Issue 1, Volume 8,
January 2009
Title of the Paper: Ionospheric Effects
on GPS Range Finding Using 3D RayTracing and NelderMead Optimisation
Algorithm
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Authors: Siti Sarah Nik
Zulkifli, Mardina Abdullah, Azami Zaharim, Mahamod Ismail
Abstract: The Earth’s ionosphere plays a crucial role in Global Positioning
System (GPS) accuracy because this layer represents the largest source of
positioning error for the users of the GPS after the turnoff of Selective
Availability (SA). This paper studies the ionospheric effect on
transionospheric signal propagation for the Earthsatellite path using 3D
Jones RayTracing utilizing NelderMead optimisation algorithm. The
ionospheric delay or advance is obtained from the difference between the
distance of the ray path from the satellite to the receiver determined from
the raytracing and the distance for propagation over the line of sight (LOS)
at the velocity of light in vacuum. The difference between the standard
dualfrequency models corrected range and LOS, known as Residual Range Error (RRE)
is calculated. Results show that the RRE of group delay value is different
from RRE of phase advance. On the other hand, the group and phase path is
longer when considering the geomagnetic field effect on both GPS frequencies
L1 and L2. The higher order term in total electron content (TEC) calculation
that relates to the refractive index is normally neglected due to its small
value, but it is clearly shown that it does have some effects in raytracing.
This analysis needs to be considered for more accurate GPS range finding.
Keywords: GPS, Ionosphere,
raytracing, NelderMead optimization, RRE
Title of the Paper: Effects of a
Supplementary Quadrature in the Collocation Method for Solving the Hartree
Fock Equations in AbInitio Calculations
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Authors: Sever
Spanulescu, Mircea Moldovan
Abstract: The collocation method for solving the HartreeFock equations of the
selfconsistent field in large atomic and molecular systems is analyzed and a
method for improving its performances by supplementary analytical and
numerical quadrature is proposed. We used monomial and Chbyshev type trial
functions and the collocation points were equidistant or Chebyshev polynomial
roots. The singularities have been avoided by a function change and analytical
expressions have been obtained for the most part of the integrated terms in
the matrix elements, except the HartreeFock potential which is treated
separately in a similar way. This apriori analytical treatment ensures a
greater speed and a lower condition number of the matrix necessary for the
expansion’s coefficient calculus, with an important effect on the overall
precision and speed. Some numerical results are presented and compared with
wellknown types of orbitals, demonstrating the performance increasing in
terms of precision and computing effort.
Keywords: Ab–initio
methods, self consistent field, HartreeFock equations, Collocation,
Evanescence
Title of the Paper: Analytical
Properties and Numerical Calculations of High Transcendental Functions
Involved in the Relativistic Amplitudes of two Photon Atomic Processes
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Authors: Adrian Costescu,
Sever Spanulescu, Cristian Stoica
Abstract: The high transcendental functions that occur in the relativistic
expressions of the amplitudes of the two photon atomic processes are
analytically treated taking advantage of their specific parameters values. We
present some identities and recurrence relationships that allow reducing the
number of needed Appell functions and transform their imaginary part in terms
of Gauss hypergeometric functions. If the physical model takes into account
only the terms up till the fourth power in Zαin the real part and the seventh
power in the imaginary part, some transcendental functions may be reduced to
elementary functions. The numerical results obtained using the presented
methods were compared with other’s authors results, displaying a very good
agreement.
Keywords: Appell
functions, Gauss hypergeometric functions, relativistic atomic processes
Issue 2, Volume 8,
February 2009
Title of the Paper: A New Boundary
Element Approach for the 3D Compressible Fluid Flow Around Obstacles
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Authors: Luminita Grecu
Abstract: The paper presents a boundary element approach for the problem of
the finite span airfoil in a subsonic compressible fluid flow. The singular
boundary integral equation equivalent with the mathematical model
characterized by partial differential equation is solved in this paper by the
use of constant and linear isoparametric boundary elements of Lagrangean type.
A special attention is given to the treatment of the singular integrals
because their evaluation major influences the numerical solutions accuracy.
Some aspects about how to treat the integrals of singular kernels in case of
solving 3D problems are presented. An efficient method that is applied
consists in using suitable geometrical transformations of coordinates to
eliminate the singularities. A computer code based on this method is made and
numerical results are obtained. The computer code is tested by making an
analytical checking and the results show the efficiency of the method.
Keywords: Boundary element
method, linear boundary element, singular integral, compressible fluid flow
Title of the Paper: More on the Green
Solow Model with Logistic Population Change
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Authors: Massimiliano
Ferrara, Luca Guerrini
Abstract: This paper generalizes the model introduced by Ferrara and Guerrini
[13], where two different research lines have been joined together: the one
studying the effects of incorporating technological progress in pollution
abatement in the SolowSwan model (Brock and Taylor [6]), and that analyzing
the role of a logistic population growth rate within the SolowSwan model
(Ferrara and Guerrini [13]). In this framework, the economy is described by a
three dimensional dynamical system, whose solution can be explicitly
determined. We note that physical capital can be expressed in closedform via
Hypergeometric functions. As well, we prove the model’s solution to be
convergent in the logrun. We characterize the economy balanced growth path
equilibrium, and find that sustainable growth occurs if technological progress
in abatement is faster than technological progress in production. An
environmental Kuznets curve may result along the transition to the balanced
growth path. If there is no technological progress in abatement, then there is
no EKC. Furthermore, the economy has a unique equilibrium (a node), which is
locally asymptotically stable.
Keywords: Green Solow,
Logistic population, Pollution, Sustainable growth, Environmental Kuznets
curve
Title of the Paper: The Study of some
Discrete ISLM Models with Tax Revenues and Time Delay
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Authors: Mihaela Neamtu,
Gabriela Mircea, Dumitru Opris
Abstract: In this paper, we study some discrete ISLM models with tax revenues
and time delay. Considering its parameters as variables, we analyze the
existence of the NeimarkSacker bifurcation. We find the normal form and its
Lyapunov coefficient. For each considered model, using programs in Maple 11 we
make some numerical simulations that verify the theoretical results.
Keywords: ISLM model, tax
revenues, NeimarkSacker bifurcation
Title of the Paper: NeimarkSacker and
Flip Bifurcations in a DiscreteTime Dynamic System for Internet Congestion
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Authors: Gabriela Mircea,
Dumitru Opris
Abstract: The aim of this paper is to study the NeimarkSacker and flip
bifurcations for the discretetime dynamic system, which describes the
Internet congestion, with a single link and two sources. We describe the
algorithm in order to determine the NeimarkSacker bifurcation and the normal
form. We establish the existence of a flip bifurcation for the case when the
model’s two parameters depend on the real parameter a, which influences the
existence of the bifurcation. The numerical simulations verify the theoretical
results.
Keywords: Internet model,
NeimarkSacker bifurcation, flip bifurcation, feedback delay, numerical
simulations
Title of the Paper: About Solutions of
Renewal Equations and Determinations of Failure Moments of a System as
Equilibrium Points
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Authors: Ilie Mitran
Abstract: The results presented in this paper lead to solving main problems of
the reliability theory: specifying the failure moments of a failure and
determining the solutions of renewal equations. We analyze the following
situations: 1. the system structure is not taken into consideration; 2. the
system structure is known. In the first case we presume that the adopted
efficiency function is the average operation time and, by using specific
methods of the theory of games, we can prove that there is no equilibrium type
solution, so the failure moment of the system cannot be precisely determined.
By solving some specific problems, type maximum or minimax, we can only get
the interval where the failure point of the system is found. The optimal
problem type maximum is solved by specific methods from the theory of games
while the optimal problem type minimax is solved by using the maximum
principle of Pontriaghin. In the second case we start from the graph structure
associated to a system with renewal operations and we build immediately the
equation system with finite differences and the system of differential
equations associated to this graph. Applying the Laplace transformation it is
determined the system availabilities and unavailabilities caused by its
subsystems. The failure moments of the system are determined as equilibrium
points but the difficulties in calculations lead to obtaining only an
approximate solution. Knowing the failure moments of the analyzed system lead
to the reconsideration of the renewal policies of the system. Practically,
there are determined the approximate solutions of the renewal equations and
their separation curve. Having these elements we can completely analyze the
renewal process; this analysis being based both on the failure moments of the
system and on the renewal costs of the analyzed system.
Keywords: Reliability
function, Markov process, Laplace transformation of availability, replacement
times
Title of the Paper: Possibilities for
Increasing the Use of Machineries Using Computer Assisted Statistical Methods
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Authors: Ilie Mitran,
Florin Dumitru Popescu, Marin Silviu Nan, Septimiu Sorin Soba
Abstract: Reliability has recently emerged from the quality concept. If
quality represents the total of a product’s qualities, which make it good for
use according to the destination, the reliability represents the capacity of
the product to maintain its quality during the entire usage time. Reliability
is the quality of the product extended through time. Reliability, maintenance,
availability and capacity related aspects have been treated distinctively up
to one moment. Analytically, the reliability represents the probability that
during a given period of time, a product will be flawless. The technological
capability or reliability represents way in which a technological system may
realize, on the entire process of fulfilling a mission, the corresponding
technological performances for its objectives. A unitary approach, considering
all the factors, in accordance to the operating conditions of technical
systems, lays the fundaments of an interdisciplinary theory, called the Theory
of safety during operation. The safety during operation, S, of a machinery or
of a technological system represents the way it will fulfill its mission,
being a function of availability A, reliability R, capacity C and maintenance
M
Keywords: Availability,
average time for good operation, maintenance, probabilistic diagrams, Duane
Issue 3, Volume 8,
March 2009
Title of the Paper: The Ramsey Model
with Logistic Population Growth and Benthamite Felicity Function Revisited
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Authors: Massimiliano
Ferrara, Luca Guerrini
Abstract: In this paper we extend the study done by Ferrara and Guerrini [12],
where two different research lines within the Ramsey model were joined
together: the one studying the role of a logistic population growth rate (Accinelli
and Brida [2]), and the one analyzing the effects of a Benthamite formulation
for the utility function. The results obtained in [12] for the special case of
a constant intertemporal elasticity of substitution (CIES) utility function
and a CobbDouglas production function are provided to be still true for a
general utility function and a neoclassical production function. We have that
the model is described by a three dimensional dynamical system, whose unique
nontrivial steady state equilibrium is a saddle point with a two dimensional
stable manifold. Consequently, the speed of convergence is determined by two
stable roots, rather than only one as in the basic Ramsey model. In addition,
in the special case of a CIES utility function and a CobbDouglas technology,
an explicit solution for the model can be derived, when capital’s share is
equal to the reciprocal of the intertemporal elasticity of substitution.
Keywords: Ramsey, Logistic
population, Benthamite, Saddle point, Exact solution
Title of the Paper: Genetic Algorithms
with NelderMead Optimization in the variational methods of Boundary Value
Problems
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Authors: Nikos E.
Mastorakis
Abstract: The pLaplacian equation is a generalization of the PDE of Laplace
Equation and in this paper, we present a way of its solution using Finite
Elements. Our method of Finite Elements leads to an Optimization Problem that
can be solved by an appropriate combination of Genetic Algorithms and NelderMead
. Our method is illustrated by a numerical example. Other methods for the
solution of other equations that contain the pLaplacian operator are also
discussed.
Keywords: Boundary Value
Problems, Finite Elements, Genetic Algorithms with NelderMead. pLaplacian,
nonNewtonian fluid flow
Title of the Paper: Troubled Asset
Relief Program, Bank Interest Margin and Default Risk in Equity Return: An
OptionPricing Model
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Authors: JyhJiuan Lin,
ChingHui Chang, JyhHorng Lin
Abstract: Will banks be willing to sell their toxic loans with the help of the
Troubled Asset Relief Program (TARP)? The answer is yes as long as bids are
high enough to tempt banks to deal. With the TARP’s help, an increase in the
toxic loans sold to the government increases the bank’s margin and decreases
the bank’s default probability in equity return when the bank encounters
greater risk. This paper concludes that setting up the TARP for the ‘bad bank’
solution may be a good move for retail banking, resulting in high margin and
low default risk when its target banks are willing sellers.
Keywords: Toxic Loans,
Interest Margin, Default Risk, Troubled Asset Relief Program
Title of the Paper: High Order
Alternating Group Explicit Finite Difference Method for Parabolic Equations
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Authors: Qinghua Feng,
Bin Zheng
Abstract: Based on the concept of domain decomposition we construct a class of
alternating group explicit method for fourth order parabolic equations.
Furthermore, an exponential type alternating group explicit method for 2D
convectiondiffusion equations is derived, which is effective in convection
dominant cases. Both of the two methods have the property of unconditional
stability and intrinsic parallelism. Domain decomposition and group computing
can be obtained in both of the two methods.
Keywords: Parabolic
equations, alternating group, parallel computation, unconditionally stable,
finite difference
Title of the Paper: Application of the
Alternating Group Explicit Method for ConvectionDiffusion Equations
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Authors: Qinghua Feng,
Bin Zheng
Abstract: Based on an unconditionally stable finite difference implicit
scheme, we present a concept of deriving a class of effective alternating
group explicit iterative method for periodic boundary value problem of
convectiondiffusion equations, and then give two iterative methods. The
methods are verified to be convergent, and have the property of parallelism.
Furthermore we construct an alternating group explicit difference method and
another iterative method. All of the methods are suitable for parallel
computation. Results of numerical experiments show that the methods are of
higher accuracy than the known methods in [1,2,6], and will not lead to
numerical instability in convection dominant case.
Keywords: Iterative
method, iterative method, parallel computing, alternating group, parabolic
equations
Issue 4, Volume 8,
April 2009
Title of the Paper: Finite Difference
Methods with Intrinsic Parallelism for Parabolic Equations
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Authors: Bin Zheng,
Qinghua Feng
Abstract: Based on eight saul’yev asymmetry schemes and the concept of domain
decomposition, a class of finite difference method (AGE) with intrinsic
parallelism for 1D diffusion equations is constructed. Stability analysis for
the method is done. We also pay attention to the implementation of the
parallel algorithms for 2D convectiondiffusion equations. Based on another
group of saul’yev asymmetry schemes and the CrankNicolson scheme we construct
a class of alternating group explicit CrankNicolson method(AGECN). Both of
the present methods are suitable for parallel computation. Stability analysis
are also given. In order to verify the methods, we present several numerical
examples at the end of the paper. Results of numerical examples show all the
methods are of high accuracy.
Keywords: Parallel
computing, domain decomposition, alternating group, parabolic equations,
finite difference
Title of the Paper: Finite Difference
Method And Iterative Method With Parallelism For Dispersive Equations
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Authors: Bin Zheng,
Qinghua Feng
Abstract: In this paper, based on the concept of domain decomposition and
alternating group, we construct a class of Finite Difference method for fifth
order dispersive equations, Stability Analysis for he method is given. Then we
construct a new alternating group explicit iterative method. Both the two
methods are suitable for parallel computation. Results of numerical
experiments show the methods are effective in computing.
Keywords: parallel
computing, dispersive equations, finite difference, iterative method,
asymmetry schemes, alternating group
Title of the Paper: Solution of the
SchrodingerMaxwell equations via Finite Elements and Genetic Algorithms with
NelderMead
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Authors: Nikos E.
Mastorakis
Abstract: In this paper the Numerical Solution of the system of PDEs of
SchrodingerMaxwell equations (with a general nonlinear term) via Finite
Elements and Genetic Algorithms with NelderMead is proposed. The method of
Finite Elements and Genetic Algorithms with NelderMead that has been proposed
by the author recently is also used. (Recently, the existence of a nontrivial
solution to the nonlinear SchrodingerMaxwell equations in R3, assuming on the
nonlinearity the general hypotheses introduced by Berestycki & Lions has been
proved).
Keywords: SchrodingerMaxwell
equations, Finite Elements, Genetic Algorithms with NelderMead
Title of the Paper: Existence,
Uniqueness and Finite Difference Solution for the Dirichlet problem of the
SchrodingerMaxwell Equations
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Authors: Nikos E.
Mastorakis
Abstract: In this paper, the existence, the Uniqueness and the Finite
Difference Scheme for the Dirichlet problem of the SchrodingerMaxwell
equations is going to be presented.
Keywords: SchrodingerMaxwell
equations, Finite Difference, Finite Difference Schemes
Title of the Paper: Applications of High
Dimensional Model Representations to Computer Vision
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Authors: Emre Demiralp
Abstract: A new and powerful method for matrix decomposition is developed in
this work. It is similar to singular value decomposition and the main idea
comes from the univariate approximation of a function, given on a planar
grid’s nodes, by two variable high dimensional model representation. The
proposed method is less iteration dependent than the singular value
decomposition and the components are determined via straightforward steps
containing recursions. It seems to have more capabilities than the singular
value decomposition as an alternative method. An illustrative application is
also given.
Keywords: Singular Value
Decomposition, High Dimensional Model Representation, Matrix Decomposition
Issue 5, Volume 8,
May 2009
Title of the Paper: Numerical
Integration of Bivariate Functions over a Non Rectangular Area by Using
Fluctuationlessness Theorem
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Authors: Ercan Gurvit,
N. A. Baykara, Metin Demiralp
Abstract: ”Fluctuation free matrix representation approximation Method”
developed by M. Demiralp can be used in approximating the multiple remainder
terms of the integral of the Multivariate Taylor expansion. This provides us
with a new numerical integration method for multivariate functions. However in
this paper instead of dealing with a single formula which takes care of the
multiple remainder terms, a new approach is undertaken. At every step of a
multivariate integration only one variable is taken care of. Thus an iterative
procedure which speeds up the computation rate is obtained.
Keywords: Multivariate
Functions, Fluctuationlessness Theorem, Numerical Integration, Explicit
Remainder Term, Taylor Expansion
Title of the Paper: Fluctuationlessness
Theorem and its Application to Boundary Value Problems of ODEs
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Authors: Nejla Altay,
Metin Demiralp
Abstract: A numerical method based on Fluctuationlessness Approximation, which
was developed recently, is constructed for solving Boundary Value Problems of
Ordinary Differential Equations on appropriately defined Hilbert Spaces. The
numerical solution is written in the form of a Maclaurin series. The unknown
coefficients of this series are determined by constructing an (n ? 2) unknown
containing linear system of equations. The eigenvalues of the independent
variable’s matrix representation are used in the construction of the matrices
and the vectors of the linear system. The numerical solution obtained by
Fluctuationlessness Approximation is then compared with the Maclaurin
coefficients of the analytical solution to observe the quality of the
convergence. Some illustrative examples are presented in order to give an idea
about the efficiency of the method explained here.
Keywords: Boundary Value
Problems, Eigenvalues, Fluctuationlessness Approximation, Hilbert Spaces
Title of the Paper: The Application of
the Fluctuation Expansion with Extended Basis Set to Numerical Integration
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Authors: Cosar
Gozukirmizi, Metin Demiralp
Abstract: According to the fluctuationlessness theorem the matrix
representation of a function can be approximated by the image of independent
variable operator’s matrix representation under that function. The independent
variable operator’s action is defined as the multiplication of the operand by
the independent variable. Hence itself and therefore its matrix representation
is universal, do not depend on the function. The application of this
approximation to numerical integration forms a quadrature whose structure can
be manipulated by changing the basis set of an ndimensional Hilbert space.
This work focuses on reflecting the effects of a complementary Hilbert space
to a restricted Hilbert subspace by forming the basis set as certain linear
combinations of some basis functions in order to improve the accuracy of the
numerical integration based on fluctuationlessness theorem.
Keywords: Numerical
Integration, Fluctuation Expansion, Fluctuationlessness Theorem, Hilbert
Spaces
Title of the Paper: A Reverse Technique
for Lumping High Dimensional Model Representation Method
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Authors: M. Alper Tunga,
Metin Demiralp
Abstract: An orthogonal hyperprismatic grid whose all nodes are accompanied by
the given function values can not be generally constructed due to the random
nature of the given function data. This prevents the reduction of the single
multivariate interpolation to more than one univariate or bivariate
interpolations even approximately. It is generally quite difficult to
determine an analytical structure for the target function in these problems.
Lumping HDMR method is an indexing based High Dimensional Model Representation
(HDMR) algorithm used to reconstruct these types of multivariate data by
imposing an indexing scheme to obtain an orthogonal geometry for the given
problem. By this way, the training of the given data can be accomplished. The
next problem is to determine a reverse algorithm for the testing data. This
work is about a new algorithm to find the correct coordinate of the given
testing data in the orthogonal geometry obtained through Lumping HDMR.
Keywords: Data
Partitioning, Multivariate Analysis, High Dimensional Model Representation,
Lumping HDMR
Title of the Paper: Truncation
Approximations For Two Term Recursive Universal Form Of Matrix Ordinary
Differential Equations
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Authors: Sevda Uskuplu,
Metin Demiralp
Abstract: This work focuses on the construction of an error bound formula for
the series solution to Okubo Form of a set linear ordinary differential
equation. Okubo Form is obtained using space extension concept which
introduces new unknowns into the equation under consideration at the expense
of a dimension growth. This is applied to the linear matrix ordinary
differential equations in this work.
Keywords: Error
estimation, Ordinary Differential Equations, Okubo form
Issue 6, Volume 8,
June 2009
Title of the Paper: Fluctuation Free
Matrix Representation Based Univariate Integration in Hybrid High Dimensional
Model Representation (HHDMR) Over Plain and Factorized HDMR
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Authors: Suha Tuna,
Burcu Tunga, N. Abdulbaki Baykara, Metin Demiralp
Abstract: High Dimensional Model Representation (HDMR) which was first
proposed fifteen years ago is still under development for the construction of
its new varieties. It is a finite term representation of a multivariate
function in terms of less variate functions. Its truncation at certain level
of variance serves as an approximation to the target function and the
truncation level is preferred to be kept at most bivariance for practical
applications. Plain HDMR is used for the functions highly additive while the
Factorized HDMR is designed for dominantly multiplicative functions. The
Hybrid HDMR (HHDMR) combines these two HDMR varieties into a new version of
HDMR and is expected to work more efficiently than plain HDMR and FHDMR. The
construction of HHDMR basically uses the components of plain HDMR since FHDMR
does the same. The definite integrals appearing in the definition of these
components are efficiently approximated by using the fluctuation free matrix
representation method which was recently developed by M. Demiralp.
Keywords: Multivariate
Functions, High Dimensional Model Representation, Approximation, Fluctuation
Free Matrix Representation
Title of the Paper: A Nonlinear
Perturbative Scheme to SolveWeight Optimization Problem of High Dimensional
Model Representation (HDMR)
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Authors: Burcu Tunga,
Metin Demiralp
Abstract: One way to increase the approximating quality of the High
Dimensional Model Representation (HDMR) truncations is to increase the
truncation order. However this is not generally desired for practical reasons
if the order climbs to the multivariances beyond the bivariance. In these
circumstances the other alternative is preferred. It is to change the
structure of HDMR. This can be done either by using a different but again
orthogonal geometry or by changing the structure of the weight function.
Weight optimization is based on the constancy maximization and in fact gives
different importances to the function values at different points of the HDMR
domain. Weight function is considered as the square of a linear combination of
certain basis functions and the linear combination coefficients are determined
to maximize the constancy. The resulting equations are nonlinear. This work
attempts to solve these equations by expanding unknowns around their certain
nominal values.
Keywords: Multivariate
Approximation, High Dimensional Model Representation, Perturbation Expansion
Title of the Paper: On the Solution of
pLaplacian for NonNewtonian Fluid Flow
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Authors: Nikos E.
Mastorakis, Hassan Fathabadi
Abstract: The pLaplacian, or the pLaplace operator, is a quasilinear
elliptic partial differential operator of 2nd order. In this paper, we examine
several numerican schemes and we investigate their solution of nonlinear
problems in fluid mechanics.
Keywords: Numerical
schemes, pLaplacian, nonNewtonian fluid flow, nonlinear diffusion, nonlinear
partial differential equation
Title of the Paper: On Different Types
of NonAdditive Set Multifunctions
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Authors: Anca Croitoru,
Alina Gavrilut, Nikos E. Mastorakis, Gabriel Gavrilut
Abstract: In this paper, we study different types of nonadditive set
multifunctions (such as: uniformly autocontinuous, nulladditive,
nullnulladditive), presenting relationships among them and some of their
properties regarding atoms and pseudoatoms. We also study nonatomicity and
nonpseudoatomicity of regular nulladditive set multifunctions defined on
the Baire (Borel respectively) ±ring of a Hausdorff locally compact space and
taking values in the family of nonempty closed subsets of a real normed
space.
Keywords: Uniformly
autocontinuous, nullnulladditive, (pseudo)atom, non(pseudo)atomic,
extension, regular, Darboux property
Title of the Paper: Fluctuationlessness
Theorem to Approximate Univariate Functions' Matrix Representations
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Authors: Metin Demiralp
Abstract: Matrix representation of functions are required to convert an
operator related problem to its algebraic counterpart over certain vectors and
matrices. The problems involving operators which are purely or partially
algebraic are most frequently encountered ones in applications. The algebraic
operator here has a Hilbert space domain defined over square integrable
univariate functions on a specified interval and its action on its argument is
just multiplication by a function. We focus on univariate functions for
simplicity in this very first step although the generalization to
multivariance seems to be rather straightforward. The main purpose of this
work is to introduce a conjecture to facilitate the numerical approximation of
the matrix representation of the above algebraic operator and then to prove it
to get an important theorem which seems to be capable of opening new very
efficient horizons in numerical analysis and in its applications. Theorem
states that the matrix representation of a univariate function is the image of
the matrix representation of the independent variable under the same function
for a finite Hilbert space. Illustrative numerical implementations are also
given.
Keywords: Matrix
Representation, Fluctuation Operator, Hilbert Spaces, Projection Operators,
Algebraic Multiplication Operators
Issue 7, Volume 8,
July 2009
Title of the Paper: A Cutting Plane
Method for Solving Convex Optimization Problems over the Cone of Nonnegative
Polynomials
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Authors: Iurie Caraus,
Ion Necoara
Abstract: Many practical problems can be formulated as convex optimization
problems over the cone of nonnegative univariate polynomials. We use a cutting
plane method for solving this type of optimization problems in primal form.
Therefore, we must be able to verify whether a polynomial is nonnegative, i.e.
if it does not have real roots or all real roots are multiple of even order.
In this paper an efficient method is derived to determine a scalar value for
which the polynomial is negative and in the case that such a value exists a
feasible cut is constructed. Our method is based on Sturm theorem, which
allows to determine the number of distinct roots of a polynomial on a given
interval, in combination with the bisection method. For numerical stability we
construct the associated Sturm sequence using Chebyshev basis, and thus we can
work with high degree polynomials, up to hundreds. Numerical results show the
efficiency of our new approach.
Keywords: Convex
optimization problems over the cone of nonnegative polynomials, cutting plane
method, Chebyshev polynomials, Sturm sequence, feasible cut
Title of the Paper: Image Enhancement
Algorithm based on Retinex for SmallBore Steel Tube Butt Weld's XRay Imaging
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Authors: Yaoyu Cheng, Yu
Wang, Yan Hu
Abstract: It is very common to use Xray digital detection for the Smallbore
steel tube butt weld. But the Xray images have some shortcomings such as that
contrast is not high, background noise is big, and the details can not be
shown obviously, these shortcomings take a great inconvenience for the
smallbore steel tube butt weld testing. So the detection efficiency can not
be increased. Based on this, the Retinex algorithm is discussed and analyzed,
such as singlescale of Retinex, multiscale of Retinex, alterable framework
of Retinex. Then it is applied to use an enhancement algorithm of improved
Alterable framework on Retinex, and use this enhancement algorithm for Xray
image. This enhancement algorithm do not ask for much contrast of original
image, which can effectively improve the original image contrast and image
quality, the details of the image achieve the best visual effects. After the
theoretical analysis and experimental results, we can see that, this
enhancement algorithm can effectively enhance the image contrast, inhibit the
background noise, compared with homomorphic filtering and histogram
equalization algorithm. The standard of the image which is processed by this
method can achieve the higher testing standard compared with homomorphic
filtering and histogram equalization algorithm.
Keywords: Radiographic
image, image enhancement, Retinex algorithm, singlescale Retinex algorithm,
Multiscale Retinex algorithm,alterable framework model, butt weld
Title of the Paper: Defect Detection and
Characteristics Description of Auto Hub Radiographic Image Based on SUSAN
Operation
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Authors: Yaoyu Cheng,
Yan Hu, Yu Wang
Abstract: The collected images’ target object is faint in the auto hub
realtime Xray detection, so it is easily making the miscarriage of justice
in the auto hub detection. Most of the current method of detection of defects
is by manual detection, so it is very difficult to improve detection
efficiency and detection accuracy. Aiming at these issues and combining with
the characteristics that auto hub’s image have so much noise source, it is
adopted SUSAN operator for defect images’ edge detection, which is based on
the image second partition, and it is achieved good results in edge detection
by this method . And then it carried through defect detected for the image,
such as, the number, level, center of gravity, area, and circle degree of
defects. This can effectively improve the detection efficiency and the
accuracy of detection. The experimental results show that the method is
feasible in practical applications, and it has strong antiinterference
ability, good realtime detection and high efficiency compared with
traditional methods.
Keywords: Auto hub, SUSAN
operation, mask, edge detection, Feature Description, Geometrical features,
Shape Features
Title of the Paper: How Many Are Good
Enough for the Adolescent Social Network Nomination
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Authors: HsiehHua Yang,
ChyiIn Wu, Man Kit Lei, HungJen Yang
Abstract: For social network analysis, the most common method used to generate
social network data is the method of Name Generator. Nonetheless, the number
of nomination has been an unsolved mystery for social networkers. Namely, for
each respondents, to name how many people are good enough to generate a stable
network, which is able to represent the truly association structure among
these respondents, still, is an empirical research question for researchers.
This study devoted to explore this question and to provide a preliminary
answer. A set of social network data was collected from a sample of Taipei
metropolitan junior high schools, including 44 classes. In each class the
students were asked to nominate ten best friends in the intimate order. It was
supposed that in each class has ten sociometric data for different nomination,
and the total amount of sociometric data was 440. The software UCINET6.0 was
applied to analyze the social network variables, and NEGOPY4.30 to define the
network position. Comparing the betweenness, constraint, and efficiency, this
study found that two names will generate more diverse network position with
unstable structure, three names are the minimum to get more stable network
structure, four or five names are needed to observe the links between boys and
girls, but more than five names seem to be redundancy.
Keywords: Social network,
Nomination number, Adolescents, Junior high school, Evaluation
Title of the Paper: Transient
Temperature Analysis of a Cylindrical Heat Equation
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Authors: KoTa Chiang,
G. C. Kuo, K.J Wang, Y. F. Hsiao, K.Y. Kung
Abstract: The method of superposition and separation variables is applied to
gain analytical solutions to the transient heat conduction for a two
dimensional cylindrical fin. The temperature distributions are generalized for
a linear combination of the product of Bessel function, Fourier series and
exponential type for nine different cases. The solutions presented in this
study can be used to verify the two or threedimensional numerical conduction
codes. Relevant connections with some other closelyrelated recent works are
also indicated.q
Keywords: Fourier series,
Heat conduction, Separation variables, Transcendent equation, Superposition
method, Temperature distribution
Title of the Paper: Efficient Algorithms
for HigherOrder Derivatives of the Continued Erlang Delay Function
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Authors: Jorge Sa
Esteves
Abstract: In this paper we analyze the partial derivatives of any order of the
continued Erlang delay function in the number of servers. Several properties
with strong analytical relations between the highorder derivatives of
Erlang’s B and C functions are established. Using these relations, three
algorithms are proposed for the numerical computation of the cited
derivatives. For comparison purposes, it is also generalized a numerical
method based on a quadrature procedure suggested by D. L. Jagerman [16]. All
the computational methods are compared in terms of stability, efficiency and
precision. Our study concludes that a recursive matrix relation presented in a
previous work [10, 11], may be used for the establishment of a simple and
reliable algorithm having the best performance considering the tradeoff of
the different criteria. Extensive computational results are presented and
discussed. In the sequel, a conjecture about the strict convexity of the first
derivative of Erlang delay function is presented and supported by numerical
evidence.
Keywords: Performance
Evaluation, Queueing Systems, Erlang’s B and C Formulas, Numerical
Differentiation
Title of the Paper: Nonparametric
Regression for Correlated Data
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Authors: Noor Akma
Ibrahim, Suliadi
Abstract: This paper considers nonparametric regression to analyze correlated
data. The correlated data could be longitudinal or clustered data. Some
developments of nonparametric regression have been achieved for longitudinal
or clustered categorical data. For data with exponential family distribution,
nonparametric regression for correlated data has been proposed using GEELocal
Polynomial Kernel (LPK). It was showed that in order to obtain an efficient
estimator, one must ignore within subject correlation. This means within
subject observations should be assumed independent, hence the working
correlation matrix must be an identity matrix. Thus to obtained efficient
estimates we should ignore correlation that exist in longitudinal data, even
if correlation is the interest of study. In this paper we propose
GEESmoothing spline to analyze correlated data and study the properties of
the estimator such as the bias, consistency and efficiency. We use natural
cubic spline and combine with GEE in estimation. We want to study numerically,
whether the properties of GEESmoothing spline are better than of GEELocal
Polynomial Kernel. Several conditions have been considered. i.e. several
sample sizes and several correlation structures. Using simulation we show that
GEESmoothing Spline is better than GEElocal polynomial. The bias of
pointwise estimator is decreasing with increasing sample size. The pointwise
estimator is also consistent even with incorrect correlation structure, and
the most efficient estimate is obtained if the true correlation structure is
used. We also give example using real data, and compared the result of the
proposed method with parametric method and GEESmoothing Spline under
independent assumption.
Keywords: Nonparametric
regression, Longitudinal binary data, Generalized estimating equation, Natural
cubic spline, Properties of estimator
Title of the Paper: Embedding Geodesic
and Balanced Cycles into Hypercubes
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Authors: PaoLien Lai,
ChangHsiung Tsai, HongChun Hsu
Abstract: A graph G is said to be pancyclic if it contains cycles of all
lengths from 4 to V (G) in G. For any two vertices u, v ? V (G), a cycle is
called a geodesic cycle with u and v if a shortest path joining u and v lies
on the cycle. Let G be a bipartite graph. For any two vertices u and v in G, a
cycle C is called a balanced cycle between u and v if dC(u, v) = max{dC(x, y)
 dG(x, u) and dG(y, v) are even, resp. for all x, y ? V (G) }. A bipartite
graph G is geodesic bipancyclic (respectively, balanced bipancyclic) if for
each pair of vertices u, v ? V (G), it contains a geodesic cycle
(respectively, balanced cycle) of every even length of k satisfying max{2dG(u,
v), 4} ? k ? V (G) between u and v. In this paper, we prove that Qn is
geodesic bipancyclic and balanced bipancyclic if n ? 2.
Keywords: Hypercube,
Interconnection networks, Edgebipancyclic, Geodesic bipancyclic, Balanced
bipancyclic
Title of the Paper: The Performance of
Robust Weighted Least Squares in the Presence of Outliers and Heteroscedastic
Errors
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Authors: Habshah Midi,
Md. Sohel Rana, A. H. M. Rahmatullah Imon
Abstract: The Ordinary Least Squares (OLS) method is the most popular
technique in statistics and is often use to estimate the parameters of a model
because of tradition and ease of computation. The OLS provides an efficient
and unbiased estimates of the parameters when the underlying assumptions,
especially the assumption of contant error variances (homoscedasticity), are
satisfied. Nonetheless, in real situation it is difficult to retain the error
variance homogeneous for many practical reasons and thus there arises the
problem of heteroscedasticity. We generally apply the Weighted Least Squares (WLS)
procedure to estimate the regression parameters when heteroscedasticity occurs
in the data. Nevertheless, there is evidence that the WLS estimators suffer a
huge set back in the presence of a few atypical observations that we often
call outliers. In this situation the analysis will become more complicated. In
this paper we have proposed a robust procedure for the estimation of
regression parameters in the situation where heteroscedasticity comes together
with the existence of outliers. Here we have employed robust techniques twice,
once in estimating the group variances and again in determining weights for
the least squares. We call this method Robust Weighted Least Squares (RWLS).
The performance of the newly proposed method is investigated extensively by
real data sets and Monte Carlo Simulations. The results suggest that the RWLS
method offers substantial improvements over the existing methods.
Keywords:
Heteroscedasticity, Outliers, Robust Estimation, Robust Weighted Least
Squares, Monte Carlo Simulation
Title of the Paper: Estimating
Regression Coefficients using Weighted Bootstrap with Probability
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Authors: Norazan M. R.,
Habshah Midi, A. H. M. R. Imon
Abstract: In this paper we propose a new Weighted Bootstrap with Probability (WBP).
The basic idea of the proposed bootstrap technique is to do resampling with
probabilities. These probabilities become the control mechanism for getting
good estimates when the original data set contain multiple outliers. Numerical
examples and simulation study are carried out to evaluate the performance of
the WBP estimates as compared to the Bootstrap 1 and DiagnosticBefore
Bootstrap estimates. The results of the study signify that the WBP method is
more efficient than the other two methods.
Keywords: Regression,
outliers, weighted bootstrap with probability, weighting function
Issue 8, Volume 8,
August 2009
Title of the Paper: Marangoni Convection
in a Variable Viscosity Fluid Layer with Feedback Control
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Authors: Norihan Md.
Arifin, Nurul Hafizah Zainal Abidin
Abstract: Feedback control was applied to the steady Marangoni convection in a
horizontal layer of fluid with variable viscosity and freeslip at the lower
boundary heated from below and cooled from above. Prediction for the onset of
convection are obtained from the analysis by numerical technique.The effects
of feedback control are studied by examining the critical Marangoni numbers
and wave numbers. It is shown that the onset of Marangoni convection with
variable viscosity can be delayed and the critical Marangoni number can be
increased through the use of feedback control.
Keywords: Linear stability
theory, Marangoni convection, Variable viscosity, Feedback control, Freeslip,
Deformable free surface
Title of the Paper: Complete
Identification of Permissible Sampling Rates for the FirstOrder Sampling of
MultiBand Bandpass Signals
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Authors: Yan Wu, Daniel
F. Linder
Abstract: The firstorder sampling of multiband bandpass signals with
arbitrary band positions is considered in this paper. Gaps between the
spectral subbands are utilized to achieve lower sampling rates than the
Nyquist. The lowest possible sampling rate along with other permissible
sampling rates is identified via a unique partition of the frequency axis.
With the complete identification of all the permissible sampling rates, a
necessary and sufficient sampling theorem for multiband bandpass signals is
presented in terms of a series of csincinterpolators.
Keywords: Multiband
bandpass signals, Sampling theorem, Firstorder sampling, Nyquist rate,
Permissible sampling rates, Aliasing, csincinterpolation
Title of the Paper: Solving Linear
Ordinary Differential Equations using Singly Diagonally Implicit RungeKutta
Fifth Order FiveStage Method
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Authors: Fudziah Ismail,
Nur Izzati Che Jawias, Mohamed Suleiman, Azmi Jaafar
Abstract: We constructed a new fifth order fivestage singly diagonally
implicit RungeKutta (DIRK) method which is specially designed for the
integrations of linear ordinary differential equations (LODEs). The
restriction to linear ordinary differential equations (ODEs) reduces the
number of conditions which the coefficients of the RungeKutta method must
satisfy. The best strategy for practical purposes would be to choose the
coefficients of the RungeKutta methods such that the error norm is minimized.
Thus, here the error norm obtained from the error equations of the sixth order
method is minimized so that the free parameters chosen are obtained from the
minimized error norm. The stability aspect of the method is also looked into
and found to have substantial region of stability, thus it is stable. Then a
set of test problems are used to validate the method. Numerical results show
that the new method is more efficient in terms of accuracy compared to the
existing method.
Keywords: RungeKutta,
Linear ordinary differential equations, Error norm
Title of the Paper: Some New Remarks
about LotkaVolterra System
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Authors: Camelia Pop,
Anania Aron
Abstract: LotkaVolterra system is a wellknown system used as mathematical
model in biology. It was proposed as model by Alfred Lotka (1925) and Vito
Volterra (1926). We are interested to study it from the mechanical geometry
point of view; more exactly we study the stability problem, the existence of
periodic solutions, the Lax formulation and numerical integration via Kahan
and LieTrotter integrators.
Keywords: HamiltonPoisson
realization, LotkaVolterra system, nonlinear stability, Arnold method,
LieTrotter integrator, Kahan integrator, Lax formulation
Title of the Paper: Nonlinear Growth
Models in the Age Measurement of the European Rabbits in Australia in the
Context of Alternative Models in Multivariate Statistics
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Authors: Adnan
Mazmanoglu, Ali Reha Unlu
Abstract: Examining the special model Lens = a exp{b / (Age + g)} which
belongs to Dudzinski and Mykytowycz (1961), and was used in a study made by
them to find the age of Oryctolagus Caniculus, which lives in Europe and is
known as the European rabbit, with live eye lens weight, we showed that
similar results can be obtained with the Gompertz and Logistic nonlinear
regression models. We determined that the results given by the models are
showing the goodness of fit, as a result of a statistical analysis.
Furthermore we showed that adding various parameters to Dudzinski and
Mykytowycz model will not change the results.
Keywords: Nonlinear
regression, logistic and gompertz model, gaussnewton iteration method, SPSS
Title of the Paper: Constructing
Knowledge in Graph Theory and Combinatorial Optimization
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Authors: Eva Milkova
Abstract: Graph theory and combinatorial optimization are powerful tools for
teachers allowing them to develop logical thinking of students, increase their
imagination and make them familiar with solutions to various practical
problems. The paper offers some ideas how to make the teaching of these
branches of applied mathematics and computer science more understandable and
attractive. A case study is described which introduces the minimum spanning
tree problem, its remarkable origin, and then its relation to the other
problems. The approach used for teaching and learning graph theory and
combinatorial optimization can serve as an inspiration for instruction of
other subjects as well.
Keywords: Graph Theory,
Graph Algorithms, Minimum Spanning Tree Problem, BreadthFirstSearch,
Education
Title of the Paper: Measurability and
Gould Integrability in Finitely Purely Atomic Multisubmeasure Spaces
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Authors: Alina Gavrilut,
Anca Croitoru, Nikos E. Mastorakis, Gabriel Gavrilut
Abstract: In this paper, we present some results concerning measurability,
Gould integrability and Lp spaces with respect to finitely purely atomic set
multifunctions.
Keywords: Finitely purely
atomic, atom, pseudoatom, multisubmeasure, measurable, Gould integral, Lp
space
Title of the Paper: Dynamical
Mathematical Models for Plates and Numerical Solution of Boundary Value and
Cauchy Problems for Ordinary Differential Equations
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Authors: Tamaz S.
Vashakmadze
Abstract: In the first part there are created and justified new 2D with
respect to spatial coordinates nonlinear dynamical mathematical models von
KarmanMindlinReissner(KMR) type systems of partial differential equations
for anisotropic porous, piezo, viscous elastic prismatic shells.
TruesdellCiarlet unsolved( even in case of isotropic elastic plates) problem
about physical soundness respect to von Karman system is decided. There is
find also new dynamical summand ( is Airy stress function) in the another
equation of von Karman type systems too. Thus the corresponding systems in
this case contains RayleighLamb wave processes not only in the vertical, but
also in the horizontal direction. For comlpleteness we also lead 2D
KirchhoffMindlinReissner type models for elastic plates of variable
thickness. Then if KMR type systems are 1D one respect to spatial coordinates
at first part for numerical solution of corresponding initialboundary value
problems we consider the finiteelement method using new class of Btype
splainfunctions. The exactness of such schemes depends from differential
properties of unknown solutions: it has an arbitrary order of accuracy respect
to a mesh width in case of sufficiently smoothness functions and Sard type
best coefficients characterizing remainder proximate members on less smoothing
class of admissible solutions. Corresponding dynamical systems represent
evolutionary equations for which the methods of Harmonic Analyses are
nonapplicable. In this connection for Cauchy problem suggests new schemes
having arbitrary order of accuracy and based on GaussHermite processes. This
processes are new even for ordinary differential equations.
Keywords: Elasticity, Poroviscosity,
Plate, Physical soundness, Finitedifference scheme, Gauss quadrature and
Hermite interpolation formula, Mesh width
Title of the Paper: On One
Generalization of Boundary Value Problem for Ordinary Differential Equations
on Graphs in the Threedimensional Space
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Authors: D. G.
Gordeziani, H. V. Meladze, T. D. Davitashvili
Abstract: The present work is the generalization of boundary value problem for
ordinary differential equations on graphs. This problem is investigated and
correctness of the stated problem is proved in [1]. The special attention is
given to construction and research of difference analogues. Estimation of
precision is given. The formulas of doublesweep method type are suggested for
finding the solution of obtained difference scheme. In this work the
boundaryvalue problems for Poisson’s equations in the threedimensional space
on some twodimensional structures with onedimensional common part is given
and investigated. This technique of investigation can be easily applied to the
more complex initial data and equations. The difference scheme for numerical
solution of this problem is constructed and estimation of precision is given.
Such problems have practical sense and they can be used for mathematical
modeling of specific problems of physics, engineering, ecology and so on.
Keywords: Differential
equations on graphs, Difference scheme
Title of the Paper: Asymptotics of
Solution and Finite Difference Scheme to a Nonlinear IntegroDifferential
Equations Associated with the Penetration of a Magnetic Field into a Substance
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Authors: Temur
Jangveladze, Zurab Kiguradze
Abstract: Asymptotics of solution and finite difference approximation of the
nonlinear integrodifferential equations associated with the penetration of a
magnetic field into a substance is studied. Asymptotic properties of solutions
for the initialboundary value problem with homogeneous as well as
nonhomogeneous Dirichlet boundary conditions are considered. The corresponding
finite difference scheme is studied. The convergence of this scheme is proven.
Numerical experiments are carried out.
Keywords: Nonlinear
integrodifferential equation, asymptotic behavior, finite difference scheme
Issue 9, Volume 8,
September 2009
Title of the Paper: On the Translation
of an Almost Linear Topology
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Authors: Gabriela
Apreutesei, Nikos E. Mastorakis, Anca Croitoru, Alina Gavrilut
Abstract: We present some characterizations of T1; T2 separation and
metrizability for the translation of an almost linear topology
Keywords: Almost linear
space, almost linear topological space, translation of a topology
Title of the Paper: Calibration and
Comparison of Schema Matchers
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Authors: Peter Martinek,
Balazs Villanyi, Bela Szikora
Abstract: Schemas used in various environments become more and more numerous,
though they do not comply to a universal standard. That is why the task of
schema matching has emerged and its main objective is to find means to map a
schema into another. Several initiations have occurred and algorithms have
been proposed to solve the problem. They muster highly enticing solutions,
though they have several flaws. We have reviewed the available algorithms and
implemented some of them. We found that the accuracy of these solutions is
strongly dependent on some well definable matcher characteristics, so if we
calibrate the matchers they perform a lot better. Taking into account this
fact we cannot compare matchers until after the necessary calibration. We
propose matcher independent procedures and mathematical formulas to perform
the highly desirable prerun configuration of candidate solutions. The
necessity of calibration implies that the unbiased comparison of solutions is
not possible until the configuration is performed. We also introduce the
technique of multiple thresholding which promises a better view of the result
list returned by the individual matchers.
Keywords: Optimization of
schema matching algorithms, Determine possible accuracy maxima, Similarity
measure methods
Title of the Paper: Classification
Approaches in OffLine Handwritten Signature Verification
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Authors: Bence Kovari,
Benedek Toth, Hassan Charaf
Abstract: The aim of offline signature verification is to decide, whether a
signature originates from a given signer based on the scanned image of the
signature and a few images of the original signatures of the signer. Although
the verification process can be thought to as a monolith component, it is
recommended to divide it into loosely coupled phases (like preprocessing,
feature extraction, feature matching, feature comparison and classification)
allowing us to gain a better control over the precision of different
components. This paper focuses on classification, the last phase in the
process, covering some of the most important general approaches in the field.
Each approach is evaluated for applicability in signature verification,
identifying their strength and weaknesses. It is shown, that some of these
weak points are common between the different approaches and can partially be
eliminated with our proposed solutions. To demonstrate this, several local
features are introduced and compared using different classification
approaches. Results are evaluated on the database of the Signature
Verification Competition 2004.
Keywords: Signature
verification; offline; classification, shape descriptor, neural network
Title of the Paper: Optimal Analysis MAX
MIN of the Dependency between the Energy Consumption of Electrical Actions and
their Operation Safety
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Authors: Ilie Mitran,
Florin Dumitru Popescu
Abstract: The study sets off the relation between the reliability of an
electric drive system and the specific consumption of energy through the
efficiency function used as a quantizing analytical element for the medium
energy consumption throughout the safe functioning period of the system. The
stability moments of the system as well as the collapse moments are determined
using the MINMAX or MAXMIN optimizing methods and also elements belonging to
the theory of probabilities and differential calculus. An essential obtained
result is represented by the dependence relation between the reduction of the
specific power consumption which corresponds to a certain increase in the safe
operation of the system. Economically, knowing these results leads to
considerable saves of materials, human resources and finances. The explanation
of these economic consequences is connected primarily with the fact that the
results presented are an immediate consequence of correlating fundamental
elements of electrical actions, system reliability and economic analysis and
calculation (based mainly on minimizing different types of costs). The purpose
of this paper is to determine, mainly, the specific electrical energy
consumption and the reliability function for extreme properties (minimum for
the specific electrical energy consumption and maximum for the reliability
function). Secondly, to determine the equilibrium point of the specific
electrical energy consumption and of the reliability of the analyzed system.
Thirdly, to draw conclusions that will allow the economic analysis.
Keywords: Reliability,
standardized energy consumption, stability moment, efficiency function
Title of the Paper: Diagonally Stable
Tridiagonal Switched Linear Systems
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Authors: Isabel Bras
Abstract: A stability analysis is carried out for certain classes of switched
linear systems with tridiagonal structure, under arbitrary switching signal.
This analysis is made using diagonal common quadratic Lyapunov functions.
Namely, necessary and sufficient conditions for the existence of such Lyapunov
functions are proposed for second order switched systems and for third order
switched systems with Toeplitz tridiagonal structure.
Keywords: Switched linear
systems, quadratic Lyapunov stability, diagonal stability
Title of the Paper: On Modeling
Ubiquitous Cloud: Estimation of Traffic
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Authors: Shuji Kawasaki,
Masakazu Higuchi, Hitomi Murakami
Abstract: The Ubiquitous Cloud is a concept of largescale information service
network as a social infrastructure. It is featured by realworld context
information extraction, user information profiling and selfcofiguration/control
of network. The objective of the research is to evaluate the network traffic
theoretically and thus give a guideline of network design. In this paper, we
especially consider those traffic factors that are related to movement of
mobile users and reatime services, and thus discuss some necessary
requirements for the network specification.
Keywords:
Contextawareness, profiling, selfreconfiguration, spatiotemporal dynamics,
longrange dependence, selfsimilarity, elephantmice flow
Title of the Paper: On Existence and
Uniqueness of the Cauchy Problem for Parabolic Equations with Unbounded
Coefficients
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Authors: Huashui Zhan
Abstract: A new kind of entropy solution to the Cauchy problem for strong
degenerate parabolic equations with unbounded coefficients is quoted. Suppose
that u0 2 L1(RN), E = fEig 2 (L2(QT ))N and divE 2 L2(QT ), by a modified
regularization method and choosing a suitable test function, the BV estimates
are got, the existence of the entropy solution is obtained. At last, by
Kruzkov bivariables method, the stability of the solutions is obtained too.
Keywords: Cauchy problem,
Degenerate parabolic equation, Existence, Unbounded coefficient
Title of the Paper: Introduction to the
Elliptical Trigonometry
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Authors: Claude Bayeh,
Mouafac Bernard, Nazih Moubayed
Abstract: Trigonometry is a branch of mathematics that deals with relations
between sides and angles of triangles. It has some relationship to geometry,
though there is disagreement on exactly what that relationship is. For some,
trigonometry is just a subtopic of geometry. The trigonometric functions are
very important in technical subjects like science, engineering, architecture,
and even medicine. In this paper, the elliptical trigonometry is introduced in
order to be in the future a part of the trigonometry topic. Thus, the
definition of this original part is presented. The elliptic trigonometric
functions are also defined. The importance of these functions in producing
different signals and forms are analyzed and discussed.
Keywords: Mathematics,
geometry, trigonometry, trigonometric functions, derivative functions,
simulation
Title of the Paper: A ThreeDimension
DoublePopulation Thermal Lattice BGK Model for Simulation of Natural
Convection Heat Transfer in a Cubic Cavity
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Authors: C. S. Nor
Azwadi, S. Syahrullail
Abstract: In this paper, a doublepopulation thermal lattice Boltzmann was
applied to solve three dimensional, incompressible, thermal fluid flow
problem. The simplest lattice BGK D3Q6 model was proposed to determine the
temperature field while D3Q15 or D3Q19 for the density and velocity fields.
The simulation of natural convection in a cubic cavity with Prandtl number
0.71 and Rayleigh number ranging from 103 to 105 were carried out and compared
with the published results in literature. It was observed that the combination
of D3Q6 and D3Q19 produces better numerical stability and accuracy compared to
D3Q6 with D3Q15 for the simulation at high Rayleigh numbers.
Keywords: Double
population, lattice Boltzmann, distribution function, BGK collision, natural
convection
Issue 10, Volume 8,
October 2009
Title of the Paper: Gravitational
Capture Using a FourBody Model
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Authors: Alexandre
Lacerda Machuy, Antonio Fernando Bertachini De Almeida Prado, Terezinha De
Jesus Stuchi
Abstract: A spacecraft (or any particle with negligible mass) suffers a
gravitational capture when its orbit changes from hyperbolic (small positive
energy) around a celestial body into elliptic (small negative energy) using
only gravitational forces. The force responsible for this modification in the
orbit of the spacecraft is the gravitational force of the third and the fourth
bodies involved in the dynamics. Those forces are equivalent of a zero cost
control applied to the spacecraft, equivalent to a continuous thrust. One of
the most important applications of this property is the construction of
trajectories to the Moon. The concept of gravitational capture is combines
with the principles of the gravityassisted maneuver and the bielliptic
transfer orbit, to generate a trajectory that requires a fuel consumption
smaller than the one required by the Hohmann transfer. The present paper study
the energy required for the ballistic gravitational capture in a dynamical
model that has the presence of four bodies. Those bodies are assumed to follow
the assumptions of the bicircular model. In particular, the
EarthMoonSunSpacecraft system is considered.
Keywords: Astrodynamics,
Celestial Mechanics, Space Trajectories, Gravitational Capture, Space Missions
Title of the Paper: A Preprocessing
Procedure for Fixing the Binary variables in the Capacitated Facility Location
Problem through Pairing and Surrogate Constraint Analysis
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Authors: Maria A.
Osorio, Abraham Sanchez
Abstract: The Osorio and Glover (2003) use of dual surrogate analysis is
exploited to fix variables in capacitated facility location problems (CFLP).
The surrogate constraint is obtained by weighting the original problem
constraints by their associated dual values in the LP relaxation. A known
solution is used to convert the objective function in a constraint that forces
the solution to be less or equal to it. The surrogate constraint is paired
with the objective function to obtain a combined constraint where negative
variables are replaced by complemented variables and the resulting constraint
used to fix binary variables in the model.
Keywords: Capacitated
Facility Location Problem, Surrogate Constraints, Duality, Constraint Pairing
Title of the Paper: A Comparative Study
of Hybrid, Neural Networks and Nonparametric Regression Models in Time Series
Prediction
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Authors: Dursun Aydin,
Mammadagha Mammadov
Abstract: This paper presents a comparative study of the hybrid models, neural
networks and nonparametric regression models in time series forecasting. The
components of these hybrid models are consisting of the nonparametric
regression and artificial neural networks models. Smoothing spline, regression
spline and additive regression models are considered as the nonparametric
regression components. Furthermore, various multilayer perceptron algorithms
and radial basis function network model are regarded as the artificial neural
networks components. The performances of these models are compared by
forecasting the series of number of produced Cars and Domestic product per
capita (GDP) data occurred in Turkey. This comparisons show that hybrid models
proposed in this paper have denoted much more excellent performance than the
hybrid models in literature.
Keywords: Time series,
Neural networks, Multilayer perceptrons, Radial basis function, Nonparametric
regression, Additive regression model, Hybrid models
Title of the Paper: A Mathematical
Theory of Psychological Dynamics
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Authors: Alin Gilbert
Sumedrea, Livia Sangeorzan
Abstract: The psychological dynamics is governed by the
”observableunobservable” systemic ratio. The plausible existence of the
dynamics of the psychological laws is justified by the presence of a complex
psychophysiological apparatus which changes the informational biofeedback
into energy. The psychological insight represented by the (unobservable)
psychological soft component obeys the functional models [6] which define the
psychological system. The psychological Gordian knot consists in identifying
the manner in which the unobservable psychological fact changes into
physiology and vice versa. The psychological literature is well represented,
especially by the behavior models of the physiological hard component [1],
[7], [17], [18]. This paper tries to develop a mathematical theory of
psychological insight. The purpose is to create an unifying theory between the
functionality of the psychological soft and of the physiological hard –
having, from our point of view, the capacity to solve the Gordian knot – based
on the results of this paper.
Keywords: Amplitude of the
tensional state, Extinction of the tensional state, Lie group, Metrics,
Neuropsychological activation, Psychological experience, Tensional dynamics
Title of the Paper: Convergence Theorems
for TotallyMeasurable Functions
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Authors: Anca Croitoru,
Alina Gavrilut, Nikos E. Mastorakis
Abstract: We establish some convergence theorems for sequences of
totallymeasurable functions with respect to a submeasure of finite variation.
We also present relationships among different types of convergences such as
convergence in submeasure, almost uniformly convergence, convergence in Lp
spaces.
Keywords:
Totallymeasurable, convergence, submeasure, Lp space
Issue 11, Volume 8,
November 2009
Title of the Paper: WeightDecay
Regularization in Reproducing Kernel Hilbert Spaces by VariableBasis Schemes
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Authors: Giorgio Gnecco,
Marcello Sanguineti
Abstract: The optimization problems associated with various regularization
techniques for supervised learning from data (e.g., weightdecay and Tikhonov
regularization) are described in the context of Reproducing Kernel Hilbert
Spaces. Suboptimal solutions expressed by sparse kernel models with a given
upper bound on the number of kernel computational units are investigated.
Improvements of some estimates obtained in Comput. Manag. Sci., vol. 6, pp.
5379, 2009 are derived. Relationships between sparseness and generalization
are discussed.
Keywords: Learning from
data, regularization, weight decay, suboptimal solutions, rates of
approximation
Title of the Paper: Sensivity and
Stability of Singular Systems under Proportional and Derivative Feedback
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Authors: M. Isabel
GarciaPlanas
Abstract: We consider triples of matrices (E; A;B), representing singular
linear time invariant systems in the form Ex_ (t) = Ax(t) + Bu(t), with E;A 2
Mp£n(C) and B 2 Mn£m(C), un der proportional and derivative feedback. Using
geometrical techniques we obtain miniversal deformations that permit us to
study sensivity and structural stability of singular systems.
Keywords: Singular linear
systems, proportional and derivative feedback, canonical reduced form,
structural invariants, structural stability
Title of the Paper: A Study of the
Inservice Hot Spot and Attendance Model of Professional Development
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Authors: LungHsing Kuo
Abstract: The purpose of this study was to present a way to identify the
inservice hot spot and create an attendance model based upon the profile
information and distance away from the hot spot. Empirical data was gathered
for verifying purpose. It was argued that distance for joining professional
development could be a factor affecting the attendance. The research data were
collected from 9824 senior high school teachers who attended inservice
advancement education activities from January to November in 2008. The
teachers' profile information was collected from “Nationwide Teacher
Inservice Education Information Web” (http://inservice.edu.tw/) database. And
then Google Earth was drawn upon to get the latitude and longitude of each
teacher’s working site and the Discipline Centers’ sites in which teachers
attended inservice advancement education activities to obtain the straight
distance. Besides, the TWD67 system—the Route Guide System devised by
Institute of Transportation, Ministry of Transportation and Communications,
Taiwan, R.O.C. was applied to obtain the distance by road. The descriptive
statistics, ttests, and oneway ANOVA were used to analyze the data. The
results of the study indicated that “hot spots” of inservice advancement
education activities which were held by Discipline Centers and which senior
high school teachers attended were mainly located in Taipei City and Kaohsiung
City. A total of ten background variables of teachers were examined to compare
mean group differences (gender, age, educational background, marital status,
additionally administrative duty, first registered specialty, total of
inservice teachers' registered specialties, school type, school size, and
school location). There were differences in the straight distance and distance
by road among teachers’ age, educational background, marital status, first
registered specialty, total of inservice teachers' registered specialties,
school type, school size, and school location.
Keywords: Inservice Hot
Spot, Professional Development, Attendance, High School Curriculum Guideline,
Discipline Centers, Inservice advancement education, straight distance,
distance by road
Title of the Paper: The Coupled Method
FuzzyAHP Applys to Solve Multicriteria Decision Making Problems
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Authors: Xinpei Jiang,
Bao Zheng, Liying Wang
Abstract: The multicriteria decision making (MCDM)problems with fuzzy
preference information on alternatives are essential problems of the
importance of weighting and ranking. In order to solve this problem,
Analytical Hierarchy Process(AHP) and fuzzy comprehensive evaluation method
are coupled to form a new approach named FuzzyAHP.This method is different
from the traditional FAHP,which used to facilitate the pairwise comparison
process and avoid the complex and unreliable process of comparing fuzzy
utilities.It utilizes the advantage of AHP on computing index weight and
comparing index in the same row than at ranking and the advantage of fuzzy
comprehensive evaluation method on establishing quantitative indexes
membership and qualitative indexes membership and classifying level.Finally, a
numerical example is presented to clarify the methodology ,the model
evaluation results showed that the proposed system is able to provide very.
good solution both in accuracy, and speed for the top managers.
Keywords: MCDM, Fuzzy ,
AHP, index , weighing, membership degree, matrix
Title of the Paper: Global
Diversification, Hedging Diversification, and Default Risk in Bank Equity: An
OptionPricing Model
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Authors: JyhHorng Lin,
JyhJiuan Lin, Rosemary Jou
Abstract: Many banks diversify their operations, either across different
national markets (global diversification), across different borrowers by
offsetting credit risks (hedging diversification), or both. Can multiple
diversifications provide greater safety for banks? This paper aims to answer
this question by using an optionbased pricing model to formulate the default
risk in bank equity returns under global and hedging diversifications. In
particular, we apply Vassalou and Xing’s (2004) formula, which is a nonlinear
optionbased function of the default probability of an individual bank’s
equity return. This formula is calculated using the contingent claim
methodology of Black and Scholes (1973) and Merton (1974). We find that the
extent of global diversification may provide greater safety for banks, but
also that the extent of hedging diversification may not.
Keywords: Default Risk,
International Lending Diversification, Loan Portfolio Swap
Issue 12, Volume 8,
December 2009
Title of the Paper: Numerical
Simulations for Dynamic Stochastic and Hybrid Models of Internet Networks
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Authors: G. Mircea, M.
Neamtu, A. L. Ciurdariu, D. Opris
Abstract: In this paper, we consider Internet models, which respond to a
congestion signal from the network described by a stochastic and hybrid
differential equation. We consider Internet networks with one source and r
access links, as well as with r sources and one access link. We analyze the
conditions for the existence of a solution and the algorithms needed to
determine the solution. We carry out numerical simulations for certain
parameter values.
Keywords: Internet models,
networks, dynamic stochastic models, stochastic delay differential equation,
Euler method, numerical simulations
Title of the Paper: Optimal Control
Applied to a Ramsey Model with Taxes and Exponential Utility
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Authors: Olivia Bundau
Abstract: In this paper we analyze an economical growth model with taxes and
exponential utility in continuous and infinite time. This economical growth
model leads to an optimal control problem. The necessary and sufficient
conditions for optimality are given. Using the optimality conditions we prove
the existence, uniqueness and stability of the study state for a differential
equations system. Also we have investigated the dependence of the steady state
(k?, c?) on the growth rate of the labor force n and the effects of fiscal
policy changes on welfare.
Keywords: Mathematical
models applied in economies, endogenous growth, optimal policy
Title of the Paper: The Study of
MicroFluid Boundary Layer Theory
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Authors: Long Li,
Huashui Zhan
Abstract: Similar to the study of Prandtl system, by the wellknown Oleinik
linear method, the paper gets existence, uniqueness of the solution for an
initial boundary problem.
Keywords: Microfluid
boundary layer, Uniqueness, Existence, Classical solution
Title of the Paper: An Improved Method
for Successive Data Schism and Interpolation
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Authors: Ahmed N. H.
Alnuaimy, Mahamod Ismail, Mohd A. M. Ali, Kasmiran Jumari
Abstract: This paper presents an improved type of data schism and
interpolation called AlnuaimyMahamod Interpolation based on the mean and
variance to calculate the entire point between two known points. A new
mathematical method is developed for interpolation from a given set of data
points in a plane and for fitting a smooth curve to the points. This method is
devised in such a way that the resultant curve will pass through the given
points and will appear smooth and natural. Data schism and interpolation
describes the behaviors of the calculated points which behave as bacteria
reproduction. This type of interpolation based on calculation of the mean and
the variance of two adjacent points and modify of these calculate values by
named factors to be used to calculate the entire points. Our type of
interpolation can be working as linear midpoint interpolation, linear
interpolation and smooth curve fitting.
Keywords: Interpolation,
midpoint interpolation, linear interpolation and smooth curve fitting
