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## ‣ Análise térmica de ligas Al-Si com adição de inoculante.; Thermal analysis of the Al-Si alloys with addition of inoculant.

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 18/12/2009
Português

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#Alumínio#Aluminum inoculation#Análise térmica#Fourier analysis#Grain refinement#Refino de grão#Thermal analysis

As ligas Al-Si hipoeutéticas têm grande importância na indústria de fundição de peças devido às excelentes propriedades de fundição, como baixo ponto de fusão e alta fluidez. A análise térmica das curvas de resfriamento medidas durante a solidificação destas ligas pode ser utilizada para controlar a formação da macroestrutura de grãos. Esta análise envolve a determinação das temperaturas de início e final de solidificação, bem como a evolução da fração de sólido com o tempo a partir da chamada análise térmica de Fourier. Apesar desta técnica ter sido aplicada a diversas ligas comerciais, existem poucos dados referentes às ligas Al-Si binárias. Os dados são ainda mais escassos quando se deseja examinar o efeito do tratamento de inoculação do metal líquido para refino de grão. O objetivo do presente trabalho é investigar o efeito do tratamento de inoculação nas ligas binárias Al-3%Si, Al-7%Si e Al-11%Si através da análise térmica e metalográfica. Foram obtidos lingotes cilíndricos a partir do vazamento da liga Al-Si líquida com ou sem a adição de inoculante na forma da liga mãe Al-3%Ti-1%B, adicionada para se obter um teor nominal de 0,05%Ti. Curvas de resfriamento foram medidas a partir de termopares inseridos no interior da cavidade do molde...

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## ‣ Analysis of body shape for differentiating among species of rajids

Fonte: Blackwell Publishing Ltd
Publicador: Blackwell Publishing Ltd

Tipo: Artigo de Revista Científica

Publicado em //2013
Português

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This study sought to differentiate the species of skates encountered in Gulf St Vincent (GSV), South Australia using normalized elliptical Fourier analysis of body shape. Significant intraspecific variation was observed among whole body shapes. This was overcome by limiting subsequent analyses to the anterior snout region, where significant differences in shape were detected among the species examined and provided a high degree of classification success for the skates of GSV. More generally, this approach has the potential to provide a cost- and time-efficient means of discrimination among species of skates. Further research is required to investigate the potentially confounding effects of sexual dimorphism and ontogenetic variation in growth to improve the efficacy of the body shape analysis of the skates and batoids species in general. In addition, this approach requires considerable development to facilitate implementation in a fishery setting.; C. Izzo and E. B. Drew

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## ‣ Fourier analysis of facial profiles of young twins

Fonte: Wiley-Liss
Publicador: Wiley-Liss

Tipo: Artigo de Revista Científica

Publicado em //2000
Português

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#Humans#Facies#Cross-Sectional Studies#Environment#Twins, Dizygotic#Twins, Monozygotic#Fourier Analysis#Child#Child, Preschool#Victoria#Female

Twins studies provide a powerful approach to determining the relative contribution of genetics and environment to observed variation. Such studies assume trait differences in monozygous (MZ) twins are due to environmental factors and those in dizygous (DZ) twins are due to both genetic and environmental factors. This study quantitated facial profiles of twins using Fourier equations, determining their value in profile analysis and the assessment of the genetic contribution to facial shape. Standardized profile slide photographs of 79 pairs of 4-6 year-old twins (37 MZ pairs, 42 DZ pairs) were scanned and x and y coordinates were extracted from each profile using sellion and Camper's plane as references. The coordinates were subjected to Fourier analysis and the normalised vertex projection coefficients were studied. The means of the differences between coefficients for MZ co-twins did not differ significantly from that of DZ co-twins, although the DZ group showed higher mean differences in the higher harmonics. Subjective examination of superimposed reconstructions showed wider variation between DZ co-twins than MZ co-twins. Correct classification of twins by discriminant function analysis using Fourier coefficients was similar for both groups (MZ: 70.3%; DZ: 73.8%). Fourier analysis could quantitate facial profiles of young children and differentiate some details...

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## ‣ Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

Fonte: SpringerOpen
Publicador: SpringerOpen

Tipo: Artigo de Revista Científica

Publicado em //2013
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#Heisenberg uncertainty principle#Local fractional Fourier operator#Schrödinger equation##Fractal time-space

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty
principle within local fractional Fourier analysis. The Schrödinger equation and
Heisenberg uncertainty principles are structured within local fractional operators.

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## ‣ Some Topics in Fourier Analysis and Approximation Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/12/1996
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This manuscript presents shortly the results obtained by participants of the
scientific seminar which is held more than twenty years under leadership of the
author at Donetsk University. In the list of references main publications are
given. These results are published in serious scientific journals and reported
at various conferences, including international ones at Moscow,ICM66;
Kaluga,1975; Kiev,1983; Haifa,1994; Z\"urich,ICM94; Moscow,1995. The area of
investigation is the Fourier analysis and the theory of approximation of
functions. Used are methods of classical analysis including special functions,
Banach spaces, etc., of harmonic analysis in finitedimensional Euclidean space,
of Diophantine analysis, of random choice, etc. The results due to the author
and active participants of the seminar, namely E. S. Belinskii, O. I.
Kuznetsova, E. R. Liflyand, Yu. L. Nosenko, V. A. Glukhov, V. P. Zastavny, Val.
V. Volchkov, V. O. Leontyev, and others, are given. Besides the participants of
the seminar and other mathematicians from Donetsk, many mathematicians from
other places were speakers at the seminar, in particular, A.A. Privalov, Z.A.
Chanturia, Yu.A. Brudnyi, N.Ya. Krugljak, V.N. Temlyakov, B.D. Kotlyar, A.N.
Podkorytov, M.A. Skopina...

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## ‣ Discrete Fourier analysis on a dodecahedron and a tetrahedron

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/03/2008
Português

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A discrete Fourier analysis on the dodecahedron is studied, from which
results on a tetrahedron is deduced by invariance. The results include Fourier
analysis in trigonometric functions, interpolation and cubature formulas on
these domains. In particular, a trigonometric Lagrange interpolation on the
tetrahedron is shown to satisfy an explicit compact formula and the Lebesgue
constant of the interpolation is shown to be in the order of $(\log n)^3$.; Comment: 31 pages, multiple figures

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## ‣ The study of translational tiling with Fourier Analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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This is a survey on the subject of the title corresponding to three lectures
I gave in June 2001 at the Workshop on Fourier Analysis and Convexity, at the
Universita di Milano-Biccoca.; Comment: 52 pages, 15 figures 2 references added (Leptin and Mueller, Mackey)
from first version

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## ‣ Fourier analysis methods for the compressible Navier-Stokes equations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/07/2015
Português

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In the last three decades, Fourier analysis methods have known a growing
importance in the study of linear and nonlinear PDE's. In particular,
techniques based on Littlewood-Paley decomposition and paradifferential
calculus have proved to be very efficient for investigating evolutionary fluid
mechanics equations in the whole space or in the torus. We here give an
overview of results that we can get by Fourier analysis and paradifferential
calculus, for the compressible Navier-Stokes equations. We focus on the Initial
Value Problem in the case where the fluid domain is the whole space or the
torus in dimension at least two, and also establish some asymptotic properties
of global small solutions. The time decay estimates in the critical regularity
framework that are stated at the end of the survey are new, to the best of our
knowledge.

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## ‣ Optimization of the Multigrid-Convergence Rate on Semi-structured Meshes by Local Fourier Analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/10/2014
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In this paper a local Fourier analysis for multigrid methods on tetrahedral
grids is presented. Different smoothers for the discretization of the Laplace
operator by linear finite elements on such grids are analyzed. A four-color
smoother is presented as an efficient choice for regular tetrahedral grids,
whereas line and plane relaxations are needed for poorly shaped tetrahedra. A
novel partitioning of the Fourier space is proposed to analyze the four-color
smoother. Numerical test calculations validate the theoretical predictions. A
multigrid method is constructed in a block-wise form, by using different
smoothers and different numbers of pre- and post-smoothing steps in each
tetrahedron of the coarsest grid of the domain. Some numerical experiments are
presented to illustrate the efficiency of this multigrid algorithm.

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## ‣ Fourier analysis of the CGMN method for solving the Helmholtz equation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The Helmholtz equation arises in many applications, such as seismic and
medical imaging. These application are characterized by the need to propagate
many wavelengths through an inhomogeneous medium. The typical size of the
problems in 3D applications precludes the use of direct factorization to solve
the equation and hence iterative methods are used in practice. For higher
wavenumbers, the system becomes increasingly indefinite and thus good
preconditioners need to be constructed. In this note we consider an accelerated
Kazcmarz method (CGMN) and present an expression for the resulting iteration
matrix. This iteration matrix can be used to analyze the convergence of the
CGMN method. In particular, we present a Fourier analysis for the method
applied to the 1D Helmholtz equation. This analysis suggests an optimal choice
of the relaxation parameter. Finally, we present some numerical experiments.

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## ‣ Discrete Fourier analysis on fundamental domain of $A_d$ lattice and on simplex in $d$-variables

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/09/2008
Português

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#Mathematics - Classical Analysis and ODEs#Mathematics - Numerical Analysis#42A15, 42B05, 65D05, 65D32

A discrete Fourier analysis on the fundamental domain $\Omega_d$ of the
$d$-dimensional lattice of type $A_d$ is studied, where $\Omega_2$ is the
regular hexagon and $\Omega_3$ is the rhombic dodecahedron, and analogous
results on $d$-dimensional simplex are derived by considering invariant and
anti-invariant elements. Our main results include Fourier analysis in
trigonometric functions, interpolation and cubature formulas on these domains.
In particular, a trigonometric Lagrange interpolation on the simplex is shown
to satisfy an explicit compact formula and the Lebesgue constant of the
interpolation is shown to be in the order of $(\log n)^d$. The basic
trigonometric functions on the simplex can be identified with Chebyshev
polynomials in several variables already appeared in literature. We study
common zeros of these polynomials and show that they are nodes for a family of
Gaussian cubature formulas, which provides only the second known example of
such formulas.; Comment: 39 pages, 10 figures

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## ‣ A Physically-Intuitive Method for Calculation of the Local Lattice Constant from a High-Resolution Transmission Electron Microscopy Image by Fourier Analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/09/2013
Português

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We have developed a physically-intuitive method to calculate the local
lattice constant as a function of position in a high-resolution transmission
electron microscopy image by performing a two-dimensional fast Fourier
transform. We apply a Gaussian filter with appropriate spatial
full-width-half-max (FWHM) bandwidth to the image centered at the desired
location to calculate the local lattice constant (as opposed to the average
lattice constant). Fourier analysis of the filtered image yields the vertical
and horizontal lattice constants at this location. The process is repeated by
stepping the Gaussian filter across the image to produce a set of local lattice
constants in the vertical and horizontal direction as a function of position in
the image. The method has been implemented in a freely available tool on
nanoHUB.; Comment: 5 pages, 3 figures

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## ‣ A new approach to the Fourier analysis on semi-direct products of groups

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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56.86043%

Let $H$ and $K$ be locally compact groups and also $\tau:H\to Aut(K)$ be a
continuous homomorphism and $G_\tau=H\ltimes_\tau K$ be the semi-direct product
of $H$ and $K$ with respect to the continuous homomorphism $\tau$. This paper
presents a novel approach to the Fourier analysis of $G_\tau$, when $K$ is
abelian. We define the $\tau$-dual group $G_{\hat{\tau}}$ of $G_\tau$ as the
semi-direct product $H\ltimes_{\hat{\tau}}\hat{K}$, where $\hat{\tau}:H\to
Aut(\hat{K})$ defined via (\ref{A}). We prove a Ponterjagin duality Theorem and
also we study $\tau$-Fourier transforms on $G_\tau$. As a concrete application
we show that how these techniques apply for the affine group and also we
compute the $\tau$-dual group of Euclidean groups and the Weyl-Heisenberg
groups.; Comment: This paper has been withdrawn by the author due to a crucial sign
error in equations and references

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## ‣ On higher order Fourier analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/03/2012
Português

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We develop a theory of higher order structures in compact abelian groups. In
the frame of this theory we prove general inverse theorems and regularity
lemmas for Gowers's uniformity norms. We put forward an algebraic
interpretation of the notion "higher order Fourier analysis" in terms of
continuous morphisms between structures called compact $k$-step nilspaces. As a
byproduct of our results we obtain a new type of limit theory for functions on
abelian groups in the spirit of the so-called graph limit theory. Our proofs
are based on an exact (non-approximative) version of higher order Fourier
analysis which appears on ultra product groups.; Comment: arXiv admin note: substantial text overlap with arXiv:1010.6211

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## ‣ On a local Fourier analysis for overlapping block smoothers on triangular grids

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/10/2015
Português

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A general local Fourier analysis for overlapping block smoothers on
triangular grids is presented. This analysis is explained in a general form for
its application to problems with different discretizations. This tool is
demonstrated for two different problems: a stabilized linear finite element
discretization of Stokes equations and an edge-based discretization of the
curl-curl operator by lowest-order N\'ed\'elec finite element method. In this
latter, special Fourier modes have to be considered in order to perform the
analysis. Numerical results comparing two- and three-grid convergence factors
predicted by the local Fourier analysis to real asymptotic convergence factors
are presented to confirm the predictions of the analysis and show their
usefulness.

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## ‣ Discrete Fourier analysis, Cubature and Interpolation on a Hexagon and a Triangle

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/12/2007
Português

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Several problems of trigonometric approximation on a hexagon and a triangle
are studied using the discrete Fourier transform and orthogonal polynomials of
two variables. A discrete Fourier analysis on the regular hexagon is developed
in detail, from which the analysis on the triangle is deduced. The results
include cubature formulas and interpolation on these domains. In particular, a
trigonometric Lagrange interpolation on a triangle is shown to satisfy an
explicit compact formula, which is equivalent to the polynomial interpolation
on a planer region bounded by Steiner's hypocycloid. The Lebesgue constant of
the interpolation is shown to be in the order of $(\log n)^2$. Furthermore, a
Gauss cubature is established on the hypocycloid.; Comment: 29 pages

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## ‣ Establishing a direct connection between detrended fluctuation analysis and Fourier analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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To understand methodological features of the detrended fluctuation analysis
(DFA) using a higher-order polynomial fitting, we establish the direct
connection between DFA and Fourier analysis. Based on an exact calculation of
the single-frequency response of the DFA, the following facts are shown
analytically: (1) in the analysis of stochastic processes exhibiting a
power-law scaling of the power spectral density (PSD), $S(f) \sim f^{-\beta}$,
a higher-order detrending in the DFA has no adverse effect in the estimation of
the DFA scaling exponent $\alpha$, which satisfies the scaling relation $\alpha
= (\beta+1)/2$; (2) the upper limit of the scaling exponents detectable by the
DFA depends on the order of polynomial fit used in the DFA, and is bounded by
$m + 1$, where $m$ is the order of the polynomial fit; (3) the relation between
the time scale in the DFA and the corresponding frequency in the PSD are
distorted depending on both the order of the DFA and the frequency dependence
of the PSD. We can improve the scale distortion by introducing the corrected
time scale in the DFA corresponding to the inverse of the frequency scale in
the PSD. In addition, our analytical approach makes it possible to characterize
variants of the DFA using different types of detrending. As an application...

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## ‣ Using cylindrical algebraic decomposition and local Fourier analysis to study numerical methods: two examples

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/02/2015
Português

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Local Fourier analysis is a strong and well-established tool for analyzing
the convergence of numerical methods for partial differential equations. The
key idea of local Fourier analysis is to represent the occurring functions in
terms of a Fourier series and to use this representation to study certain
properties of the particular numerical method, like the convergence rate or an
error estimate.
In the process of applying a local Fourier analysis, it is typically
necessary to determine the supremum of a more or less complicated term with
respect to all frequencies and, potentially, other variables. The problem of
computing such a supremum can be rewritten as a quantifier elimination problem,
which can be solved with cylindrical algebraic decomposition, a well-known tool
from symbolic computation.
The combination of local Fourier analysis and cylindrical algebraic
decomposition is a machinery that can be applied to a wide class of problems.
In the present paper, we will discuss two examples. The first example is to
compute the convergence rate of a multigrid method. As second example we will
see that the machinery can also be used to do something rather different: We
will compare approximation error estimates for different kinds of
discretizations.; Comment: The research was funded by the Austrian Science Fund (FWF): J3362-N25

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## ‣ Shape analysis of different populations of clams in relation to their geographical structure

Fonte: Zoological Society of London
Publicador: Zoological Society of London

Tipo: Artículo
Formato: 22195 bytes; application/pdf

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#Ruditapes decussatus#Ruditapes philippinarum#geographical variation#image analysis#elliptic Fourier analysis#multivariate classification

10 pages, 6 figures, 5 tables.; Bivalves are excellent candidates for geographically based studies of the morphological variation in individuals of different populations based on the analysis of their shape profiles. In this study, we quantified the overall shell shape differences in individuals of different populations of Ruditapes decussatus and Ruditapes philippinarum in relation to their geographical and genetic distances. A total of 395 and 124 individuals of R. decussatus (nine populations) and R. philippinarum (four populations), respectively, were sampled in different Mediterranean and Atlantic coastal locations. Pictures of the left valve were taken from all individuals. Their profiles were analysed using elliptic Fourier analysis. Mean outlines were computed. In order to classify different individuals for species, the coefficients of harmonic equations were analysed by partial least square discriminant analysis and soft independent modelling of class analogy. The results showed a high percentage of correct classification (99%) between the two species in the independent test. We found that the morphological distance between R. philippinarum and R. decussatus is higher than the morphological distance among populations of the same species. The absence of correspondence between the geographical location and the pattern of morphological and genetic variation indicates the occurrence of a reaction norm in the morphological adaptation of shell shapes to different local environmental conditions.; We would like to thank Davide Cascione for his help during the process of image acquisition. Jacopo Aguzzi is a Fellow of the ‘Juan de la Cierva’ Postdoctoral Program (MECSpain).; Peer reviewed

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## ‣ The determination of short circuits and grounding faults in electric power systems using time-frequency analysis

Fonte: Journal of Energy in Southern Africa
Publicador: Journal of Energy in Southern Africa

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/05/2015
Português

Relevância na Pesquisa

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#Fourier analysis#short circuits in electrical power systems#modelling electrical power systems#time-frequency analysis

In order to ensure that electrical energy reaches consumers uninterrupted, researchers constantly try to improve power transmission lines. To realize this improvement, probable faults should be analysed through every known method, and new methods should also be implemented. In this study, firstly, the Keban power transmission line located in the Eastern Anatolia region of Turkey was modelled. After that, probable short circuit scenarios were applied on the model, and the short circuit faults in the scenarios were analysed by using the Fourier analysis. The Fourier analysis is a mathematical method that is used as an effective way to determine the sudden changes in the frequency and time band. The study was successful in determining phase and grounding faults through the analyses of the scenarios using Fourier analysis. The fact that the mathematical method was applied on the probable scenarios on a physical model increases the importance of the study.

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