Abstract: Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.
Abstract: Saddlepoint approximations is one of the tools to obtain
an expressions for densities and distribution functions. We approximate
the densities of the observed gaps between the hypopnea events
using the Huzurbazar saddlepoint approximation. We demonstrate the
density of a maximum likelihood estimator in exponential families.
Abstract: Both the minimum energy consumption and
smoothness, which is quantified as a function of jerk, are generally
needed in many dynamic systems such as the automobile and the
pick-and-place robot manipulator that handles fragile equipments.
Nevertheless, many researchers come up with either solely
concerning on the minimum energy consumption or minimum jerk
trajectory. This research paper proposes a simple yet very interesting
when combining the minimum energy and jerk of indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of the minimum energy, the minimum jerk and combining them
together are found using the dynamic optimization methods together
with the numerical approximation. This is to allow us to simulate
and compare visually and statistically the time history of state inputs
employed by combining minimum energy and jerk designs. The
numerical solution of minimum direct jerk and energy problem are
exactly the same solution; however, the solutions from problem of
minimum energy yield the similar solution especially in term of
tendency.
Abstract: The design problem of Infinite Impulse Response (IIR)
digital filters is usually expressed as the minimization problem of
the complex magnitude error that includes both the magnitude and
phase information. However, the group delay of the filter obtained
by solving such design problem may be far from the desired group
delay. In this paper, we propose a design method of stable IIR digital
filters with prespecified maximum group delay errors. In the proposed
method, the approximation problems of the magnitude-phase and
group delay are separately defined, and these two approximation
problems are alternately solved using successive projections. As a
result, the proposed method can design the IIR filters that satisfy the
prespecified allowable errors for not only the complex magnitude but
also the group delay by alternately executing the coefficient update
for the magnitude-phase and the group delay approximation. The
usefulness of the proposed method is verified through some examples.
Abstract: In comparison to the original SVM, which involves a
quadratic programming task; LS–SVM simplifies the required
computation, but unfortunately the sparseness of standard SVM is
lost. Another problem is that LS-SVM is only optimal if the training
samples are corrupted by Gaussian noise. In Least Squares SVM
(LS–SVM), the nonlinear solution is obtained, by first mapping the
input vector to a high dimensional kernel space in a nonlinear
fashion, where the solution is calculated from a linear equation set. In
this paper a geometric view of the kernel space is introduced, which
enables us to develop a new formulation to achieve a sparse and
robust estimate.
Abstract: In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.
Abstract: The nickel and gold nanoclusters as supported
catalysts were analyzed by XAS, XRD and XPS in order to
determine their local, global and electronic structure. The present
study has pointed out a strong deformation of the local structure of
the metal, due to its interaction with oxide supports. The average
particle size, the mean squares of the microstrain, the particle size
distribution and microstrain functions of the supported Ni and Au
catalysts were determined by XRD method using Generalized Fermi
Function for the X-ray line profiles approximation. Based on EXAFS
analysis we consider that the local structure of the investigated
systems is strongly distorted concerning the atomic number pairs.
Metal-support interaction is confirmed by the shape changes of the
probability densities of electron transitions: Ni K edge (1s →
continuum and 2p), Au LIII-edge (2p3/2 → continuum, 6s, 6d5/2 and
6d3/2). XPS investigations confirm the metal-support interaction at
their interface.
Abstract: This paper is an extension of a previous work where a diagonally implicit harmonic balance method was developed and applied to simulate oscillatory motions of pitching airfoil and wing. A more detailed study on the accuracy, convergence, and the efficiency of the method is carried out in the current paperby varying the number of harmonics in the solution approximation. As the main advantage of the method is itsusage for the design optimization of the unsteady problems, its application to more practical case of rotor flow analysis during forward flight is carried out and compared with flight test data and time-accurate computation results.
Abstract: The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p
Abstract: In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw
Abstract: In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To
this purpose, we consider two stages of approximation.
First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems
and optimal control problems. Finally numerical examples is
proposed.
Abstract: In this paper, we were introduces a skin detection
method using a histogram approximation based on the mean shift
algorithm. The proposed method applies the mean shift procedure to a
histogram of a skin map of the input image, generated by comparison
with standard skin colors in the CbCr color space, and divides the
background from the skin region by selecting the maximum value
according to brightness level. The proposed method detects the skin
region using the mean shift procedure to determine a maximum value
that becomes the dividing point, rather than using a manually selected
threshold value, as in existing techniques. Even when skin color is
contaminated by illumination, the procedure can accurately segment
the skin region and the background region. The proposed method may
be useful in detecting facial regions as a pretreatment for face
recognition in various types of illumination.
Abstract: An analytical solution for dispersion of a solute in the
peristaltic motion of a couple stress fluid in the presence of magnetic
field with both homogeneous and heterogeneous chemical reactions is
presented. The average effective dispersion coefficient has been found
using Taylor-s limiting condition and long wavelength approximation.
The effects of various relevant parameters on the average effective
coefficient of dispersion have been studied. The average effective
dispersion coefficient tends to decrease with magnetic field parameter,
homogeneous chemical reaction rate parameter and amplitude ratio
but tends to increase with heterogeneous chemical reaction rate
parameter.
Abstract: A computationally simple approach of model order
reduction for single input single output (SISO) and linear timeinvariant
discrete systems modeled in frequency domain is proposed
in this paper. Denominator of the reduced order model is determined
using fuzzy C-means clustering while the numerator parameters are
found by matching time moments and Markov parameters of high
order system.
Abstract: A self-association model has been used to understand
the concentration dependence of free energy of mixing (GM), heat of
mixing (HM), entropy of mixing (SM), activity (a) and microscopic
structures, such as concentration fluctuation in long wavelength limit
(Scc(0)) and Warren-Cowley short range order parameter ( 1
α )for Cu-
Tl molten alloys at 1573K. A comparative study of surface tension of
the alloys in the liquid state at that temperature has also been carried
out theoretically as function of composition in the light of Butler-s
model, Prasad-s model and quasi-chemical approach. Most of the
computed thermodynamic properties have been found in agreement
with the experimental values. The analysis reveals that the Cu-Tl
molten alloys at 1573K represent a segregating system at all
concentrations with moderate interaction. Surface tensions computed
from different approaches have been found to be comparable to each
other showing increment with the composition of copper.
Abstract: The density estimates considered in this paper comprise
a base density and an adjustment component consisting of a linear
combination of orthogonal polynomials. It is shown that, in the
context of density approximation, the coefficients of the linear combination
can be determined either from a moment-matching technique
or a weighted least-squares approach. A kernel representation of
the corresponding density estimates is obtained. Additionally, two
refinements of the Kronmal-Tarter stopping criterion are proposed
for determining the degree of the polynomial adjustment. By way of
illustration, the density estimation methodology advocated herein is
applied to two data sets.
Abstract: In seismic survey, the information regarding the
velocity of compression wave (Vp) as well as shear wave (Vs) are
very useful especially during the seismic interpretation. Previous
studies showed that both Vp and Vs determined by above methods
are totally different with respect to each other but offered good
approximation. In this study, both Vp and Vs of consolidated granite
rock were studied by using ultrasonic testing method and seismic
refraction method. In ultrasonic testing, two different condition of
rock are used which is dry and wet. The differences between Vp and
Vs getting by using ultrasonic testing and seismic refraction were
investigated and studied. The effect of water content in granite rock
towards the value of Vp and Vs during ultrasonic testing are also
measured. Within this work, the tolerance of the differences between
the velocity of seismic wave getting from ultrasonic testing and the
velocity of seismic wave getting from seismic refraction are also
measured and investigated.