• Korean Journal of Optics and Photonics
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• v.13 no.6
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• pp.473-478
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• 2002

Circular slab waveguides are conformally mapped into straight waveguides. In the outer cladding region with monotonically increasing index profile, modified Airy functions (MAF) of traveling-wave form are introduced to express the leaky mode. Field distributions and losses calculated by the proposed method are compared with those obtained by the WKB (Wentzel-Kramers-Brillouin) method. Detailed numerical examples are presented and compared with the conventional WKB methods, demonstrating our method not only allows a converging field at turning points but also guarantees fine accuracy.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.411-421
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• 2007

The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.37 no.2
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• pp.28-37
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• 2000

An almost exact eigenvalue equation for optical fibers with graded-index profile Is derived mathematically based on a combination of the modified Airy functions and the WKB trial solution. By applying proper boundary conditions, a phase shift correction term $\delta$ is found out which improves the inherent error problems of the conventional WKB method. It is shown through computer simulations that results of the derived eigenvalue equation are in excellent agreement with those of the finite-element method.

• Advances in Computational Design
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• v.5 no.2
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• pp.147-175
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• 2020

To achieve appropriate stresses, two new rectangular elements are presented in this study. For reaching this aim, a complementary energy functional is used within an element for the analysis of plane problems. In this energy form, the Airy stress function will be used as a functional variable. Besides, some basic analytical solutions are found for the stress functions. These trial functions are matched with each element number of degrees of freedom, which leads to a number of equations with the anonymous constants. Subsequently, according to the principle of minimum complementary energy, the unknown constants can be expressed in terms of displacements. This system can be rewritten in terms of the nodal displacement. In this way, two new hybrid-rectangular triangular elements are formulated, which have 16 and 40 degrees of freedom. To validate the outcomes, extensive numerical studies are performed. All findings clearly demonstrate accuracies of structural displacements, as well as, stresses.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.875-883
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• 2017

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$, where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.3
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• pp.345-352
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• 2013

In this research, a study on stress shape functions was conducted to analyze the contact stress problem by using a hybrid photoelasticity. Because the contact stress problem is generally solved as a half-plane problem, the relationship between two analytical stress functions, which are compositions of the Airy stress function, was similar to one of the crack problem. However, this relationship in itself could not be used to solve the contact stress problem (especially one with singular points). Therefore, to analyze the contact stress problem more correctly, stress shape functions based on the condition of two contact end points had to be considered in the form of these two analytical stress functions. The four types of stress shape functions were related to the stress singularities at the two contact end points. Among them, the primary two types used for the analysis of an O-ring were selected, and their validities were verified in this work.

• Journal of information and communication convergence engineering
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• v.12 no.2
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• pp.83-88
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• 2014

The simultaneous suppression of sidelobes and the sharpening of the central peak in the process of diffraction pattern detection based on asymmetric apodization have been investigated. Asymmetric apodization is applied to a semicircular array of two-dimensional (2D) aperture functions, which is a series of 'coded-phase arrays of semicircular rings randomly distributed over the central circular region of a pupil function' and is similar to that used in the field of diffractive optics. The point spread function (PSF) of an imaging system with asymmetric apodization of the discrete type has been found to possess a good side with suppressed sidelobes, whereas its bad side contains enhanced sidelobes. Further, the diffracted field characteristics are obtained in the presence of these aperture functions. Asymmetric apodization is helpful in improving the performance of the optical gratings or 2D arrays used in real-time imaging techniques.

• Steel and Composite Structures
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• v.31 no.3
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• pp.243-259
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• 2019

This study deals with the nonlinear static analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical shells subjected to axial load based on the classical shell theory. Detailed studies for both nonlinear buckling and post-buckling behavior of truncated conical shells. The truncated conical shells are reinforced by single-walled carbon nanotubes which alter according to linear functions of the shell thickness. The nonlinear equations are solved by both the Airy stress function and Galerkin method based on the classical shell theory. In numerical results, the influences of various types of distribution and volume fractions of carbon nanotubes, geometrical parameters, elastic foundations on the nonlinear buckling and post-buckling behavior of FG-CNTRC truncated conical shells are presented. The proposed results are validated by comparing with other authors.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.543-560
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• 2006

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

• JSTS:Journal of Semiconductor Technology and Science
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• v.10 no.3
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• pp.203-212
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• 2010

In this paper, we present an analytical model for the first eigen energy level ($E_0$) of the carriers in the inversion layer in present generation MOSFETs, having ultrathin gate oxides and high substrate doping concentrations. Commonly used approaches to evaluate $E_0$ make either or both of the following two assumptions: one is that the barrier height at the oxide-semiconductor interface is infinite (with the consequence that the wave function at this interface is forced to zero), while the other is the triangular potential well approximation within the semiconductor (resulting in a constant electric field throughout the semiconductor, equal to the surface electric field). Obviously, both these assumptions are wrong, however, in order to correctly account for these two effects, one needs to solve Schrodinger and Poisson equations simultaneously, with the approach turning numerical and computationally intensive. In this work, we have derived a closed-form analytical expression for $E_0$, with due considerations for both the assumptions mentioned above. In order to account for the finite barrier height at the oxide-semiconductor interface, we have used the asymptotic approximations of the Airy function integrals to find the wave functions at the oxide and the semiconductor. Then, by applying the boundary condition at the oxide-semiconductor interface, we developed the model for $E_0$. With regard to the second assumption, we proposed the inclusion of a fitting parameter in the wellknown effective electric field model. The results matched very well with those obtained from Li's model. Another unique contribution of this work is to explicitly account for the finite oxide-semiconductor barrier height, which none of the reported works considered.