• Journal of electromagnetic engineering and science
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• v.2 no.2
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• pp.87-92
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• 2002

A short-ended electromagnetically coupled coaxial dipole array antenna is investigated theoretically. The antenna has an advantage of structural simplicity. The integral equations are derived for the proposed structure by use of the Fourier transform and mode expansion, and the simultaneous linear equations are obtained. The slot electric field and strip current are obtained by solving the simultaneous linear equations. The effects of slot and strip numbers on the radiation efficiency, beamwidth and directivity gain of the antenna are presented.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.113-126
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• 2015

Recently, Liu and Wang generalized Appell's and Lauricella's hypergeometric functions. Motivated by the work of Liu and Wang, the main object of this paper is to present new generalizations of Appell's and Lauricella's hypergeometric functions. Some integral representations, transformation formulae, differential formulae and recurrence relations are obtained for these new generalized Appell's and Lauricella's functions.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.97-109
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• 2006

In this paper, the authors introduce new classes of p-valent functions defined by Dziok-Srivastava linear operator and the multiplier transformation and study their properties by using certain first order differential subordination and superordination. Also certain inclusion relations are established and an integral transform is discussed.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.491-502
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• 2005

The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.487-503
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• 2019

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

• Geophysics and Geophysical Exploration
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• v.2 no.1
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• pp.17-25
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• 1999

A traveltime tomography has been carried out by transforming electromagnetic data in frequency domain to wave-like domain. The transform uniquely relates a field satisfying a diffusion equation to an integral of the corresponding wavefield. But direct transform of frequency domain magnetic fields to wave-field domain is ill-posed problem because the kernel of the integral transform is highly damped. In this study, instead of solving such an unstable problem, it is assumed that wave-fields in transformed domain can be approximated by sum of ray series. And for further simplicity, reflection and refraction energy compared to that of direct wave is weak enough to be neglected. Then first arrival can be approximated by calculating the traveltime of direct wave only. But these assumptions are valid when the conductivity contrast between background medium and the target anomalous body is low enough. So this approach can only be applied to the models with low conductivity contrast. To verify the algorithm, traveltime calculated by this approach was compared to that of direct transform method and exact traveltime, calculated analytically, for homogeneous whole space. The error in first arrival picked by this study was less than that of direct transformation method, especially when the number of frequency samples is less than 10, or when the data are noisy. Layered earth model with varying conductivity contrasts and inclined dyke model have been successfully imaged by applying nonlinear traveltime tomography in 30 iterations within three CPU minutes on a IBM Pentium Pro 200 MHz.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• The Journal of Advanced Prosthodontics
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• v.1 no.1
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• pp.26-30
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• 2009

STATEMENT OF PROBLEM. Qualitative and semi-quantitative methods have been developed for TMJ sound classification, but the criteria presented are completely inhomogeneous. Thus, to develop more objective criteria for defining TMJ sounds, electroacoustical systems have been developed. We used Joint vibration analysis in the BioPAK system(Bioresearch Inc., Milwaukee, USA) as the electrovibratography. PURPOSE. The aim of this study was to examine the TMJ sounds with repect to frequency spectra patterns and the integral > 300 Hz /< 300 Hz ratios via six-months follow-up. MATERIAL AND METHODS. This study was done before and after the six-months recordings with 20 dental school students showed anterior disk displacement with reduction. Joint vibrations were analyzed using a mathematical technique known as the Fast Fourier Transform. RESULTS. In this study Group I and Group II showed varied integral > 300 /< 300 ratios before and after the six-months recordings. Also, by the comparative study between the integral > 300 /< 300 ratios and the frequency spectrums, it was conceivable that the frequency spectrums showed similar patterns at the same location that the joint sound occurred before and after the six-months recordings. while the frequency spectrums showed varied patterns at the different locations that the joint sound occurred before and after six-month recordings, it would possibly be due to the differences in the degree of internal derangement and/or in the shape of the disc. CONCLUSIONS. It is suggested that clinicians consider the integral > 300 /< 300 ratios as well as the frequency spectrums to decide the starting-point of the treatment for TMJ sounds.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.425-440
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• 2005

In this paper, the behavior of a crack between two half-planes of functionally graded materials subjected to arbitrary tractions is resolved using a somewhat different approach, named the Schmidt method. To make the analysis tractable, it is assumed that the Poisson's ratios of the mediums are constants and the shear modulus vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite different from those adopted in previous works. Numerical examples are provided to show the effect of the crack length and the parameters describing the functionally graded materials upon the stress intensity factor of the crack. It can be shown that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation method. As a special case, when the material properties are not continuous through the crack line, an approximate solution of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near the crack tips is negligible. It is found that the stress singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.