

by Noor Habibah Arshad, Saharbudin Naim Tahir Shah, Azlinah Mohamed, Abdul Manaf Mamat

Abstract:
Information inside the database is shared by multiple
parties such as internal users, partners, contractors and others.
Sensitive data stored in database could be a target to attackers. The
attacker for data stored in database not only from external but also
from within the organization. Adding the database encryption,
valuable information in database becomes more secure since the
encrypted data ensure the confidentiality of the data. A new affine
block cipher named Enhanced Affine Block Cipher technique is
proposed for database encryption. This algorithm improves the
weakness of the original affine cipher. The new encoding schema and
modification Cipher Block Chaining (CBC) mode of operation for
block cipher is designed for the new algorithm and then the prototype
of the system is built and implemented into existing system for
protecting user password. The result has shown that the algorithm is
working properly, where the decryption process produced similar
output as the original plaintext and it ran through specified
configuration and evaluated thoroughly with respect to database
approach and algorithm technique to prove the design.

__Keywords:__

Database, Enhanced Affine Block Cipher,
Encryption, Decryption.

Full Paper, pp.
115-122

Maximizing Coverage in a Connected and
K-Covered Wireless Sensor Network Using
Genetic Algorithms

by Tahir Emre Kalayc?, Kas?m Sinan Y?ld?r?m, Aybars U?gur

Abstract:
We are interested in an initial deployment strategy
that maximizes the coverage area of wireless sensor network
while preserving connectivity between nodes provided that all
given hotspot regions are covered by at least k sensors. Sensing
coverage of a sensor network characterizes how well an area is
monitored or tracked by sensors. Connectivity is an important
requirement that shows how nodes in a sensor network can
effectively communicate. Some hotspot areas in the network
are more important than other areas and need to be covered
by more sensors. We propose a genetic algorithm based solution
to find an optimal sensor node distribution. Experimental results
are presented to evaluate our algorithm.

__Keywords:__

Wireless Sensor Networks, Genetic Algorithm,
Coverage, Connectivity, k-Coverage,Optimization.

Full Paper, pp.
123-130

Growth of a Class of Plurisubharmonic Function
in a Unit Polydisc I

by Amritasu Sinha

Abstract:
The Growth of a non- constant analytic function of
several complex variables is a very classical concept, but for a finite
domain it is a recent concept initiated by Juneja and Kapoor[1],and
later on substantiated by Sinha[2]. A Unit Polydisc is the most
fundamental example of a Compact Riemann Surface, there is an
upsurge in the area as being reflected in[4,5]. This is a very important
concept and its applications can also be seen in Complex Analytical
Dynamics. However in this present article we shall be concentrating
on the growth parameter ?type? for such functions and also describe
its Geometrical Properties.We have investigated upon some finer
results on the growth of slowly varying functions.
The above concept of Growth can also be utilized in Computer aided
Tomography[7].

__Keywords:__

Analytic Function, Complex Analytical
Dynamics,Growth Parameter, Type.

Full Paper, pp.
50-54

On the Ermanno-Bernoulli and Quasi-Ermanno-Bernoulli constants for
linearizing dynamical systems

by F.I. Arunaye, H.White

Abstract:
It is well known that the Ermanno-Bernoulli
constants derived from the Laplace-Runge-Lenz vector of dynamical
systems are efficiently used to reduce them to a system of harmonic
oscillator(s) and conservation law in the context of point and
nonlocal symmetries of dynamical systems. In this paper, we review
Ermanno-Bernoulli constants and observe that one can also use
analogous constants obtained from the Hamilton vector of dynamical
systems to serve the same purpose. We report the generic natural
variables for reducing such dynamical systems in two-dimensions
and three-dimensions to a system of one harmonic oscillator and two
harmonic oscillators respectively, and a conservation law with some
examples. We also note that the symmetry groups obtained from the
reduced systems using the alternative constants are realizations of
those obtained from Ermanno-Bernoulli constants. We also report
here that the symmetries of the original dynamical systems can be
obtained from symmetries of the reduced systems.

__Keywords:__

Quasi, Constants, Symmetries, Vectors, Conservation,
Oscillators, Laplace-Runge-Lenz, Hamilton, Coordinates,
Dynamical.

Full Paper, pp.
55-60

A New Method for Enhanced Information
Content in Product Model

by L?zl?Horv?h

Abstract:
This paper introduces a new method in order to
establish a better communication between engineers and modeling
procedures during lifecycle management of product information in
computer based engineering systems. The proposed method is
intended as one of the initial attempts for resolution of an inherent
conflict in product modeling. This conflict is between information
content based thinking of engineer and information based processing
in classical product modeling systems. The author applies a new
sector of product model that describes information content for
engineering activities. This sector controls engineering object data in
the second sector for classical product model entities. In this manner,
the new modeling can be interconnected with existing modeling in
industrially applied engineering systems. Information content is
stored in interconnected levels of the product model for human
intent, meaning of concepts, engineering objectives, contexts, and
decisions. This paper explains basic concepts, refers to research in
the related topics, introduces role of humans and human-computer
interactions in the proposed modeling, and details information
content based product modeling. Following this, it emphasizes
difficulties of decisions in case of high number of dependencies
amongst engineering objects in large product models and proposes a
new method for change management in those models.
Implementation of the proposed product modeling methods can be
realized in industrial professional modeling systems by using of their
functionality for open architecture.

__Keywords:__

Product modeling, Lifecycle management of
product information, Information content based product model,
Design intent, Product changes, Affect zone of modified engineering
object.

Full Paper, pp.
61-69

Elements of Security Aspects in Wireless
Networks: Analysis and Integration

by Bojan M. Bakmaz, Miodrag R. Bakmaz, Zoran S. Bojkovic

Abstract:
Security is a very critical part of wireless
networks. This work presents a survey of some recent security
aspects in wireless networks and discuss challenges in
designing integrated security platform in wireless network
environment. Firstly, recent security issues together with
general security analysis, criteria and threats are emphasized.
Starting from the point that security in wireless networks
mainly involves authentication, confidentiality, integrity and
authorization, integration of different wireless networks is
analyzed. The importance of secure handover between
heterogeneous networks is emphasized, too.

__Keywords:__

ntegrated security platform, handover, security
treats, wireless networks.

Full Paper, pp.
70-75

Analyzing the set of uncontrollable second order
generalized linear systems

by M. Isabel Garcia-Planas, J. Clotet

Abstract:
In this paper we consider the space of second order generalized time-invariant linear
systems, Ex? = A1x? + A2x + Bu, where E, A1, A2 2 Mn(C), B 2 Mn?m(C).
We study the controllability of second order generalized systems by means the rank of a
certain constant matrix that we will call ?the controllability matrix? of second order generalized
linear systems. We use this matrix to study the geometry of the set of uncontrollable systems
and we explicit the subset contained in the set of standardizable ones.

__Keywords:__

Second order linear systems, Feedback equivalence, Bundles.

Full Paper, pp.
76-83

Investigation of the Impact of Pilot Signals
on the Performance of OFDMA Systems

by M. Haridim, M. Bank, V.Vulfin

Abstract:
We introduce a new simulation
method for OFDMA systems. The proposed
method allows for the study of the impact of
deterioration of subcarriers orthogonality,
non-ideal synchronization and the phase noise
of local oscillators. Using the proposed
simulation method we have studied the impact
of pilot signals on OFDMA performance.
Results are compared to the performance of
FBS systems which are a modified version of
OFDMA systems using no pilot signals.

__Keywords:__

OFDMA, pilots, Doppler, FBS,
simulation.

Full Paper, pp.
84-91

An Efficient Load Balancing Technology in CDN

by Yun Bai, Bo Jia, Jixiang Zhang, Qianggou Pu, Nikos Mastorakis

Abstract:
The existing load balancing technology in CDN only emphasizes even load distribution among servers, and it doesn?t make full use of network topology information and file access history, so user request can?t get timely response. To solve the above problem, this paper puts forward a load balancing algorithm based on the Distributed binning strategy. This algorithm can make full use of network topology information and file access history as well as server load information, analyzing the popularity of files with the access history of the clusters of clients from the servers, efficiently finishing distribution and routing of the high popularity files among servers so that users can closely obtain the required contents, ease Internet congestion and enhance response speed of user accessing websites.

__Keywords:__

CDN, distributed binning strategy; history record, load balancing, network topology

Full Paper, pp.
92-96

Issue 4, Volume 1, 2007

Motion Controller Design for the Speed Control of DC Servo Motor

by Mehmet Akari and ?smail Temiz

Abstract:
This paper presents a study on
speed control problem for Direct Current
(DC) servo motor. In this study DC servo
motor?s mathematical model and equations
were extracted and there were three different
motion controller designed for controlling the
angular velocity. It was created simulation
model at the Matlab programme and
implemented proportional-integral, fuzzy
and adaptive neuro fuzzy inference system
controllers respectively while it was working
variable conditions. At the servo motor
application it is expected that no overshoot,
settling reference value quickly and
minimum influence on the system stability.

__Keywords:__

DC Servo Motor, Proportional-
Integral, Fuzzy, Adaptive Neuro Fuzzy
Inference System

Full Paper, pp.
131-137

Integration method and Runge-Kutta method

by Wannaporn Sanprasert and Ungsana Chundang

Abstract:
In [1], M. Podisuk, U.
Chundang and W. Sanprasert
introduced the integration method for
finding the numerical solution of the
initial value problem of ordinary
differential equation which turned out
to be the multi-step method. In this
paper, the single step method of this
integration method with the help of
Gauss-Legendre Quadrature
integration formula and the Taylor
series expansion is explored. The
results of some examples that include
the initial value problem of fourth
order of ordinary differential equation
are shown. These results are
compared to the results that obtain by
the Runge-Kutta method.

__Keywords:__

Gauss-Quadrature-formula
Gauss-Legendre-Quadrature-formula
Integration-method Initial-valueproblem
Taylor series expansion
Runge-Kutta-method

Full Paper, pp.
138-143

Smoothing curve by orthogonal polynomials

by Sukpak Pansomboon and Pongpan Rattanathanawan

Abstract:
The interpolation by
polynomial of degree n, p (x) n , may
smooth any curve y = f (x) with the
condition that this polynomial must
passes through n +1 points of the
curve y = f (x) . This condition may
make the shape of the curve of
y p (x) n = different from the exact
shape of curve of y = f (x) especially
in the case that the points of f (x) are
obtained from an experiment which
may not be the exact point of the
curve y = f (x) . But the least square
approximation by orthogonal
polynomial, q (x) n , may give the better
shape than the interpolation by
polynomial, p (x) n . However the curve
of y q (x) n = may not pass through
any exact point of the curve y = f (x) .
M.Podisuk, P.Rattanathanawan and
P.Phataranavik in [1] introduced the
sequences of orthogonal polynomials
with step functions as their weight
functions but they did not use them
for least square approximation. In this
paper, the sequences of orthogonal
polynomials with step functions as
their weight functions will be used for
least square approximation.

Full Paper, pp.
144-150

Machine learning approach to authorship attribution of literary texts

by Urszula Sta?czyk, Krzysztof A.Cyran

Abstract:
Machine learning approaches are employed in the variety of feature
extraction and classification tasks because of their efficiency in
dealing with huge amount of data. The paper addresses the application
of Artificial Neural Networks as the processing engine for textual analysis
of literature oriented at authorship attribution, which falls within the scope
of data mining techniques. Author identification is a problem of significant
importance not only from academic or historic point of view as in cases
of disputed authorship of some literary works but in more current and sinister
affairs of forensic nature as well. To solve the problem various methodologies
have been employed or invented, belonging either to statistic-dedicated
computations or machine learning algorithms, the example of the latter
category presented in the paper.

__Keywords:__

Machine learning, stylometry, artificial neural networks, author identification

Full Paper, pp.
151-158

On employing elements of Rough Set Theory to stylometric analysis of literary texts

by Urszula Stanczyk, Krzysztof A. Cyran

Abstract:
Rough Set Theory deals with imperfect knowledge about the Universe and objects that comprise it,
and such knowledge can be interpreted and manipulated in many ways. The paper describes application
of rough set-based approach to the problem of stylometric analysis of texts that by the notion of writer
invariant enables to identify authors of disputed or unattributed works. Writer invariant is the primary
stylometric concept which corresponds to such unique characteristic that expresses the writing style
of a person, allowing for distinguishing texts authored by this person from all others. It can be obtained
in a myriad of techniques usually belonging with either statistical analysis or machine learning
methodologies, with RST addressed in this paper being the example of the latter category.

__Keywords:__

Stylometry, rough sets, authorship attribution, relative reduct, decision algorithm.

Full Paper, pp.
159-166