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.

An Empirical Evaluation of CAPM's validity in the British Stock Exchange

by Nikolaos Loukeris

Abstract: The CAPM under the
means of the two step regression procedure indicated that the cross section of
average excess security return is positively related to beta. Under a frame of
Computational Econometrics the two step regression procedure is implemented into
CAPM, concluding that the strict CAPM test rejects the second H0 hypothesis on
the market risk premium, hence the slope of the Security Market Line (SML) is
different from the slope of SML indicated by CAPM. Consequently the CAPM has not
a statistical significance in Portfolio Selection.

__Keywords:__

Capital Asset Pricing Model, Two Step Regressions Procedure, Financial
Management

Full Paper, pp. 1-8

Stability of AQM Algorithms in Low Congestion Scenarios

by Pawel Mrozowski, Andrzej Chydzinski

Abstract: It is well known
that maintaining a stable queue size and high throughput in routers operating in
high bandwidth-delay product networks is a difficult task. Fortunately, some
newly proposed active queue management solutions (by Sun et al. and Ren et al.)
seem to work quite well in such environments. In this paper we demonstrate that
two additional factors make the task of achieving a stable queue size and high
throughput very difficult. Namely, when the congestion level is low or the
target queue size is short, none of the known AQMs performs reasonably well -
the queue is very unstable and the throughput often goes far below fifty percent
of the link capacity. Therefore, new AQM algorithms, able to work well in such
scenarios, are needed.

__Keywords:__

Active queue management, Internet routers, packet queueing, performance
evaluation

Full Paper, pp. 9-16

Applications of the Four Color Problem

by Marius-Constantin O. S. Popescu, Nikos E. Mastorakis

Abstract: In this paper are
followed the necessary steps for the realisation of the map’s coloring, matter
that stoud in the attention of many mathematicians for a long time. It is
debated the matter of the four colors, but also the way of solving by
implementing of an algorithm in the MAP-MAN application. Also, it is tackled the
maps drawing in real time within GPS system satellites, using more colors
depending on the covered route and the landforms met.

__Keywords:__

The issue of the fourth colors, The MAPMAN application, Software for GPS

Full Paper, pp. 17-26

A Binary Search Algorithm for a Special Case of Minimizing the Lateness on a Single Machine

by Nodari Vakhania

Abstract: We study the
problem of scheduling jobs with release times and due-dates on a single machine
with the objective to minimize the maximal job lateness. This problem is
strongly NP-hard, however it is known to be polynomially solvable for the case
when the processing times of some jobs are restricted to either p or 2p, for
some integer p. We present a polynomial-time algorithm based on binary search
when job processing times are less restricted; in particular, when they are
mutually divisible. We first consider the case when the following condition
holds: for any pair of jobs, if one is longer than another then the due-date of
the former job is no larger than that of the latter one. We also study cases
when a slight modification of our algorithm gives an optimal solution for the
version without the restriction on job due-dates.

__Keywords:__

Algorithm, scheduling, single processor, release date, due-date, lateness

Full Paper, pp. 45-50

by Diana Savin

Abstract: In this paper we
solve the Diophantine equations (x^5 + y^5)/(x+y)=5z^5 and (x^5 +
y^5)/(x+y)=z^5, in special conditions

__Keywords:__

Cyclotomics fields, Diophantine equations

Full Paper, pp. 51-59

by Zaid T. Balkhi

Abstract: Most of production
inventory systems is interested in determining the optimal stopping and
restarting times of producing certain commodity. In this paper, a multi-item
production inventory model under resource constraints is considered. For any
product, each of the production, the demand, and the deterioration rates in any
cycle as well as all cost parameters are treated as known and arbitrary
functions of time. Shortage for each product is allowed but it is partially
backlogged. All cost components are affected by both inflation and time value of
money. The existence of resource constraints implies the use of Linear
Programming in order to determine the optimal production rates for each item.
The objective is to find the optimal production and restarting times for each
product in any cycle so that the overall total inventory cost for all products
is minimized. A formulation of the problem is developed and rigorous
optimization techniques are used to show the uniqueness and global optimality of
the solution. An illustrative example which show the applicability of the
theoretical results is provided.

__Keywords:__

Linear programming, Inventory control, Multiitem production, Varying Parameters,
Optimality

Full Paper, pp. 27-34

Mathematical Model for Sounding Rockets, using Attitude and Rotation Angles

by Teodor-Viorel Chelaru, Cristian Barbu

Abstract: The paper purpose
is to present some aspects regarding the calculus model and technical solutions
for multistage sounding rockets used to test spatial equipment and scientific
measurements. The calculus methodology consists in numerical simulation of
sounding rocket evolution for different start conditions. The rocket model
presented will be with six DOF and variable mass. At this item, as novelty of
the work we will use simultaneously the rotation angles and the attitude angles
for describing the kinematical equations of the movement. The results analyzed
will be the flight parameters and the ballistic performances. The conclusions
will focus technical possibilities to realize sounding multi-stage rocket
recycling military rocket engines.

__Keywords:__

Multi-stage, Mathematic model, Sounding rocket, Simulation, Rotation angles

Full Paper, pp. 35-44

Parallel Finite Difference Methods for Phase Change Problems in Materials

by Chr. A. Sfyrakis

Abstract: The great
complexity of the problems in phase change materials to us to develop from a
fast and methods to solve with parallel programming techniques.

__Keywords:__

Finite difference methods, simplified phase-field models, Parabolic system,
explicit Euler scheme, Crank-Nicolson-ADI method, Error estimates, parallel
implementation

Full Paper, pp. 61-69

Classification of the Students' Scores based on some Artificial Neural Networks

by Hu Hongping, Bai Yanping

Abstract: In this paper, the
data of students’ scores are analyzed by using the nonlinear BP neural network
algorithm with a hidden layer, the probabilistic neural network algorithm, the
perceptron algorithm and self-organizing compete neural network algorithm. We
take 3000 students’ scores on only course to be analyzed and classified. Among
these scores, 121 students’ scores are trained and 2879 students’ scores are
tested by the probabilistic neural network algorithm, the nonlinear BP neural
network algorithm and the perceptron neural network algorithm. By comparing
these three kinds of neural network algorithms, we can get the following
results: the train errors of these three neural network algorithms are all zero,
but the test errors of these three neural network algorithms are different.and
the test error of the probabilistic neural network algorithm is less than those
of the nonlinear BP neural network algorithm and the perceptron algorithm; the
train time of the BP neural network algorithm is longer than those of the
probabilistic neural network algorithm and the perceptron algorithm;the test
time of the probabilistic neural network algorithm is longer that those of the
nonlinear BP neural network algorithm and the perceptron algorithm. The correct
rate of the probabilistic neural network algorithm heads to 99.06% when
net.spread. The correct rate of the BP neural network algorithm changes from
98.51% to 99.06%. But the correct rate of the perceptron neural network
algorithm is too low and changes from 20% to 30%. Therefore by considering the
correct rate and the whole time of classification, we obtain that the
probabilistic neural network algorithm is more suitable for solving the
classification of the students’ scores on only one course. And we take 1680
students' scores on five course to be analyzed and classified. Among these
scored, 179 students' scores are trained and 1501 students’ scores are tested by
the nonlinear BP neural network algorithm with the momentum factor, the
nonlinear BP neural network algorithm with the gradient descent method, the
probabilistic neural network algorithm and the self-organizing complete network
algorithm. By comparing these kinds of neural network algorithms, we can get the
following results: the train errors of the probabilistic neural network
algorithm are all zero,those of the BP neural network algorithm with the
momentum factor are all less than 0.0089, those of the BP neural network
algorithm with the gradient descent method are all less than 0.0536, and those
of the self-organizing compete neural network algorithm are all less than 0.4
and are all more than 0.2436; the test errors of the probabilistic neural
network algorithm all equal to 0.0799, but those of the BP neural network
algorithm with the momentum factor are all less than 0.0738, those of the BP
neural network algorithm with the gradient descent method are all less than
0.1332, and those of the self-organizing compete neural network algorithm are
all less than 0.3888 and are all more than 0.1871; the train times of the the
probabilistic neural network algorithm are all less than 0.0469,those of the BP
neural network algorithm with the momentum factor are all less than 33.0156 and
are all more than 29.6875, those of the BP neural network algorithm with the
gradient descent method are almost 24.3594 and are mostly less than 7.1875, and
those of the self-organizing compete neural network algorithm are all less than
332.9219 and are all more than 310.0156; the test times of the probabilistic
neural network algorithm are the least and are all less than 0.1719 and more
than 1406, but those of the other neural network algorithms are all less than
0.0938; the train correct rates of the probabilistic neural network algorithm
are all 100% when net.spread , those of the BP neural network algorithm with the
momentum factor are all less than 99.44% and are all more than 97.77%, those of
the BP neural network algorithm with the gradient descent method are all less
than 93.30% and are all more than 86.59%, and the those of the self-organizing
compete neural network algorithm are all less than 40%;the test correct rates of
the probabilistic neural network algorithm are all 80.01%, those of the BP
neural network algorithm with the momentum factor are all less than 87.67% and
are all more than 81.55%, those of the BP neural network algorithm with the
gradient descent method are all less than 82.41% and are all more than 66.69%,
and those of the self-organizing compete neural network algorithm are all less
than 53.23%.Therefore by considering the correct rates and the whole times of
classification, we obtain that the probabilistic neural network algorithm and
the BP neural network algorithm are more suitable for solving the classification
of the students’ scores on five courses.

__Keywords:__ The Students’ Scores, BP Neural Network, Probabilistic Neural
Network, Perceptron Neural network, Self-organizing Compete Neural Network,
Train error, Test error, Train time, Test time,Train Correct Rate, Test Correct
Rate

A

Full Paper, pp. 70-78