• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.747-775
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• 2020

In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, $$(P)\;\{(-{\Delta}_p)^su={\lambda}{\mid}u{\mid}^{q-2}u+{\frac{{\mid}u{\mid}^{p{^*_s}(t)-2}u}{{\mid}x{\mid}^t}}{\hspace{10}}in\;{\Omega},\\u=0{\hspace{217}}in\;{\mathbb{R}}^N{\backslash}{\Omega},$$ where Ω ⊂ ℝ^N is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < t < sp < N, 1 < q < p < p^∗_s where $p^*_s={\frac{N_p}{N-sp}}$, $p^*_s(t)={\frac{p(N-t)}{N-sp}}$, are the fractional critical Sobolev and Hardy-Sobolev exponents respectively. The fractional p-laplacian (-∆_p)^su with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by $\displaystyle(-{\Delta}_p)^su(x)=2{\lim_{{\epsilon}{\searrow}0}}\int{_{{\mathbb{R}}^N{\backslash}{B_{\epsilon}}}}\;\frac{{\mid}u(x)-u(y){\mid}^{p-2}(u(x)-u(y))}{{\mid}x-y{\mid}^{N+ps}}dy$, x ∈ ℝ^N. The main goal of this work is to show how the usual variational methods and some analysis techniques can be extended to deal with nonlocal problems involving Sobolev and Hardy nonlinearities. We also prove that for some α ∈ (0, 1), the weak solution to the problem (P) is in C^1,α(${\bar{\Omega}}$).

• Korean Journal of Optics and Photonics
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• v.22 no.6
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• pp.247-255
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• 2011

The optical performance of LLF(Lenticular Lens Film)-based backlight was studied by using optical simulation as functions of the aspect ratio and the refractive index of lenticular lenses. In order to perform reliable simulation, the BSDF(bi-directional scattering distribution function) of the scattering dots on the bottom surface of the light guide plate was obtained as a superposition of the Lambertian and the elliptic Gaussian distribution components by comparing the experimental results and the simulation for the luminance distribution on the light guide. Based on this approach, an appropriate BSDF of the scattering dots of the light guide was constructed. The resultant values of the optimized aspect ratio and the refractive were found to be 1.25 and 1.65, respectively. In spite of the hybrid aspects of LLF incorporating both diffusing and collimating functions, the optical performance, in particular the on-axis luminance of LLF-based backlight was inferior by about 20% compared to that of conventional backlights adopting one prism film. However, the combination of two lenticular lens films resulted in comparable luminance gain as well as smooth decrease in the luminance with the viewing angle without exhibiting any side lobes.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.24 no.2
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• pp.84-88
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• 2012

A numerical skill for effective treatment of inclined boundaries in a finite element method is introduced. A finite element method has been frequently used to simulate hydraulic phenomena in a coastal zone since it can be applied to irregular and complex geometry. In case elliptic partial equations are governing equations for a finite element model, however, there is a difficulty in treating boundary conditions properly for cases in which boundaries are vertically inclined. In this study, a method to treat such inclined boundaries using Bessel functions for a finite element method is introduced and compared with analytical solutions.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.651-659
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• 2001

The main purpose of this paper is to present an analytical method for free vibration of stepped horizontally curved members on two-parameter elastic foundation. The ordinary differential equations governing the free vibration of such beams are derived as non-dimensional forms including the effects of rotatory inertia and shear deformation. The governing equations are solved numerically for the circular, parabolic, sinusoidal and elliptic curved beams with hinged-hinged, hinged-clamped and clamped-clamped end constraints. As the numerical results, the lowest four natural frequency parameters are presented as the functions of various non-dimensional system parameters. Also the typical mode shapes are presented.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.673-682
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• 1997

The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.787-797
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• 1986

An implicit approach is employed to obtain a general boundary integral formulation of axisymmetric elastic problems in terms of a pair of singular integral equations. The corresponding kernel functions from the solutions of Navier's equation are derived by applying a three dimensional integral and a direct axisymmetrical approach. A numerical discretization schem including the evaluation of Cauchy principal values of the singular integral is described. Finally the typical axisymmetric elastic models are analyzed, i.e. the hollow sphere, the constant thickness and the V-notched round bar.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.917-926
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• 1994

Let ($M, G_M, F$) be a (p+q)-dimensional Riemannian manifold with a foliation F of codimension q and a bundle-like metric $g_M$ with respect to F ([9]). Aside from the Laplacian $\bigtriangleup_g$ associated to the metric g, there is another differnetial operator, the Jacobi operator $J_D$, which is a second order elliptic operator acting on sections of the normal bundle. Its spectrum isdiscrete as a consequence of the compactness of M. The study of the spectrum of $\bigtriangleup_g$ acting on functions or forms has attracted a lot of attention. In this point of view, the present authors [7] have studied the spectrum of the Laplacian and the curvature of a compact orientable cosymplectic manifold. On the other hand, S. Nishikawa, Ph. Tondeur and L. Vanhecke [6] studied the spectral geometry for Riemannian foliations. The purpose of the present paper is to study the relation between two spectra and the transversal geometry of cosymplectic foliations. We shall be in $C^\infty$-category. Manifolds are assumed to be connected.

• Journal of Yeungnam Medical Science
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• v.39 no.2
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• pp.98-107
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• 2022

Background: Stroke patients usually experience damage to multiple functions and a long rehabilitation period. Hence, there is a large volume of patient clinical information. It thus takes a long time for clinicians to identify the patient's information and essential pieces of information may be overlooked. To solve this, we stored the essential clinical information of stroke patients in a blockchain and implemented the blockchain technology using the Java programming language. Methods: We created a mini blockchain to store the medical information of patients using the Java programming language. Results: After generating a unique pair of public/private keys for identity verification, a patient's identity is verified by applying the Elliptic Curve Digital Signature Algorithm based on the generated keys. When the identity verification is complete, new medical data are stored in the transaction list and the generated transaction is verified. When verification is completed normally, the block hash value is derived using the transaction value and the hash value of the previous block. The hash value of the previous block is then stored in the generated block to interconnect the blocks. Conclusion: We demonstrated that blockchain can be used to store and deliver the patient information of stroke patients. It may be difficult to directly implement the code that we developed in the medical field, but it can serve as a starting point for the creation of a blockchain system to be used in the field.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.3
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• pp.13-25
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• 2004

The key exchange protocols are very crucial tools to provide the secure communication in the broadband satellite access network. They should be required to satisfy various requirements such as security, key confirmation, and key freshness. In this paper, we present the guideline of security functions in BSAN(Broadband Satellite Access Network), and analyze the specification of the security primitives and the hey exchange Protocols for the authenticated key agreement between RCST(Return Channel Satellite Terminal) and NCC(fretwork Control Centre). In addition, we propose the security specification for a domestic broad satellite network based on the analysis on the analysis profile of ETSI(European Telecommunications Standards Institute) standards. The key exchange protocols proposed in ETSI standard are vulnerable to man-in-the-middle attack and they don't provide key confirmation. To overcome this shortcoming, we propose the 4 types of the key exchange protocols which have the resistant to man-in-the-middle-attack, key freshness, and key confirmation, These proposed protocols can be used as a key exchange protocol between RCST and NCC in domestic BSAN. These proposed protocols are based on DH key exchange protocol, MTI(Matsumoto, Takashima, Imai) key exchange protocol, and ECDH(Elliptic Curve Diffie-Hellman).

• Journal of Communications and Networks
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• v.17 no.5
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• pp.453-462
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• 2015

Body area networks (BANs) have emerged as an enabling technique for e-healthcare systems, which can be used to continuously and remotely monitor patients' health. In BANs, the data of a patient's vital body functions and movements can be collected by small wearable or implantable sensors and sent using shortrange wireless communication techniques. Due to the shared wireless medium between the sensors in BANs, it may be possible to have malicious attacks on e-healthcare systems. The security and privacy issues of BANs are becoming more and more important. To provide secure and correct association of a group of sensors with a patient and satisfy the requirements of data confidentiality and integrity in BANs, we propose a novel enhanced secure sensor association and key management protocol based on elliptic curve cryptography and hash chains. The authentication procedure and group key generation are very simple and efficient. Therefore, our protocol can be easily implemented in the power and resource constrained sensor nodes in BANs. From a comparison of results, furthermore, we can conclude that the proposed protocol dramatically reduces the computation and communication cost for the authentication and key derivation compared with previous protocols. We believe that our protocol is attractive in the application of BANs.