Mathematical, Computational, Physical, Electrical and Computer Engineering

Commenced in January 1999 | Frequency: Monthly | Edition: International | Paper Count: 11 |

11

10002966

Soliton Interaction in Multi-Core Optical Fiber: Application to WDM System

The analytical bright two soliton solution of the 3-
coupled nonlinear Schrödinger equations with variable coefficients in
birefringent optical fiber is obtained by Darboux transformation
method. To the design of ultra-speed optical devices, Soliton
interaction and control in birefringence fiber is investigated. Lax pair
is constructed for N coupled NLS system through AKNS method.
Using two-soliton solution, we demonstrate different interaction
behaviors of solitons in birefringent fiber depending on the choice of
control parameters. Our results shows that interactions of optical
solitons have some specific applications such as construction of logic
gates, optical computing, soliton switching, and soliton amplification
in wavelength division multiplexing (WDM) system.

10

10002994

Generic Model for Timetabling Problems by Integer Linear Programming Approach

The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It is widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming models to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describes about creating a general model which solves different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.

9

10003018

A Survey on Quasi-Likelihood Estimation Approaches for Longitudinal Set-ups

The Com-Poisson (CMP) model is one of the most popular discrete generalized linear models (GLMS) that handles both equi-, over- and under-dispersed data. In longitudinal context, an integer-valued autoregressive (INAR(1)) process that incorporates covariate specification has been developed to model longitudinal CMP counts. However, the joint likelihood CMP function is difficult to specify and thus restricts the likelihood-based estimating methodology. The joint generalized quasi-likelihood approach (GQL-I) was instead considered but is rather computationally intensive and may not even estimate the regression effects due to a complex and frequently ill-conditioned covariance structure. This paper proposes a new GQL approach for estimating the regression parameters (GQL-III) that is based on a single score vector representation. The performance of GQL-III is compared with GQL-I and separate marginal GQLs (GQL-II) through some simulation experiments and is proved to yield equally efficient estimates as GQL-I and is far more computationally stable.

8

10003035

Cooling-Rate Induced Fiber Birefringence Variation in Regenerated High Birefringent Fiber

In this paper, we have reported birefringence
manipulation in regenerated high birefringent fiber Bragg grating
(RPMG) by using CO2 laser annealing method. The results indicate
that the birefringence of RPMG remains unchanged after CO2 laser
annealing followed by slow cooling process, but reduced after fast
cooling process (~5.6×10-5). After a series of annealing procedures
with different cooling rates, the obtained results show that slower the
cooling rate, higher the birefringence of RPMG. The volume, thermal
expansion coefficient (TEC) and glass transition temperature (Tg)
change of stress applying part in RPMG during cooling process are
responsible for the birefringence change. Therefore, these findings
are important to the RPMG sensor in high and dynamic temperature
environment. The measuring accuracy, range and sensitivity of
RPMG sensor is greatly affected by its birefringence value. This
work also opens up a new application of CO2 laser for fiber annealing
and birefringence modification.

7

10003165

Approximating Maximum Speed on Road from Curvature Information of Bezier Curve

Bezier curves have useful properties for path
generation problem, for instance, it can generate the reference
trajectory for vehicles to satisfy the path constraints. Both algorithms
join cubic Bezier curve segment smoothly to generate the path. Some
of the useful properties of Bezier are curvature. In mathematics,
curvature is the amount by which a geometric object deviates from
being flat, or straight in the case of a line. Another extrinsic example
of curvature is a circle, where the curvature is equal to the reciprocal
of its radius at any point on the circle. The smaller the radius, the
higher the curvature thus the vehicle needs to bend sharply. In this
study, we use Bezier curve to fit highway-like curve. We use
different approach to find the best approximation for the curve so that
it will resembles highway-like curve. We compute curvature value by
analytical differentiation of the Bezier Curve. We will then compute
the maximum speed for driving using the curvature information
obtained. Our research works on some assumptions; first, the Bezier
curve estimates the real shape of the curve which can be verified
visually. Even though, fitting process of Bezier curve does not
interpolate exactly on the curve of interest, we believe that the
estimation of speed are acceptable. We verified our result with the
manual calculation of the curvature from the map.

6

10003206

Propagation of Cos-Gaussian Beam in Photorefractive Crystal

A physical model for guiding the wave in
photorefractive media is studied. Propagation of cos-Gaussian beam
as the special cases of sinusoidal-Gaussian beams in photorefractive
crystal is simulated numerically by the Crank-Nicolson method in
one dimension. Results show that the beam profile deforms as the
energy transfers from the center to the tails under propagation. This
simulation approach is of significant interest for application in optical
telecommunication. The results are presented graphically and
discussed.

5

10003220

An Approximation Method for Exact Boundary Controllability of Euler-Bernoulli System

The aim of this work is to study the numerical
implementation of the Hilbert Uniqueness Method for the exact
boundary controllability of Euler-Bernoulli beam equation. This study
may be difficult. This will depend on the problem under consideration
(geometry, control and dimension) and the numerical method used.
Knowledge of the asymptotic behaviour of the control governing the
system at time T may be useful for its calculation. This idea will
be developed in this study. We have characterized as a first step, the
solution by a minimization principle and proposed secondly a method
for its resolution to approximate the control steering the considered
system to rest at time T.

4

10003235

An Estimation of Variance Components in Linear Mixed Model

In this paper, a linear mixed model which has two
random effects is broken up into two models. This thesis gets
the parameter estimation of the original model and an estimation’s
statistical qualities based on these two models. Then many important
properties are given by comparing this estimation with other general
estimations. At the same time, this paper proves the analysis of
variance estimate (ANOVAE) about σ2 of the original model is equal
to the least-squares estimation (LSE) about σ2 of these two models.
Finally, it also proves that this estimation is better than ANOVAE
under Stein function and special condition in some degree.

3

10003327

Application of Adaptive Genetic Algorithm in Function Optimization

The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

2

10003419

Membership Surface and Arithmetic Operations of Imprecise Matrix

In this paper, a method has been developed to
construct the membership surfaces of row and column vectors and
arithmetic operations of imprecise matrix. A matrix with imprecise
elements would be called an imprecise matrix. The membership
surface of imprecise vector has been already shown based on
Randomness-Impreciseness Consistency Principle. The Randomness-
Impreciseness Consistency Principle leads to defining a normal law
of impreciseness using two different laws of randomness. In this
paper, the author has shown row and column membership surfaces
and arithmetic operations of imprecise matrix and demonstrated with
the help of numerical example.

1

10004912

Selection of Designs in Ordinal Regression Models under Linear Predictor Misspecification

The purpose of this article is to find a method
of comparing designs for ordinal regression models using
quantile dispersion graphs in the presence of linear predictor
misspecification. The true relationship between response variable
and the corresponding control variables are usually unknown.
Experimenter assumes certain form of the linear predictor of the
ordinal regression models. The assumed form of the linear predictor
may not be correct always. Thus, the maximum likelihood estimates
(MLE) of the unknown parameters of the model may be biased due to
misspecification of the linear predictor. In this article, the uncertainty
in the linear predictor is represented by an unknown function. An
algorithm is provided to estimate the unknown function at the
design points where observations are available. The unknown function
is estimated at all points in the design region using multivariate
parametric kriging. The comparison of the designs are based on
a scalar valued function of the mean squared error of prediction
(MSEP) matrix, which incorporates both variance and bias of the
prediction caused by the misspecification in the linear predictor. The
designs are compared using quantile dispersion graphs approach.
The graphs also visually depict the robustness of the designs on the
changes in the parameter values. Numerical examples are presented
to illustrate the proposed methodology.