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Issue 1, Volume 9,
January 2010
Title of the Paper: Comparison of Spline Approximation with the Modified Likelihoods in the Presence of Nuisance
Parameter
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Authors: Ahmet Sezer
Abstract: The likelihood functions from independent studies can be easily
combined, and the combined likelihood function serves as a meaningful
indication of the support the observed data give to the various parameter
values. This fact has led many scientists to suggest using the likelihood
function as a summary of post-data uncertainty concerning the parameter.
Indeed, likelihood functions have several desired properties . They are
objective, in that they depend only on the agreed-upon model and the data.
They are also flexible, allowing us to combine information about competing
models across studies. However, a serious difficulty arises because likelihood
functions may not be expressible in a compact, easily-understood mathematical
form suitable for communication or publication. For example, likelihood
functions in mixture models may only be computable for individual values of
the parameters and otherwise cannot be given in ”closed form”. To overcome
this difficulty, we propose to approximate loglikelihood functions by using
piecewise polynomials governed by a minimal number of parameters
Keywords: Likelihood,
Approximation
Title of the Paper: An Application of
Fuzzy Time Series to Improve ISE Forecasting
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Authors: Memmedaga
Memmedli, Ozer Ozdemir
Abstract: The problem of fuzzy time series forecasting plays an important role
in many scientific areas such as statistics and neural networks. While
forecasting fuzzy time series, most of forecasting applications use the same
length of intervals. The determination of length of intervals is significant
and critical in fuzzy time series forecasting. The usage of convenient
performance measure may also have an important affect for forecasting studies.
MSE (Mean squared error) as a performance measure is widely used in many
studies. The aim of this paper is to improve fuzzy time series forecasting by
using different length of intervals with neural networks according to various
performance measures. For this reason, we take ISE (Istanbul stock exchange)
national-100 index as a large data set for forecasting. We use various
performance measures such as MSE, RMSE (Root mean squared error), MAE (Mean
absolute error) and MAPE (Mean absolute percentage error) to compare
forecasting performances with different length of intervals. The empirical
results show that the most convenient length of intervals can be chosen as 300
by comparing overall performance of MSE, RMSE, MAE and MAPE by using neural
networks.
Keywords: Forecasting,
Fuzzy time series, Neural networks, ISE national-100 index, Performance
measures, Length of intervals
Title of the Paper: The Computation of Abelian Subalgebras in Low-Dimensional Solvable Lie Algebras
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Authors: Manuel
Ceballos, Juan Nunez, Angel F. Tenorio
Abstract: The main goal of this paper is to compute the maximal abelian
dimension of each solvable nondecomposable Lie algebra of dimension less than
7. To do it, we apply an algorithmic method which goes ruling out non-valid
maximal abelian dimensions until obtaining its exact value. Based on
Mubarakzyanov and Turkowsky’s classical classifications of solvable Lie
algebras (see [13] and [19]) and the classification of 6-dimensional nilpotent
Lie algebras by Goze and Khakimdjanov [7], we have explicitly computed the
maximal abelian dimension for the algebras given in those classifications.
Keywords: Solvable Lie
algebra, maximal abelian dimension
Title of the Paper: A Note on
Skew-Normal Distribution Approximation to the Negative Binomal Distribution
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Authors: Jyh-Jiuan Lin,
Ching-Hui Chang, Rosemary Jou
Abstract: This article revisits the problem of approximating the negative
binomial distribution. Its goal is to show that the skew-normal distribution,
another alternative methodology, provides a much better approximation to
negative binomial probabilities than the usual normal approximation.
Keywords: Central Limit
Theorem, cumulative distribution function (cdf), skew-normal distribution,
skew parameter
Title of the Paper: Partial State-Owned
Bank Interest Margin, Default Risk, and Structural Breaks: A Model of
Financial Engineering
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Authors: Jyh-Horng Lin,
Ching-Hui Chang, Rosemary Jou
Abstract: Recent reports demonstrate that the grip of nationalism is tightest
in banking (Economist, 2009a), and in France and Britain, politicians powering
taxpayers’ money into ailing banks are demanding that the cash be lent at home
(Economist, 2009b). This paper proposes a call option model for bank interest
margin and default risk valuation based on an event-dependent, structural
break framework under the return of banking nationalization. The primary
feature is the existence of the discontinuity and fat tails of asset returns
and risks caused by structural changes. We show that an increase in the
structural breaks in mean return discontinuity and volatility fluctuation
caused by the increasing degree of the bank’s partial nationalization
increases the bank’s interest margin and default risk. We conclude that
nationalization may be a high return-volatility structure break.
Keywords: Partial
Nationalization, Structural Change, Retail Banking, Interest Margin
Title of the Paper: Descriptor
Techniques for Modeling of Swirling Fluid Structures and Stability Analysis
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Authors: Diana Alina
Bistrian, Florica Ioana Dragomirescu, George Savii
Abstract: In this paper we develop descriptor techniques for modeling swirling
hydrodynamic structures. Using the descriptor notation we obtain the
generalized eigenvalue formulation for differential-algebraic equations
describing the spatial stability of the fluid flow. We describe the general
framework for spatial stability investigation of vortex structures in both
viscous and inviscid cases. The dispersion relation is analytically
investigated and the polynomial eigenvalue problem describing the viscous
spatial stability is reduced to a generalized eigenvalue problem in operator
formulation using the companion vector technique. A different approach is
assessed for spatial inviscid study when the stability model is obtained by
means of a class of shifted orthogonal basis and a spectral differentiation
matrix is derived to approximate the discrete spatial derivatives. Both
schemes applied to a swirling fluid profile provide good results.
Keywords: Hydrodynamic
stability, Swirling flow, Descriptor operators, Spectral collocation
Title of the Paper: Uniqueness of
Positive Solutions for Degenerate Logistic Neumann Problems in a Half Space
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Authors: Wei Dong,
Tieguo Ji
Issue 2, Volume 9,
February 2010
Title of the Paper: Quintic B-Spline
Curve Generation using Given Points and Gradients and Modification based on
Specified Radius of Curvature
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Authors: Tetsuzo
Kuragano
Abstract: A method to generate a quintic B-spline curve which passes through
the given points is described. In this case, there are four more unknown
control point positions than there are equations. To overcome this problem
three methods are described. First, solve the underdetermined system as it
stands. Secondly, decrease the number of unknown control point positions in an
underdetermined system in order to convert it to a determined system. Third, a
method to increase the number of equations is employed to change an
underdetermined system to a determined system. In addition to this, another
method to generate a quintic B-spline curve using given points with gradients
in sequence is described. In this case, a linear system will be either
overdetermined, determined or underdetermined. This depends on the number of
given points with gradients in sequence. Additionally, a method to modify a
quintic B-spline curve is described. The objective is to change an
aesthetically unpleasing curve to an aesthetically pleasing curve. Algebraic
functions are used to determine an aesthetically pleasing radius of curvature
distribution. This is accomplished by minimizing the difference between the
quintic B-spline curves radius of curvature and the specified radius of
curvature using the least-squares method. Examples of curve generation are
given.
Keywords: B-spline curve
generation, curvature vector, given points, given points with gradients,
underdetermined system, overdetermined system, curve shape modification
Title of the Paper: Image Hiding Based
on Circular Moire Fringes
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Authors: Minvydas
Ragulskis, Algiment Aleksa, Jurate Ragulskiene
Abstract: Circular time-averaging moire technique is exploited to hide an
image in a background moire grating. The secret image can be visualized when
the encoded image is oscillated around a pre-defined axial point. It is a new
visual decoding scheme when the secret image is embedded into a circular moire
grating and can be interpreted by a naked eye. The encoded secret image is not
shared into components; this is a one image method. Computational examples are
used to demonstrate the functionality of the method. The property of the human
visual system to average fast dynamical processes being not able to follow
rapid oscillatory motions is exploited to decode the secret image.
Keywords: Visual
Cryptography, Moire fringes, Bessel Functions
Title of the Paper: Use of Vodcasting in
Higher Education to Improve Student Learning
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Authors: Javier Bilbao,
Eugenio Bravo, Olatz Garcia, Concepcion Varela, Purificacion Gonzalez, Izaskun
Baro, Miguel Rodriguez
Abstract: In several countries the curricula for the different degrees of the
universities is changing to adapt it to the Anglo-Saxon model of four years.
In this context, several degrees must reduce the hours for classroom and this
affects in a higher way to some subjects. Some of them can see reduced their
teaching hours even to the half. So, it is necessary to adopt some measures in
order to maintain the level of the degree (it would be very difficult to
increase this level in such situation of reducing a lot of teaching hours) and
to take advantage of the change and adapt the subjects to the new century and
technologies. One of these measures that we can take is to use the Information
and Communication Technologies (ICT) out of the classroom. In this way, we are
developing a vodcast. The information in electronic form (as well as the
access to this information) has very specific characteristics and the aim of
all of us who make use of this information is getting the most out. Simply to
prepare a text and place in cyberspace is wasting much of the potential we
have at our disposal. To insert static images helps to improve the
information. Accompanying text with audio enriches considerably the text. And
to produce a combined video image and sound is the most comprehensive offering
that can be done to anyone seeking information. Vodcasting can be a powerful
tool to use in some subjects. The generalization of this idea is not probed.
But we are developing our vodcast for subjects of Mathematics of the first
year of Engineering degrees and it seems that the tool is very well accepted
by students.
Keywords: Vodcasting,
higher education, video podcast, vodcast, learning, educational innovation,
information in electronic form, knowledge
Title of the Paper: Comparison of the
Results of Factorial Experiments, Fractional Factorial Experiments, Regression
Trees and MARS for Fuel Consumption Data
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Authors: Betul Kan,
Berna Yazici
Abstract: In this study effects that are significant on the fuel consumption
of F-4 aircrafts are analyzed by using different statistical methods and the
results of those different methods are compared. The response variable of
every possible combination of factors and interactions are analyzed to provide
information about main effect(s) and interaction effect(s). MARS is applied in
order to find the relationship and a tree model in order to summarize the
relationship of main effects and the interactions on a plot. Also a 25
factorial experiment with 4 replications is performed to determine the
significant main effects and interactions. The analysis is repeated for
one-half fractional factorial experiment. A comparison of performance of the
methods is made in order to investigate their applicability.
Keywords: Regression
trees, MARS, factorial experiments, fractional factorial experiments, basis
function, GCV (Generalized Cross Validation), recursive partitioning, AID
(Automatic Interaction Detection)
Title of the Paper: Stochastic Optimal
Control for Small Noise Intensities: The Discrete-Time Case
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Authors: Hugo
Cruz-Suarez, Rocio Ilhuicatzi-Roldan
Abstract: This paper deals with Markov Decision Processes (MDPs) on Borel
spaces with an infinite horizon and a discounted total cost. It will be
considered a stochastic optimal control problem which arises by perturbing the
transition law of a deterministic control problem, through an additive random
noise term with coefficient epsilon. In the paper, we will analyze the
behavior of the optimal solution (optimal value function and optimal policy)
of the stochastic system, when the coefficient epsilon goes to zero.
Specifically, conditions given in the paper guarantee the uniform on compact
sets convergence of both the optimal value function and the optimal policy of
the stochastic system to the optimal value function and the optimal policy of
the deterministic one, when epsilon goes to zero, respectively. Finally, two
examples which illustrate the developed theory are presented.
Keywords: Stochastic
Optimization, Markov Decision Process, Dynamic Programming, Total Discounted
Cost, Deterministic Approximation, Inventory/Production System
Title of the Paper: Optimization of
Stepped Shells
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Authors: J. Lellep, E.
Puman, L. Roots, E. Tungel
Abstract: Problems of analysis and optimization of axisymmetric shells of
piece wise constant thickness are studied. The cases of quasistatic and
dynamic loading are considered separately whereas the shells may be
manufactured from both, elastic and inelastic materials. Minimum weight
designs of inelastic shells of piece wise constant thickness are established
under the condition that the limit load is fixed. Also the designs of maximum
load carrying capacity are determined for given weight (material volume) of
the shell. Necessary optimality conditions are derived with the aid of
variational methods of the theory of optimal control. Particular cases of
maximization of the load carrying capacity of spherical caps and conical
shells are studied in a greater detail in the cases of von Mises and Hill’s
materials.
Keywords: Optimization,
optimal control, inelastic material, crack, conical shell, spherical shell,
cylindrical shell
Title of the Paper: Generalized
Concentration/Inequality Indices of Economic Systems Evolving in Time
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Authors: Guglielmo
D'Amico, Giuseppe Di Biase
Abstract: In this paper time evolving indices are defined and studied through
the introduction of a population structure chancing during the time. These
indices are useful to describe the concentration (or inequality) of the wealth
in a stochastic model of the wealth evolution. Here some static indices
usually used in literature are generalized. In particular the paper shows how
it is possible to generalize the Herfindahl-Hirschman and Gini indices and the
Theil’s entropy. These indices become stochastic processes of which the
moments and the asymptotic behavior is provided. A computation of such indices
and their asymptotic behavior in different economical scenarios concludes the
paper.
Keywords: Population
dynamic, Herfindahl-Hirschman index, Gini index, Theil’s entropy, Rewards
Issue 3, Volume 9,
March 2010
Title of the Paper: When are the Value
Iteration Maximizers Close to an Optimal Stationary Policy of a Discounted
Markov Decision Process? Closing the Gap between the Borel Space Theory and
Actual Computations
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Authors: Raul Montes-De-Oca,
Enrique Lemus-Rodriguez
Abstract: Markov Decision Processes [MDPs] have been repeteadly used in
Economy and Engineering but apparently are still far from achieving its full
potential due to the computational difficulties inherent to the subject due to
the usual impossibility of finding explicit optimal solutions. Value iteration
is an elegant, theoretical method of approximating an optimal solution,
frequently mentioned in Economy when MDPs are used. To extend its use and
benefits, improved understanding of its convergence is needed still even if it
would appear not to be the case. For instance, the corresponding convergence
properties of the policies is still not well understood. In this paper we
further analyze this issue: using Value Iteration, if a stationary policy fN
is obtained in th N-th iteration, such that the optimal discounted rewards of
f and fN are close, we would like to know whether are the corresponding
actions f (x) and fN(x) necessarily close for each state x? To our knowledge
this question is still largely open. In this paper it is studied when it is
possible to stop the value iteration algorithm so that the corresponding
maximizer stationary policy fN approximates an optimal policy both in the
total discounted reward and in the action space (uniformly over the state
space). In this article the action space is assumed to be a compact set and
the reward function bounded. An ergodicity condition on the transition
probability law and a structural condition on the reward function are needed.
Under these conditions, an upper bound on the number of steps needed in the
value iteration algorithm, such that its corresponding maximizer is a uniform
approximation of the optimal policy, is obtained.
Keywords: Markov decision
process, compact action space, bounded reward, expected total discounted
reward, approximation of optimal policies by means of value iteration policies
Title of the Paper: Numerical Solutions
for a Class of Nonlinear Systems and Application to Stochastic Resonance
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Authors: Romeo Negrea,
Andrei Eckstein, Florin Alexa
Abstract: We study a nonlinear system under regime switching and subject to an
environmental noise. The stochastic differential equations with Markovian
switching (SDEwMSs), one of the important classes of hybrid systems, have been
used to model many physical systems that are subject to frequent unpredictable
structural changes. The research in this area has been both theoretical and
applied. Most of SDEwMSs do not have explicit solutions so it is important to
have numerical solutions. It is surprising that there are not any numerical
methods established for SDEwMSs yet, although the numerical methods for
stochastic differential equations (SDEs) have been well studied. We will
considered some more general conditions for the coefficient functions and
prove a result on the existence using the Schauder’s fixed point theorem
extended some similarly results on linear systems. The most important results
in this paper is to develop a numerical scheme for SDEwMSs and estimate the
error between the numerical and exact solutions. Also, we study the
application of these system to control the electronic circuits using the
benefit of stochastic resonance
Keywords: Stochastic
differential equation with Markovian switching, pathwise uniqueness, fixed
point technique, numerical solution, Euler-Maruyama method, stopping times,
stochastic resonance
Title of the Paper: Traveling Wave
Solutions for the Fifth-Order Sawada-Kotera Equation and the General Gardner
Equation by (G'/G)-Expansion Method
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Authors: Qinghua Feng,
Bin Zheng
Abstract: In this paper, a generalized (G'/G)-expansion method is used to seek
more general exact solutions of the fifth-order Sawada-Kotera equation and the
general Gardner equation. As a result, the traveling wave solutions with three
arbitrary functions are obtained including hyperbolic function solutions,
trigonometric function solutions and rational solutions. The method appears to
be easier and faster by means of some mathematical software.
Keywords: (G'/G)-expansion
method, Traveling wave solutions, fifth-order Sawada-Kotera equation, general
Gardner equation, exact solution, evolution equation, nonlinear equation
Title of the Paper: Traveling Wave
Solution for the BBM Equation with any Order by (G'/G)-Expansion Method
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Authors: Qinghua Feng,
Bin Zheng
Abstract: In this paper, we will try to construct the travelling wave
solutions of the BBM equation with any order by using a generalized
(G'/G)-expansion method. The BBM equation is reduced to a nonlinear ordinary
differential equations (ODE) by using a simple transformation. As a result,
the traveling wave solutions of the BBM equation are expressed in three forms:
hyperbolic function solutions, trigonometric function solutions and rational
solutions.
Keywords: (G'/G)-expansion
method, Traveling wave solutions, BBM equation, exact solution, evolution
equation, nonlinear equation
Title of the Paper: Traveling Wave
Solutions for the Variant Boussinseq Equation and the (2+1)-Dimensional
Nizhnik-Novikov-Veselov (NNV) System By (G'/G)-Expansion Method
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Authors: Qinghua Feng,
Bin Zheng
Abstract: In this paper, using the generalized (G'/G)-expansion method, new
explicit travelling wave solutions for the variant Boussinseq equation and the
(2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) system are obtained with the
aid of Mathematica.
Keywords: (G'/G)-expansion
method, Traveling wave solutions, (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV)
system, variant Boussinseq equation, exact solution, evolution equation,
nonlinear equation
Title of the Paper: Traveling Wave
Solutions for the Fifth-Order Kdv Equation and the BBM Equation by
(G'/G)-Expansion Method
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Authors: Qinghua Feng,
Bin Zheng
Abstract: In this paper, we demonstrate the effectiveness of the
(G'/G)-expansion method by seeking more exact solutions of the fifth-order Kdv
equation and the BBM equation. By the method, the two nonlinear evolution
equations are separately reduced to non-linear ordinary differential equations
(ODE) by using a simple transformation. As a result, the traveling wave
solutions are obtained in three arbitrary functions including hyperbolic
function solutions, trigonometric function solutions and rational solutions.
When the parameters are taken as special values, we also obtain the soliton
solutions of the fifth-order Kdv equation. The method appears to be easier and
faster by means of a symbolic computation system.
Keywords: (G'/G)-expansion
method, Traveling wave solutions, BBM equation, fifth-order Kdv equation,
exact solution, evolution equation, nonlinear equation
Title of the Paper: Iterative Strategies
for Obstacle Avoidance of a Redundant Manipulator
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Authors: Cornel Secara,
Luigi Vladareanu
Abstract: This paper presents four different iterative strategies for obstacle
avoidance of a redundant manipulator. The end-effector task consists in
generating the references along the contour of a curve. The proposed
strategies are iterative in the sense that the joint configuration computed in
the previous step represents the current point around which the methods
provide the next joint configuration corresponding to the imposed end-effector
posture. The objective of the strategies is to simultaneously minimize the
endeffector location error and the manipulator total joint displacement while
the collision with the obstacle is avoided. The strategies are implemented
using the Matlab software and the comparative simulation results are obtained
for a planar redundant manipulator with four degrees of freedom and with its
end-effector following the contour of a circle, whose surface is considered to
be restrictive for all elements of the manipulator.
Keywords: Redundancy
resolution, iterative strategy, obstacle avoidance, multiple criteria
Issue 4, Volume 9,
April 2010
Title of the Paper: Producer's
Replenishment Policy for an EPQ Model with Rework and Machine Failure Taking
Place in Backorder Reloading Time
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Authors: Kuang-Ku Chen,
Yuan-Shyi Peter Chiu, Chia-Kuan Ting
Abstract: This paper studies the optimal producer?s replenishment policy for
an economic production quantity (EPQ) model with rework and breakdown taking
place in backorder replenishing time. A recent published article has studied
the lot-sizing problem on an imperfect quality EPQ model. However, another
reliability factor - random machine breakdown is inevitable in most real-life
production systems. To deal with stochastic machine failures, production
planners must practically calculate the mean time between failures (MTBF) and
establish the robust plan accordingly, in terms of the optimal production run
time that minimizes total production-inventory costs for such an unreliable
system. This study extends Chiu’s work and assumes that a machine failure
takes place in the backorder replenishing stage. Mathematical modeling and
cost analysis are employed. The renewal reward theorem is used to cope with
variable cycle length. Convexity of the long-run average cost function is
proved and an optimal manufacturing lot-size that minimizes the expected
overall costs for such an imperfect system is derived. Numerical example is
provided to demonstrate its practical usages.
Keywords: Optimization,
Lot size, Breakdown, Backorder, Production run time, Rework, Inventory
Title of the Paper: Applying the New
Primer on Prime Numbers
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Authors: Ernest G. Hibbs
Abstract: We have a new model for understanding the behavior of prime numbers
that considers the increments as sums of second derivatives. We use the
perfectly alternating double-threaded helix prime number growth structure that
dominated the first 500 prime numbers after a modulo 6 operation. The
multiples of 6 influence the two threads in a 3-D manner. Electromagnetic
reversal patterns between the threads and the thread bonds indicate a
coordinated 3-D multi-physics growth rate of the prime numbers. The harmonic
patterns of a newly mapped 10-step model are also introduced. This new concept
is presented as a framework to help apply approaches to understanding and
solving our hardest multi-physics and Millennium problems. The last sections
of this paper suggest how to apply, adapt, or correlate this framework to with
WSEAS research. An exciting electromagnetic multidirectional vector model is
the result of applying this framework by forcing a 90-degree molecular bond
concept.
Keywords: Prime Numbers,
Double Helix, Riemann Hypothesis, Second Derivative, Millennium Problems
Title of the Paper: On the
Eigenstructures of Functional K-Potent Matrices and their Integral Forms
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Authors: Yan Wu, Daniel
F. Linder
Abstract: In this paper, a functional k-potent matrix satisfies the equation,
where k and r are positive integers, and are real numbers. This class of
matrices includes idempotent, Nilpotent, and involutary matrices, and more. It
turns out that the matrices in this group are best distinguished by their
associated eigen-structures. The spectral properties of the matrices are
exploited to construct integral k-potent matrices, which have special roles in
digital image encryption.
Keywords: Nilpotent,
Idempotent, Involutary, Unipotent, Skewed k-potent Matrix, Diagonalizability,
Image Encryption
Title of the Paper: Exact Solutions
through Symmetry Reductions for a New Integrable Equation
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Authors: Maria Luz
Gandarias, Maria Santos Bruzon
Abstract: In this work we study a new completely integrable equation from the
point of view of the theory of symmetry reductions in partial differential
equations. This equation has been proposed by Qiao and Liu in [24] and it
possesses peak solitons. We obtain the classical symmetries and the classical
symmetries of the associated potential system admitted, then, we use the
transformations groups to reduce the equations to ordinary differential
equations. Physical interpretation of these reductions and some exact
solutions are also provided. Among them we obtain a travelling wave with
decaying velocity and an smooth soliton solution.
Keywords: Symmetries,
partial differential equation, exact solutions
Title of the Paper: Major Issues in
Designing an Undergraduate Program in Nanotechnology: The Mexican Case
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Authors: Armando
Barranon, Antonio Juanico
Abstract: Major Issues for developing an Undergraduate Program in
Nanotechnology are hereby described. Nanotechnology Courses are designed so
that students may apply the Nanosciences, Biotechnology and Information
Sciences convergence model to develop new materials and applications
Nanotechnology. Infrastructure and Human Resources turn out to be crucial for
establishing a successful Nanotechnology Undergraduate Program. Several
Mexican National Nanotechnology Labs will be cooperating for student
internships and students may continue doing postgraduate studies at those
centers of research. Societal and Environmental impacts of Nanotechnology are
also addressed in the Undergraduate Program in Nanotechnology proposed in this
article. Women participation is expected, considering recent statistics of
women participation in undergraduate engineering programs related to
Nanotechnology. Mexican government has been funding to the federal and state
level the university where this program will be launched, as part of a
national effort to provide universities all along the Mexican territory.
Keywords: Undergraduate
Program in Nanotechnology, PROMEP scholarships, PRONABES scholarships, NBI
model, Nanotechnology faculty, Mexico
Title of the Paper: Classical Potential
Symmetries of the K(m, n) Equation with Generalized Evolution Term
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Authors: Maria S. Bruzon,
Maria L. Gandarias
Abstract: We consider a K(m, n) equation with generalized evolution term which
is of considerable interest in mathematical physics. We classify the nonlocal
symmetries, which are known as potential symmetries, for this equation. It
turns out that potential symmetries exist only if the parameters n, m and l
satisfy certain relationship.
Keywords: Potential
symmetries, Partial differential equation, Exact Solutions
Issue 5, Volume 9,
May 2010
Title of the Paper:
The Numerical Solution of Obstacle Problem by
Self Adaptive Finite Element Method
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Authors: Lian Xue,
Minghui Wu
Abstract: In this paper, the bisection of the local mesh refinement in self
adaptive finite element is applied to the obstacle problem of elliptic
variational inequalities .We try to find the approximated region of the
contact in the obstacle problem efficiently .Numerical examples are given for
the obstacle problem.
Keywords: Obstacle
problem, variational inequalities, self adaptive finite element, bisection,
triangulation refinement
Title of the Paper:
Multidimensional Unreplicated Linear
Functional Relationship Model with Single Slope and Its Coefficient of
Determination
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Authors: Chang Yun Fah,
Omar Mohd Rijal, Syed Abdul Rahman Abu Bakar
Abstract: Multidimensional unreplicated linear functional relationship model
(MULFR) with single slope is considered where p-dimensional measurement errors
are introduced. When the ratio of error variances is known, the parameters’
estimation can be considered as a generalization of the unreplicated linear
functional relationship model. However, investigation on unbiased property of
the estimators are not strict-forward. Taylor approximation is applied to show
the intercept and slope estimators are approximately unbiased. The consistency
property is discussed using Fisher Information Matrix. The coefficient of
determination for MULFR model and its properties are also studied. A
simulation study is carried out to evaluate the proposed estimators of the
intercept and slope, and the coefficient of determination. This coefficient of
determination provides a useful analysis tool for many image processing
applications. A numerical example for JPEG compressed image quality assessment
is explained.
Keywords: Coefficient of
determination; Image quality; JPEG compression; Measurement errors;
Unreplicated linear functional relationship
Title of the Paper:
Elastic-Plastic Analysis of a Thin Rotating
Disk of Exponentially Variable Thickness with Inclusion
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Authors: Sanjeev
Sharama, Manoj Sahni, Ravindra Kumar
Abstract: Transition theory has been used to derive the elastic-plastic and
transitional stresses. Results obtained have been discussed numerically and
depicted graphically. It has been observed that for disc with exponentially
varying thickness (k=2), high angular speed is required for initial yielding
at internal surface as compared to the flat disc and exponentially varying
thickness for k=4 onwards. Thus we can conclude that flat disc (C=0.75) is on
the safer side of the design as it requires high percentage increase in
angular speed to become fully plastic as compared to the flat disc with the
compressible factors (C=0,0.25,etc.).
Keywords: Elastic,
plastic, compressibility, transitional stresses, isotropic, rotating disk
Title of the Paper:
Running Damage Extraction Technique for
Identifying Fatigue Damaging Events
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Authors: Z. M. Nopiah,
M. N. Baharin, S. Abdullah, M. I. Khairir, A. Ariffin
Abstract: This paper presents the development of a new fatigue data editing
technique, called Running Damage Extraction (RDE), for summarising long
records of fatigue data. This technique is used to extract fatigue damaging
events in the record that cause the majority of fatigue damage, whilst
preserving the load cycle sequence. In this study, fatigue damaging events are
identified from the characteristic of abrupt changes that exist in the fatigue
data. Then, these events are combined to produce a mission signal which has
equivalent statistics and fatigue damage to the original signal. The objective
of this study is to observe the capability of RDE technique for summarising
long records of fatigue data. For the purpose of this study, a collection of
nonstationary data that exhibits random behavior was used. This random data
was measured in the unit of microstrain on the lower suspension arm of a car.
Experimentally, the data was collected for 60 seconds at a sampling rate of
500 Hz, which gave 30,000 discrete data points. Global signal statistical
value indicated that the data were non Gaussian distribution in nature. The
result of the study indicates that this technique is applicable in detecting
and extracts fatigue damaging events that exist in fatigue data.
Keywords: Abrupt changes,
fatigue data, global statistics, nonstationary data, RDE technique
Title of the Paper:
Time Complexity Estimation and Optimisation
of the Genetic Algorithm Clustering Method
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Authors: Z. M. Nopiah,
M. I. Khairir, S. Abdullah, M. N. Baharin, A. Arifin
Abstract: This paper presents the time complexity estimation and optimisation
of the genetic algorithm clustering method. The tested feature in the
clustering algorithm is the population limit function. For the purpose of the
study, segmental kurtosis analysis was done on several segmented fatigue time
series data, which are then represented in two-dimensional heteroscaled
datasets. These datasets are then clustered using the genetic algorithm
clustering method and the runtime of the algorithm is measured against the
number of iterations. Polynomial fitting is used on the runtime data to
determine the time complexity of the algorithm. Analysis is repeated with the
inclusion of the population limit in the clustering algorithm. The results of
the analysis will be used to determine the significance of including the
population limit function in the algorithm for optimal performance.
Keywords: Genetic
algorithms, fatigue damage, clustering, time complexity, big-O notation,
algorithm efficiency
Title of the Paper:
The Morlet Wavelet Analysis for Fatigue
Feature Clustering
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Authors: S. Abdullah, T.
E. Putra, M. Z. Nuawi, Z. M. Nopiah, A. Arifin, L. Abdullah
Abstract: This paper presents clustering of fatigue features resulted from the
segmentation of SAESUS time series data. The segmentation process was based on
the Morlet wavelet coefficient amplitude level which produced 49 segments that
each has overall fatigue damage. Observation of the fatigue damage and the
wavelet coefficients was made on each segment. At the end of the process, the
segments were clustered into three in order to identify any improvements in
the data scattering for fatigue data clustering prospects. This algorithm
produced a more reliable and suitable method of segment by segment analysis
for fatigue strain signal segmentation. According to the findings, the higher
Morlet wavelet coefficient presented damaging segment, otherwise, it was
non-damaging segment. This indicated that the relationship between the Morlet
wavelet coefficient and the fatigue damage was strong and parallel.
Keywords: Fatigue strain
signal, segmentation, fatigue damage, Morlet wavelet coefficient, clustering
Title of the Paper:
Towards a Mathematical Theory of Unconscious
Adaptation and Emotions
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Authors: Alin Gilbert
Sumedrea
Abstract: The psychological adaptability is realized through the conscious and
the unconscious mechanisms. Even though the functionality of the mechanisms
involved emphasizes different approaches, the main reason for these -
approaches - is the obtaining of the maximum adaptability which has to protect
the person at the conscious level. The invisible unconscious mechanisms have a
major role in the process of psychological adaptation. The unconscious
contribution does not eliminate completely the danger of psychological
collapse, and this accredits the idea of the existence of a psychological
guarantee only for proper inquirer stimuli. The incapacity of the
consciousness filters to mediate the transactions of unconscious offers
changes the adaptability process in an approach which is not entirely
controllable. The uncontrollable part validates the approach of the imposing
of own unconscious offers in the environment. The emotion analyzed at the
conscious level translates the uncertainty of the validation of the
transactions of unconscious offers with the environment as tensional state.
The mathematical approach of this paper describes the need for psychological
stimulation as a facet of adaptability and the emotional mechanisms as devices
of the preserving of tensional states.
Keywords: Coordinate
systems, Dynamics, Emotion, Group theory, Mechanism, Symmetry group,
Unconscious adaptability
Title of the Paper:
MHD Viscous Flow and Heat Transfer Induced by
a Permeable Shrinking Sheet with Prescribed Surface Heat Flux
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Authors: Fadzilah Md
Ali, Roslinda Nazar, Norihan Md Arifin
Abstract: The problem of magnetohydrodynamic (MHD) boundary layer flow and
heat transfer due to a permeable shrinking sheet with prescribed surface heat
flux is studied. The viscous fluid is electrically conducting in the presence
of a uniform applied magnetic field and the induced magnetic field is
neglected. The transformed nonlinear ordinary differential equations are
solved numerically via the implicit finite-difference scheme known as the
Keller-box method. Both two-dimensional and axisymmetric cases are considered.
The results for the skin friction coefficient and the wall temperature, as
well as the velocity and temperature profiles are presented and discussed for
various parameters. Dual solutions exist for certain range of the suction
parameter and Hartmann number. It is found that the boundary layer separation
is delayed with Hartmann number.
Keywords: Boundary layer,
Heat transfer, Magnetohydrodynamic, Shrinking sheet, Suction, Surface heat
flux
Title of the Paper:
Thermal and Solutal Marangoni Mixed
Convection Boundary Layer Flow
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Authors: Norihan Md.
Arifin, Fadzilah Md. Ali, Roslinda Nazar, Ioan Pop
Abstract: An analysis is performed for mixed convection thermal and solute
concentration Marangoni boundary layer that can be formed along the surface,
which separates two immiscible fluids in surface tension flows. Similarity
equations for the case in which an external pressure gradient is imposed are
derived. The dimensionless governing equations of the flow field are solved
numerically using the shooting method. The effect of flow parameters on the
velocity, temperature and concentration are computed and presented in tables
and figures.
Keywords: Marangoni flow,
Thermosolutal, Mixed convection, Boundary layer
Title of the Paper:
Modeling Put-Option Margin and Default Risk
when Labor has a Voice in Bank Governance Mechanism
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Authors: Chuen-Ping
Chang, Jyh-Jiuan Lin, Jeng-Yan Tsai
Abstract: Although considerable research effort has been put toward modeling
governance mechanisms for the purpose of valuing investment decisions written
on them, little attention has been paid to the effects of governance
mechanisms by labor voice on bank operations management. Like entrenched
operations management, entrenched labor cannot be gotten rid of easily. This
paper demonstrates how labor voice determines the optimal bank interest margin
and default risk decisions. Our model is based on a regime giving corporate
governance power to current labor and then labor’s objective is equivalent to
minimizing the equity value of the put option. We show that the governance
voice pushes bank interest margin determination toward shareholder value
maximization. However, an opportunity cost of bank governance from listening
labor voice is increasing the bank’s default risk in equity returns.
Keywords: Bank Interest
Margin, Default Risk, Labor Voice, Put Option
Issue 6, Volume 9,
June 2010
Title of the Paper:
Estimating Bias and RMSE of Indirect Effects
using Escaled Residual Bootstrap in Mediation Analysis
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Authors: Anwar
Fitrianto, Habshah Midi
Abstract: It is a common practice to estimate the parameters of mediation
model by using the Ordinary Least Squares (OLS) method. The construction of T
statistics and confidence interval estimates for making inferences on the
parameters of a mediation model, particularly the indirect effect, is usually
are based on the assumption that the estimates are normally distributed.
Nonetheless, in practice many estimates are not normal and have a heavy tailed
distribution which may be the results of having outliers in the data. An
alternative approach is to use bootstrap method which does not rely on the
normality assumption. In this paper, we proposed a new bootstrap procedure of
indirect effect in mediation model which is resistant to outliers. The
proposed approach was based on residual bootstrap which incorporated rescaled
studentized residuals, namely the Rescaled Studentized Residual Bootstrap
using Least Squares (ReSRB). The Monte Carlo simulations showed that the ReSRB
is more efficient than some existing methods in the presence of outliers.
Keywords: Mediation
analysis, outliers, bootstrap, studentized residuals, indirect effect
Title of the Paper:
Duality, Barycentric Coordinates and
Intersection Computation in Projective Space with GPU support
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Authors: Vaclav Skala
Abstract: This paper presents solution of selected problems using principle of
duality and projective space representation. It will be shown that alternative
formulation in the projective space offers quite surprisingly simple solutions
that lead to more robust and faster algorithms which are convenient for use
within parallel architectures as GPU (Graphical Processor
Units-NVIDIA-TESLA/Fermi) or SCC (Intel-Single-chip Cloud Computing), which
can speed up solutions of numerical problems in magnitude of 10-100. There are
many geometric algorithms based on computation of intersection of lines,
planes etc. Sometimes, very complex mathematical notations are used to express
simple mathematical solutions, even if their formulation in the projective
space offers much more simple solution. It is shown that a solution of a
system of linear equations is equivalent to generalized cross product, which
leads with the duality principle to new algorithms. This is presented on a new
formulation of a line in 3D given as intersection of two planes which is
robust and fast, based on duality of Plucker coordinates. The presented
approach can be used also for reformulation of barycentric coordinates
computations on parallel architectures. The presented approach for
intersection computation is well suited especially for applications where
robustness is required, e.g. large GIS/CAD/CAM systems etc.
Keywords: Computer
graphics, homogeneous coordinates, Plucker coordinates, principle of duality,
line and plane intersections computation, projective geometry, barycentric
coordinates.
Title of the Paper:
Lattice Boltzmann Numerical Scheme for the
Simulation of Natural Convection in an Inclined Square Cavity
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Authors: C. S. Nor
Azwadi, N. I. Nik Izual
Abstract: In this paper, a mesoscale numerical method was applied to solve two
dimensional, incompressible, thermal fluid flow problem. This study presents
numerical prediction of natural convection heat transfer inside an inclined
square cavity with perfectly conducting boundary conditions for the top and
bottom walls. The lattice Boltzmann scheme with uniform mesh resolution was
applied as a numerical research tool. The inclination angels were varied from
20° to 160° with 20° intervals. The results were presented in terms of
streamlines and isotherms plots, and average Nusselt number in the system. We
found that the flow structure together with the heat transfer mechanism are
significantly dependence on the magnitude of the inclination angles. Good
agreements were obtained when compared with the results published by other
researchers in previous studies.
Keywords: Double
population, lattice Boltzmann, distribution function, BGK collision, natural
convection
Title of the Paper:
Estimations and Predictions using Record
Statistics from the Modified Weibull Model
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Authors: Vasile Preda,
Eugenia Panaitescu, Alina Constantinescu, Supian Sudradjat
Abstract: This paper develops Bayesian and non-Bayesian analysis in the
context of record statistics values from the modified Weibull distribution. We
obtained non-Bayes estimators using MLE and Bayes estimators using the general
entropy loss functions. This was done with respect to the conjugate prior for
the shape parameter. Finally, Bayesian predictive density function, which is
necessary to obtain bounds for predictive interval of future record, is
derived. The results may be of interest in a situation where only record
values are stored.
Keywords: Bayesian and
non-Bayesian estimation, Bayesian prediction, Entropy loss function, Modified
Weibull distribution, Record values, Record statistics
Title of the Paper:
Binary Response Modeling and Validation of
its Predictive Ability
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Authors: Habshah Midi,
Sohel Rana, S. K. Sarkar
Abstract: Assessment of the quality of the logistic regression model is
central to the conclusion. Application of logistic regression modeling
techniques without subsequent performance analysis regarding predictive
ability of the fitted model can result in poorly fitting results that
inaccurately predict outcomes on new subjects. It is not unusual for
statisticians to check fitted model with validation. Validation of predictions
from logistic regression models is of paramount importance. Model validation
is possibly the most important step in the model building sequence. Model
validity refers to the stability and reasonableness of the logistic regression
coefficients, the plausibility and usability of the fitted logistic regression
function, and the ability to generalize inferences drawn from the analysis.
The aim of this study is to evaluate and measure how effectively the fitted
logistic regression model describes the outcome variable both in the sample
and in the population. A straightforward and fairly popular split-sample
approach has been used here to validate the model. The present study have
dealt with how to measure the quality of the fit of a given model and how to
evaluate its performance regarding the predictive ability in order to avoid
poorly fitted model. Different summary measures of goodness-of-fit and other
supplementary indices of predictive ability of the fitted model indicate that
the fitted binary logistic regression model can be used to predict the new
subjects.
Keywords: Validation,
training sample, deviance, prediction error rate, ROC curve
Title of the Paper:
Application of the (G'/G)-Expansion Method
for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota Equation
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Authors: Bin Zheng
Abstract: In this paper, a generalized (G'/G)-expansion method is used to seek
more general exact solutions of the integrable sixth-order
Drinfeld-Sokolov-Satsuma-Hirota equation. As a result, the traveling wave
solutions with three arbitrary functions are obtained including hyperbolic
function solutions, trigonometric function solutions and rational solutions.
The method appears to be easier and faster by means of some mathematical
software.
Keywords: (G'/G)-expansion
method, Traveling wave solutions, integrable sixth-order
Drinfeld-Sokolov-Satsuma-Hirota equation, nonlinear heat conduction equation,
exact solution, evolution equation, nonlinear equation
Title of the Paper:
Exact Solutions for Two Non-linear Equations
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Authors: Bin Zheng
Abstract: In this paper, we test the validity and reliability of the
(G'/G)-expansion method by applying it to get the exact traveling wave
solutions of the (2+1) dimensional Boussinesq and Kadomtsev-Petviashvili
equation and the nonlinear heat conduction equation. The traveling wave
solutions are obtained in three forms. Being concise and less restrictive, the
method can also be applied to many other nonlinear partial differential
equations.
Keywords: (G'/G)-expansion
method, Traveling wave solutions, (2+1) dimensional Boussinesq and
Kadomtsev-Petviashvili equation, nonlinear heat conduction equation, exact
solution, evolution equation, nonlinear equation
Title of the Paper:
New Exact Traveling Wave Solutions for Some
Non-linear Evolution Equations by (G'/G)-Expansion Method
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Authors: Bin Zheng
Abstract: In this paper, we study the application of the known generalized
(G'/G)-expansion method for seeking more exact traveling solutions solutions
and soliton solutions of the ZK-MEW equation and the (2+1) dimensional
Boiti-Leon-Pempinelli equation. As a result, we come to the conclusion that
the traveling wave solutions for the two non-linear equations are obtained in
three arbitrary functions including hyperbolic function
solutions,trigonometric function solutions and rational solutions. The method
appears to be easier and faster by means of some mathematical software.
Keywords: (G'/G)-expansion
method,Traveling wave solutions,ZK-MEW equation, (2+1) dimensional
Boiti-Leon-Pempinelli equation,exact solution, evolution equation, nonlinear
equation
Title of the Paper:
A Note for Plane Laplace's Exterior Boundary
Value Problems
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Authors: Yaoming Zhang,
Wenzhen Qu, Bin Zheng
Abstract: The solution of conventional boundary integral equations (CBIEs)
sometimes does not exist or is not unique, which has been demonstrated in a
large number of numerical experiments. According to the authors’ opinion,
there exist two reasons which can lead to this phenomenon. One reason is that
the solution of the CBIEs can not describe the behavior of the solution of the
corresponding boundary value problem at infinity accurately; the other one is
that the form of exterior boundary value problem has deficiency, which is
still a problem to be solved but has not attracted adequate attention. In this
paper, a sufficient and necessary condition with respect to the Dirichlet
exterior boundary value problem, which can ensure the existence and uniqueness
of the solution, is provided and fully proved. Based on the proposed
condition, equivalent boundary integral equations (EBIEs) for exterior
problems are established. In addition, an extremum principle on the exterior
domain is introduced in this paper.
Keywords: Laplace
equation, exterior boundary value problem, BEM, Equivalent boundary integral
equations, Extremum principle , Numerical method
Title of the Paper:
Equivalent Boundary Integral Equations for
Plane Poisson's Exterior Boundary Value Problems
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Authors: Yaoming Zhang,
Wenzhen Qu, Bin Zheng
Abstract: The solution of conventional boundary integral equations (CBIEs)
sometimes does not exist or is not unique, which has been demonstrated in a
large number of numerical experiments. According to the authors’ opinion,
there exist two reasons which can lead to this phenomenon. One reason is that
the solution of the CBIEs can not describe the behavior of the solution of the
corresponding boundary value problem at infinity accurately; the other one is
that the form of exterior boundary value problem has deficiency, which is
still a problem to be olved but has not attracted adequate attention. Many
examples illustrate that CBIEs are not equivalent to the Poisson’s exterior
boundary value problem. In this paper, the equivalent boundary integral
equations (EBIEs) for Poisson’s exterior boundary value problems are
established.
Keywords: Poisson
equation, exterior boundary value problem, BEM, EBIEs, Equivalent boundary
integral equations, Extremum principle
Issue 7, Volume 9,
July 2010
Title of the Paper:
Robust Individuals Control Chart for Change
Point Model
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Authors: Ng Kooi Huat,
Habshah Midi
Abstract: Control charts are used to monitor for changes in a process by
distinguishing between common and special causes of variability. When a
control chart signals, process engineers must initiate a search for the
special cause of the process disturbance. Identifying which combination of the
many process variables is responsible for a change in the process allows
engineers to improve quality by preventing or avoiding changes in those
variables which lead to poor quality. We examine a process-monitoring tool
that not only provides speedy detection regardless of the magnitude of the
process shift, but also provides useful change point statistics. Robustness
against assignable causes of variation appears to be important and a
likelihood ratio method is used to develop test statistics for step change
shifts. The performance of the proposed methodology is demonstrated with
numerical example and simulation studies.
Keywords: Change Point
Estimation, Statistical Process Control, In-Control, Out-of-Control, Outlier,
Maximum-Type
Title of the Paper:
Wavelets Modelling of Water, Energy and
Electricity Consumption in Spain
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Authors: C.
Gonzalez-Concepcion, M. C. Gil-Farina, C. Pestano-Gabino
Abstract: Wavelet techniques possess many desirable properties, some of which
are useful in economics and finance, but many of which are not. In this paper
we use wavelets to reveal the different cycles that are hidden by the data.
So, we consider some of the advantages and drawbacks of this time series
multiresolution analysis technique for the purpose of obtaining simultaneous
time and frequency information in determining the periodicity and the
modelling of the water consumption in Santa Cruz de Tenerife (Canary Islands,
Spain), energy and electricity consumption in Spain.
Keywords: Wavelets, Time
series, Scale domain, Water, energy and electricity consumption
Title of the Paper:
Optimal Conditions for the Control Problem
Associated to an Economic Growth Process Exposed to a Risk Factor
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Authors: Olivia Bundau,
Adina Juratoni
Abstract: The aim of this paper is to extend the study done by [6]. Here two
different research lines have been joined together: the one studying an
endogenous economical growth model in the case of which the occurrence of a
disaster is possible, and the one analyzing the same model but with logistic
population growth and the Cobb- Douglas production function. First economical
growth model leads to an optimal control problem with an infinite horizon. For
this problem we will prove that the solution of the optimal control problem
verifies Euler-Lagrange’s equation. Using these necessary conditions we will
determine the consumption evolution equation. Also, we will prove a necessary
optimality condition in terms of value function. In the second model we will
analyze an economic growth process with logistic population growth and the
Cobb-Douglas production function. The model is a version of the Ramsey model
in the case of which the occurrence of a disaster is possible. Mathematical
modeling of this economical growth process leads to an optimal control problem
with an infinite horizon. The necessary conditions for optimality are given.
Keywords: Mathematical
models applied in economies, endogenous growth, natural disaster,logistic
population
Title of the Paper:
Study on Feature Extraction and
Classification of Ultrasonic Flaw Signals
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Authors: Yanhua Zhang,
Lu Yang, Jianping Fan
Abstract: One of the most important techniques of ultrasonic flaw
classification is feature extraction of flaw signals,which directly affects
the accuracy and reliability of flaw classification.Based on the
non-stationary characteristic of ultrasonic flaw signals, a new feature
extraction method of ultrasonic signals based on empirical mode decomposition
(EMD) is put forward in the paper. Firstly, the original ultrasonic flaw
signals are decomposed into a finite number of stationary intrinsic mode
functions (IMFs) by EMD, and the Fourier transformation of IMF is made. The
next step is to find a set of classification values from time domain and
frequency domain of IMFs relating to flaw information, and to analyze these
classification values and construct vector as signal eigenvector for
identification. According to specific characteristics of ultrasonic echo
signal, identification defect diagnosis system for ultrasonic echo signal
based on BP is built up, and the specific structure of BP neural network is
designed. Finally BP neural network is made as decision-making classifier,
signal eigenvector is inputted and flaw type is outputted. Experimental
results show that the method has better performance in detecting ultrasonic
flaw signals.
Keywords: Ultrasonic
signal; empirical mode decomposition (EMD); intrinsic mode function; feature
extraction; neural network; eigenvector
Title of the Paper:
Bayes Estimators of Modified-Weibull
Distribution Parameters using Lindley's Approximation
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Authors: Vasile Preda,
Eugenia Panaitescu, Alina Constantinescu
Abstract: For Modified-Weibull distribution we have obtained the Bayes
Estimators of scale and shape parameters using Lindley's approximation
(L-approximation) under various loss functions. The proposed estimators have
been compared with the corresponding MLE for their risks based on
corresponding simulated samples.
Keywords: Bayesian
estimation, Lindley's approximation, Maximum likelihood estimates, Modified
Weibull distribution, Monte Carlo simulation
Title of the Paper:
Diagonally Implicit Runge-Kutta Nystrom
General Method Order Five for Solving Second Order IVPs
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Authors: Fudziah Ismail
Abstract: A diagonally implicit Runge-Kutta-Nystrom General (SDIRKNG) method
of fifth order with an explicit first stage for the integration of
second-order IVPs is presented. A standard set of test problems are tested
upon and the numerical results are compared when the same set of test problems
are reduced to first-order system and solved using existing fifth order singly
diagonally implicit Runge-Kutta method. The time taken to solve each problem
over all the stepsizes are also compared. The results suggest the superiority
of the new method.
Keywords: Diagonally
implicit, Runge-Kutta-Nystrom, Second-order IVPs
Title of the Paper:
Diffusion and Semi-Convexity of Fuzzy Set
Multifunctions
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Authors: Alina Gavrilut,
Anca Croitoru, Nikos E. Mastorakis
Abstract: We present some properties regarding diffusion and semi-convexity
for fuzzy set multifunctions defined on a ring of subsets of an abstract
nonvoid space and taking values in the family of all nonvoid closed subsets of
a real normed space.
Keywords: Diffused,
semi-convex, fuzzy set multifunction, non-atomicity, Darboux property,
regular, multimeasure, null-additive
Title of the Paper:
Stochastic, Fuzzy and Hybrid Monetary Models
with Delay
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Authors: G. Mircea, M.
Pirtea, M. Neamtu, D. Opris
Abstract: This paper addresses an autonomous stochastic system with delay and
associated fuzzy and hybrid models, which describe a monetary system involving
interest rate, investment demand and price index. We analyze the deterministic
model and the stochastic model with perturbation. For the stochastic system
with delay we identify the differential equations for the mean values as well
as for the mean square value. The last part of the paper includes numerical
simulations and conclusions.
Keywords: Monetary system,
deterministic model with delay, stochastic delay system, fuzzy, hybrid system
Title of the Paper:
Stochastic, Fuzzy, Hybrid Delayed Dynamics
Heterogeneous Competitions with Product Differentiation
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Authors: Mihaela Neamtu,
Marilen Pirtea, Gabriela Mircea, Dumitru Opris
Abstract: In this paper, we study the heterogeneous duopoly with product
differentiation, in which one firm is quantity setter and the other is price
setter. The deterministic and stochastic models with delay are presented and
fuzzy and hybrid models, as well. For the stochastic disturbance model with
delay, sufficient conditions are done so that the steady state is
asymptotically stable in mean and in mean square. Using programs in Maple 13
we make some numerical simulations that verify the theoretical results.
Keywords: Delay dynamics,
stochastic differential equations, heterogeneous duopoly competition, product
differentiation, fuzzy model, hybrid model, fixed time delay
Issue 8, Volume 9,
August 2010
Title of the Paper:
Effect of Rotation and Magnetic Field on
Thermal Instability of a Viscoelastic Fluid Permeated with Suspended Particles
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Authors: A. K. Aggarwal,
Anushri Verma
Abstract: The effect of rotation and magnetic field on the thermal instability
of Walters’ (model ) viscoelastic fluid permeated with suspended particles is
considered. For stationary convection, Walters’ viscoelastic fluid behaves
like a Newtonian fluid. It is found that, for the case of stationary
convection, the rotation and magnetic field have stabilizing effect whereas
the suspended particles has destabilizing effect on the system. The principle
of exchange of stabilities is satisfied in the absence of magnetic field. The
magnetic field, viscoelasticity and rotation introduce oscillatory modes in
the systems which were non-existent in their absence.
Keywords: Rotation,
magnetic field, thermal instability, viscoelasticity, suspended particles
Title of the Paper:
The Haar Wavelets used how Expansion Function
in the Method of the Moments in the Solution of Some Electrostatic Problems
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Authors: Aldo Artur
Belardi, Jose Roberto Cardoso, Carlos A. Franca Sartori
Abstract: This work presents the methodology from the determination the charge
superficial density and electrical fields, in three simple structures to a
finite straight wire, square plane plates and the capacitance between to plane
plate, all finite and submitted to a constant potential. That involves the
method of the moments using as expansion function the Haar wavelets instead of
the pulse function, in order to reach a good precision and reducing the
computational execution time. We also intend to take advantages of the
wavelets application through the Cholesky decomposition, talking about
formation of scattered matrixes, and the detection of nulls values.
Keywords: Moments,
Wavelets, Electrostatic
Title of the Paper:
Deterministic and Stochastic Cournot Duopoly
Games with Tax Evasion
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Authors: Mihaela Neamtu
Abstract: In this paper the static model of the Cournot duopoly with tax
evasion is analyzed. A study for the local stability of the stationary states
is carried out in the case of the dynamic model with tax evasion and delay.
Also, the stochastic approach is taken into consideration. Numerical
simulations are performed for the above mentioned processes. Finally,
conclusions regarding the economic processes are provided.
Keywords: Cournot
competition, rent seeking games, stochastic differential equations, product
differentiation, time delay, Hopf bifurcation, tax evasion
Title of the Paper:
Using CPSO for the Engineering Optimization
Problems
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Authors: Ching-Long Su,
Shutan Hsieh
Abstract: The aim of this study is to solve the optimization problems of
different engineering designs by using nonlinear mixed integer programming
mode. In the past, this type of engineering design optimization problem has
been widely studied and discussed. They are usually solved through
mathematical programming method or heuristics. However, there are more
constraints and more constraints that cannot be satisfied. In solving this
type of problems, we used a penalty guided cooperative particle swarm
optimization to avoid the disadvantage of decreased efficiency from the
increase of search spatial dimension and to raise the efficiency. In resolving
some engineering design problems, the results shows that the solutions found
by cooperative particle swarm optimization are equal or better than the
best-known solutions from past literature. Thus, the results of this study
indicate that cooperative particle swarm optimization is another effective
method to find solutions to optimization problems.
Keywords: Engineering
optimization, Nonlinear mixed integer programming, Cooperative particle swarm
optimization
Title of the Paper:
Deterministic, Uncertainty and Stochastic
Models of Kaldor-Kalecki Model of Business Cycles
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Authors: Gabriela
Mircea, Mihaela Neamtu, Dumitru Opris
Abstract: This paper presents the Kaldor-Kalecki nonlinear business cycle
model of the income. It will take into consideration the investment demand in
the form suggested by Rodano. We will analyze the deterministic, uncertainty
and stochastic Kaldor-Kalecki models. The dynamics of the mean values and the
square mean values of the model’s variables are set. Numerical examples are
given in the end, to illustrate our theoretical results.
Keywords: Business cycle
model, deterministic model with delay, Kaldor-Kalecki model, uncertain system,
stochastic system
Title of the Paper:
The Analysis of Mathematical Models
Associated to Some Economic Growth Processes with Endogenous Population
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Authors: Olivia Bundau,
Mihaela Neamtu
Abstract: The aim of this paper is to extend the study done by [5]. Here, we
will analyze two mathematical models associated to some economic growth
processes with endogenous population depending on the current fertility. The
first model is a version of the Ramsey model in continuous and infinite time
with the Cobb-Douglas production function. In the second model we consider the
AK production function. The mathematical models of these economical growth
processes lead to two optimal control problems with an infinite horizon. The
necessary conditions for optimality are given for both economic problems.
Using the optimality conditions we prove the existence, the uniqueness and the
stability of the steady states.
Keywords: Mathematical
models applied in economies, endogenous growth, endogenous population,
optimization problems
Title of the Paper:
Evaluation of Steady State Vector of Fuzzy
Autocatalytic Set of Fuzzy Graph Type-3 of an Incineration Process
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Authors: Sumarni Abu
Bakar, Tahir Ahmad, Sabariah Baharun
Abstract: Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates
the concept of fuzzy, graph and autocatalytic set. It was initially defined
and used in the modeling of a clinical waste incineration process which has
produced more accurate results than using crisp graph. As it is a newly
developed theory, FACS seems to have great potentials in generating new
mathematical theory. This paper employs Markov chain to the evaluation of
steady state of an incineration process. Novel definition of transition
probability matrix of FACS is presented. Steady state vector of Markov chain
for incineration process is determined and graph of convergence of its norm
difference is presented. This study led to some relation of Markov process and
Perron-Frobenius Theorem.
Keywords: Fuzzy
Autocatalytic Set, Fuzzy Graph, Incineration Process, Perron-Frobenius
Theorem, Transition Probability Matrix, Markov process
Issue 9, Volume 9,
September 2010
Title of the Paper:
Transformation of Fuzzy State Space Model of
a Boiler System: A Graph Theoretic Approach
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Authors: Noor Ainy
Harish, Razidah Ismail, Tahir Ahmad
Abstract: Graph theory has many real-world applications and is rich in
theoretical results, especially for studying interconnection among elements in
natural and man-made systems. In recent studies of complex control system,
directed graph was introduced to define and interpret the interconnection
structure underlying the dynamics of the interacting subsystems. Similarly,
Fuzzy State Space Model (FSSM) was developed for solving inverse problem in
multivariable control system. Thus, this paper aims to describe the
transformation of FSSM of a Boiler system using a graph theoretic approach.
The main subsystems of the Boiler system are furnace, superheater, drum, riser
and reheater. These subsystems are transformed into vertices whereas the
interconnections between subsystems are associated with edges of the graph.
Here, the Autocatalytic Set (ACS) is a subgraph, whereby each of the nodes has
at least one incoming link from a node belonging to the same subgraph. The
concept of ACS is integrated to reveal some properties of the new graphical
representation of FSSM such that irreducible graph, adjacency matrix and the
relationship of an ACS to Perron Frobenius Eigenvector. These properties
indicate initial findings that will lead to further exploration in Fuzzy
Graphical representation.
Keywords: Combined Cycle
Power Plant, State Space, Multi-connected System, Adjacency Matrix
Title of the Paper:
A New Diagonally Implicit Runge-Kutta-Nystrom
Method for Periodic IVPs
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Authors: Norazak Senu,
Mohamed Suleiman, Fudziah Ismail, Mohamed Othman
Abstract: A new diagonally implicit Runge-Kutta-Nystrom (RKN) method is
developed for the integration of initial-value problems for second-order
ordinary differential equations possessing oscillatory solutions. Presented is
a method which is three-stage fourth-order with dispersive order six and
'small' principal local truncation error terms and dissipation constant. The
analysis of phase-lag, dissipation and stability of the method are also given.
This new method is more efficient when compared with current methods of
similar type for the numerical integration of second-order differential
equations with periodic solutions, using constant step size.
Keywords:
Runge-Kutta-Nystrom methods; Diagonally implicit; Phase-lag; Oscillatory
solutions
Title of the Paper:
Vibrations of Cylindrical Shells with
Circumferential Cracks
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Authors: Jaan Lellep,
Larissa Roots
Abstract: An approximate method for the vibration analysis of stepped shells
accounting for the influence of cracks located at re-entrant corners of steps
is presented. Introducing the additional compliance function it is shown that
the flexibility of the shell near cracks can be prescribed by means of the
compliance of the structure. The latter is coupled with the stress intensity
factor, which is known from the linear elastic fracture mechanics. Theoretical
analysis is developed for circular cylindrical shells, provided the shell wall
has an arbitrary number of steps and circular cracks of constant depth.
Various combinations of end conditions are considered.
Keywords: Crack, cylinder,
free vibration, elasticity, axisymmetric response, stepped shell
Title of the Paper:
About Three Important Transformations Groups
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Authors: Monica A. P.
Purcaru, Mirela Tarnoveanu, Laura Ciupala
Abstract: In the present paper we introduce the concepts of conformal metrical
d-structure and of conformal metrical N-linear connection with respect to the
conformal metrical d-structure, corresponding to an 1-form on a generalized
Hamilton space. We determine the set of all conformal metrical N-linear
connections in the case when the nonlinear connection is arbitrary and we find
important examples and particular cases. We find the transformations group of
these connections. We study the role of the torsion d-tensor fields Tijk, Sijk
and Sijk in this theory, especially in the determination of the set of all
semisymmetric conformal metrical N-linear connections with respect to the
conformal metrical d-structure, corresponding to the same nonlinear connection
N. We give the transformations group of these connections and other two
important groups and we find their remarkable invariants. Finally we determine
the set of all metrical N-linear connections in the case when the nonlinear
connection is arbitrary, we give important examples and particular cases and
for the case when the nonlinear connection is fixed we find the
transformations group of these connections.
Keywords: Second order
cotangent bundle, nonlinear connection, N-linear connection, metrical
d-structure, conformal metrical d-structure, conformal metrical N-linear
connection, semisymmetric conformal metrical N-linear connection
Title of the Paper:
Spectral Techniques for Solving PDE Stability
Model of Vortex Rope
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Authors: Diana Alina
Bistrian
Abstract: In this paper spectral methods are applied to investigate the
hydrodynamic instability of swirling flow with application to Francis
hydraulic turbine. Spectral methods imply representing the problem solution as
truncated series of smooth global functions. An 2 L - projection and the
collocation methods are developed assessing both analytically methodology and
computational techniques using symbolic and numerical conversions. Remarks
concerning the efficiency and the accuracy of each method in this case are
presented. The model of the trailing vortex is used to validate the numerical
algorithms with existing results in the literature. All the results are
compared to existing ones and they prove to agree quite well. The advantages
of using this methods in flow control problems are pointed out.
Keywords: Hydrodynamic
instability, swirling flow, projection algorithm, spectral collocation, vortex
hydrodynamics, vortex rope
Title of the Paper:
Blow-up Solutions of Degenerate Parabolic
Problems
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Authors: P. Sawangtong,
W. Jumpen
Abstract: In this article, we study the degenerate parabolic problem, q ( ) q
( ), t x x x u ? xβ u = x f u satisfying the Dirichlet boundary condition and
a nonnegative initial condition where q and β are given constants and f is a
suitable function. We show that under certain conditions the degenerate
parabolic problem has a blow-up solution and the blow-up set of such a blow-up
solution is the whole domain of x. Furthermore, we give the sufficient
condition to blow-up in finite time. Finally, we generalize the degenerate
parabolic problem into the general form, ( ) ( ( ) ) ( ) ( ). t x x k x u ? p
x u = k x f u Under appropriate assumptions on functions k, p and f , we still
obtain the same results as the previous problem.
Keywords: Degenerate
parabolic problems, Finite time blow-up, Blow-up set, Blow-up solution
Title of the Paper:
Quantum Theory of Fields from Planck to
Cosmic Scales
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Authors: Siavash H.
Sohrab
Abstract: A scale invariant model of statistical mechanics is applied to
describe a modified statistical theory of turbulence and its quantum
mechanical foundations. Hierarchies of statistical fields from cosmic to
Planck scales are described. Energy spectrum of equilibrium isotropic
turbulence is shown to follow Planck law. Predicted velocity profiles of
turbulent boundary layer over a flat plate at four consecutive scales of LED,
LCD, LMD, and LAD are shown to be in close agreement with the experimental
observations in the literature. The physical and quantum nature of time is
described and a scale-invariant definition of time is presented and its
relativistic behavior is examined. New paradigms for physical foundations of
quantum mechanics as well as derivation of Dirac relativistic wave equation
are introduced.
Keywords: Theory of
turbulence, Quantum mechanics, Relativity, Dirac and Schrodinger equations,
TOE
Issue 10, Volume 9,
October 2010
Title of the Paper:
The Effect of Time Scales on SIS Epidemic
Model
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Authors: Wichuta
Sae-Jie, Kornkanok Bunwong, Elvin J. Moore
Abstract: The distribution of diseases is one of the most interesting
real-world phenomena which can be systematically studied through a
mathematical model. A well-known simple epidemic model with surprising
dynamics is the SIS model. Usually, the time domains that are widely used in
mathematical models are limited to real numbers for the case of continuous
time or to integers for the case of discrete time. However, a disease pandemic
such as an influenza pandemic regularly disappears from a population and then
recurs after a period of time. Additionally, collecting actual data
continuously is time-consuming, relatively expensive, and really impractical.
It seems that using a continuous-time model to describe observed data may not
always be possible due to time domain conflict. The purpose of this paper is,
therefore, to study the qualitative behavior of SIS models on continuous,
discrete, and mixed continuous-discrete time scales. We investigate their
dynamic behavior and examine how this behavior changes in the different time
scale domains. We show that the dynamic behavior can change in a systematic
manner from simple stable steady-state solutions for the continuous time
domain to complicated chaotic solutions for the discrete-time domain.
Keywords: Bifurcation,
Chaos, Limit cycles, Period doubling, SIS epidemic model, Time scales calculus
Title of the Paper:
A New Approach to Pair Approximation Method
for Spatial Model in Ecology
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Authors: Kornkanok
Bunwong
Abstract: A mathematical model using either mean-field approximation or pair
approximation has both advantage and limitation. Mean-field approximation is
suitable for describing behaviors of a large system; however, it neglects the
scale of individual interaction. On the other hand, pair approximation is
suitable for studying local interaction especially singles and pairs; however,
the mathematical formulas are still limited. Thus, choosing the right model
for the right purpose is recommended. The objective of this paper is to
develop the techniques of pair approximation by using probability averaged
value based on probability distribution; for example, multinomial distribution
and Poisson distribution. These extended formulas are suitable for a model
composed of individuals whose event rates are additionally affected by their
nearby neighbor. Finally, we apply these tools to a simple SIS epidemic model.
Keywords: Multinomial
distribution, Poisson distribution, Pair approximation, Spatial interaction,
Lattice model, Ecology, Epidemiology
Title of the Paper:
A Simulation Approach: Improving Patient
Waiting Time for Multiphase Patient Flow of Obstetrics and Gynecology
Department (O&G Department) in Local Specialist Centre
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Authors: A. F.
Najmuddin, I. M. Ibrahim, S. R. Ismail
Abstract: An outpatient clinic is a very complex department to manage. The
management of the outpatient department should given greater emphasis on its
medical facilities in order to ensure the services provided are in high
quality, which conforms to customer or patient satisfaction. Long waiting time
for treatment at the department is always the main problem faced by the
management, and even worst the consultation time is tremendously shorter than
the waiting time. This situation has been a common complaint by the patients
and remains to occur even though an appointment system is implemented. The
implementation of inefficient appointment and inconsistent service time
contributes to the dissatisfaction among patients as well as giving a huge
impact to the healthcare’s overall operations. Therefore, the purpose of this
study is to analyze the multiphase patient flow system in Obstetrics and
Gynecology Department (O&G Department) of a specialist centre by developing a
simulation model that illustrates the actual patient flow in the department.
The Arena 7.0 software package is used to develop the simulation model in
order to examine the patient flow, especially the waiting time involved. In
addition, 120 questionnaires were distributed to patients to gather direct
responds and opinions towards the services provided. The information gathered
was used to aid the model improvement process. The result obtained from the
simulation model shows that a long waiting time does exist in the system.
Based on the developed simulation model, two proposed experimentation are
being done to find the right solutions to reduce the patients’ waiting time
and at the same time enhanced the quality of services of the O&G Department.
The proposed experimentation model can be effective to the system and is
possible to be implemented in the department.
Keywords: Arena,
multiphase patient flow, simulation model, simulation technique, lengthy
waiting time, service time
Title of the Paper:
Statistical Analysis and Evaluation of Hurst
Coefficient for Annual and Monthly Precipitation Time Series
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Authors: Alina
Barbulescu, Cristina Serban, Carmen Maftei
Abstract: A major issue in time series analysis and particularly in the study
of meteorological time series is to model and to predict their behaviour. The
first step to reach this goal is the data analysis. It is what we shall do in
this article, focusing on the long range dependence (LRD) property. Various
estimators of LRD have been proposed. Their accuracy have been generally
tested using simulated time series since sometimes only their asymptotic
property are known, or worse, no asymptotic property have been proved. For ten
annual and monthly data series collected in Dobrudja region, for 41 years, we
did the statistical analysis and we compare the results.
Keywords: Normality,
homoscedasticity, long – range dependence, Hurst coefficient
Title of the Paper:
Implementation of MPI Environment for Solving
Large Systems of ODEs using Block Method
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Authors: Z. A. Majid, S.
Mehrkanoon, K. I. Othman, M. Suleiman
Abstract: Parallel 2-point and 3-point block method will simultaneously
compute the numerical solutions at two and three points respectively are
suitable for solving large system of first order ordinary differential
equations (ODEs) using variable step size. The Gauss Seidel iteration will be
implemented for the block methods. The parallelism across the system is
considered for the parallelization of the proposed methods using the Message
Passing Interface (MPI) communication environment which runs on High
Performance Computing (HPC). Numerical examples are given to illustrate the
efficiency of the parallel implementation of the proposed method using 2, 4
and 6 processors with respect to the sequential one.
Keywords: 2-point block,
3-point block, ODEs, parallel method, block method, parallelism
Title of the Paper:
A Study of the Impact of the Initial Energy
in a Close Approach of a Cloud of Particles
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Authors: Vivian Martins
Gomes, Antonio F. B. A. Prado
Abstract: In this paper we perform a study of the effects of a close approach
in the three-dimensional space between a planet and a cloud of particles, with
the goal of understanding the dispersion of this cloud in terms of the
variations of velocity, energy, angular momentum and inclination. It is
assumed that the cloud is formed at the periapsis and the particles differ
only by the magnitude of the velocity at this point. In this research we use
the three-dimensional circular restricted three-body problem as the basic
model for this close approach. A numerical algorithm is developed and
implemented to study this problem and then it is applied to a cloud of
particles, based in an analytical description of the close approach maneuver
in the three-dimensional space. Analytical equations based in the patched
conics approximation are used to calculate the variation in velocity, angular
momentum, energy and inclination of the spacecraft that performs this
maneuver.
Keywords: Astrodynamics,
artificial satellites, orbital dynamics, swing-by
Issue 11, Volume 9,
November 2010
Title of the Paper:
Demonic Fuzzy Operators
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Authors: Huda Alrashidi,
Fairouz Tchier
Abstract: We deal with a relational algebra model to define a refinement fuzzy
ordering (demonic fuzzy inclusion) and also the associated fuzzy operations
which are fuzzy demonic join (tfuz), fuzzy demonic meet (ufuz) and fuzzy
demonic composition ( 2 fuz). We give also some properties of these operations
and illustrate them with simple examples. Our formalism is the relational
algebra.
Keywords: Fuzzy sets,
demonic operators, demonic fuzzy operators, demonic fuzzy ordering
Title of the Paper:
Analysis of Chain Reaction Between Two Stock
Indices Fluctuations by Statistical Physics Systems
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Authors: Jiguang Shao,
Jun Wang
Abstract: In this paper, we consider the statistical properties of chain
reaction of stock indices. The theory of interacting systems and statistical
physics are applied to describe and study the fluctuations of two stock
indices in a stock market, and the properties of the interacting reaction of
the two indices are investigated in the present paper. In this work,
stochastic analysis and the two random paths model are used to study the
probability distribution for the chain reaction of stock indices, further we
show the asymptotical behavior of probability measures of the fluctuations for
the two stock indices model. In the last part, we discuss the convergence of
the finite dimensional probability distributions for the financial model.
Keywords: Stock Index,
Chain Reaction, Statistical Analysis, Fluctuation, Statistical Physics, Gibbs
Probability Measure
Title of the Paper:
Matrix Nonstandard Numerical Schemes for
Epidemic Models
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Authors: Gilberto
Gonzalez-Parra, Rafael J. Villanueva, Abraham J. Arenas
Abstract: This paper is concerned with the construction and developing of
several nonstandard finite difference (NSFD) schemes in matrix form in order
to obtain numerical solutions of epidemic models. In particular, we deal with
a classical SIR epidemic model and a seasonal model associated with the
evolution of the transmission of respiratory syncytial virus RSV in the human
population. The first model is an autonomous differential equation system, and
the second one is a nonautonomous one which generally is more difficult to be
solved. The numerical schemes developed here can be used in other general
epidemic models based on ordinary differential equations. One advantage of the
developed methodology is that can be used easily by the scientific community
without special knowledge. In addition, these NSFD schemes which are based on
the the nonstandard finite difference methods developed by Mickens solve
numerically systems describing epidemics with less computational effort.
Finally, with these matrix NSFD schemes it can be exploited more easily matrix
operations advantages.
Keywords: Matrix
difference scheme, Nonstandard schemes, Matrix computation, Numerical
solution, Epidemic model
Title of the Paper:
A Study of Vehicle Characteristics of
Signalized Intersection based on Queuing Theory
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Authors: Lian Xue,
Minghui Wu, Hui Yan
Abstract: This paper uses queuing theory to study the features of the
vehicle’s arriving and passing of the signalized intersection. The first part
of this paper presents the background, purpose and meaning. In the second
part, the arrival process and serving process are studied, especially the
delay process is mainly analyzed including the dispersion vehicle headway time
distribution and vehicle delay at signalized intersections is analyzed. In the
third part, time series, cubic spline difference and gray prediction, RBF
neural network are used to get the number of vehicles arrived outside of next
18 cycles. Based on the queuing theory, the forth part introduces a predict
model on the vehicle’s arrival. It predicts a certain intersections’ average
length, average waiting time and average length of stay in the next 18 cycles.
The fifth part optimizes the intersection signal timing and gets the best
signal cycle time. Scientific model and more complete analysis are founded in
the paper. These methods have a good reference value to the relevant
departments.
Keywords: Signalized
intersection, vehicle characteristics, queuing theory, RBF neural network,
forecast, timing optimization
Issue 12, Volume 9,
December 2010
Title of the Paper:
On a Degenerate Parabolic Equation from
Finance
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Authors: Huashui Zhan
Abstract: Consider the degenerate parabolic equation
 , which comes from
mathematics finance, and in which u(t, x) is the utility function of a agent’s
decision under risk. By Oleinik’s line method, the existence and the
uniqueness of the local classical solution for the initial boundary problem of
the equation are got. Also, the global entropy solution of the Cauchy problem
is discussed.
Keywords: Degenerate
parabolic equation, existence, uniqueness, initial boundary problem, global
entropy solution
Title of the Paper:
Locating Zeros of Polynomials Associated with
Daubechies Orthogonal Wavelets
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Authors: Jalal Karam
Abstract: In the last decade, Daubechies orthogonal wavelets have been
successfully used and proved their practicality in many signal processing
paradigms. The construction of these wavelets via two channel perfect
reconstruction filter bank requires the identification of necessary conditions
that the coefficients of the filters and the roots of binomial polynomials
associated with them should exhibit. In this paper, the low pass and high pass
filters that generate a Daubechies mother wavelet are considered. From these
filters, a new set of high pass and low pass filters are derived by using the
”Alternating Flip” techniques. The new set of filters maintain perfect
reconstruction status of an input signal, thus allowing the construction of a
new mother wavelet and a new scaling function that are reflective to those of
the originals. Illustration are given and new reflective wavelets are derived.
Also, a subclass of polynomials is derived from this construction process by
considering the ratios of consecutive binomial polynomials’ coefficients. A
mathematical proof of the residency of the roots of this class of polynomials
inside the unit circle is presented along with an illustration for db6, a
member of the Daubechies orthogonal wavelets family. The Kakeya-Enestrom
theorem is discussed along with some of its generalizations. Finally, a
?-dependent difference among the coefficients of the new set of polynomials is
examined and optimized locations of the roots are derived.
Keywords: Zeros,
Polynomials, Daubechies Orthogonal Wavelets, Reflective Wavelets,
Kakeya-Enestrom Theorem
Title of the Paper:
Improvements of Preconditioned SOR Iterative
Method for L-Matrices
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Authors: Shi-Liang Wu,
Cui-Xia Li, Ting-Zhu Huang
Abstract: In this paper, we present some comparison theorems on preconditioned
iterative method for solving L-matrices linear systems. Comparison results and
numerical examples show that the rate of convergence of the preconditioned
Gauss-Seidel iterative method is faster than the rate of convergence of the
preconditioned SOR iterative method.
Keywords: Preconditioner;
L-matrix; SOR method; Gauss-Seidel method; Spectral radius; Iteration
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