• 대한수학회보
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• 제55권4호
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• pp.1161-1178
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• 2018

In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.343-357
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• 2015

Using the fixed point method, we prove the Hyers-Ulam stability of lin- ear mappings in Banach modules over a unital C*-algebra and in non-Archimedean Banach modules over a unital C*-algebra associated with the orthogonally Cauchy- Jensen additive functional equation.

• International Journal of CAD/CAM
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• 제9권1호
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• pp.103-109
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• 2010

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow respectively. Experimental results on geometric data acquired from real life demonstrate that the symmetric conformal mapping is insensitive to the boundary occlusions. The method outperforms all the others in terms of robustness. The method has the potential to be generalized to high genus surfaces using hyperbolic curvature flow.

• 한국해양공학회지
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• 제19권5호
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• pp.78-82
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• 2005

The motion response results of a submerged submarine section in waves are presented. The numerical method is based on Cauchy's integral and 3 degrees-of-freedom motions of submarine sections are calculated in two dimensions, in regular waves. The fully nonlinear free surface and body boundary conditions are applied to the present problem, and the viscous effects on the submarine are modeled by Morison's formulas. The motions of submarine sections in beam sea are directly simulated and the effects of wave frequency, snorkel depth, and bridge are discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권2호
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• pp.85-97
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• 2000

A quadrature rule for the solution of Cauchy singular integral equation is constructed and investigated. This method to calculate numerically singular integrals uses classical Jacobi quadratures adopting Hunter's method. The proposed method is convergent under a reasonable assumption on the smoothness of the solution.

• 한국지하수토양환경학회지:지하수토양환경
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• 제20권2호
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• pp.10-21
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• 2015

The present study introduces a novel numerical approach for solving dispersion dominated problems with Cauchy boundary condition in an Eulerian-Lagrangian scheme. The study reveals the incapability of traditional Neuman approach to address the dispersion dominated problems with Cauchy boundary condition, even though it can produce reliable solution in the advection dominated regime. Also, the proposed numerical approach is applied to a real field problem of radioactive contaminant migration from radioactive waste repository which is a major current waste management issue. The performance of the proposed numerical approach is evaluated by comparing the results with numerical solutions of traditional FDM (Finite Difference Method), Neuman approach, and the analytical solution. The results show that the proposed numerical approach yields better and reliable solution for dispersion dominated regime, specifically for Peclet Numbers of less than 0.1. The proposed numerical approach is validated by applying to a real field problem of radioactive contaminant migration from radioactive waste repository of varying Peclet Number from 0.003 to 34.5. The numerical results of Neuman approach overestimates the concentration value with an order of 100 than the proposed approach during the assessment of radioactive contaminant transport from nuclear waste repository. The overestimation of concentration value could be due to the assumption that dispersion is negligible. Also our application problem confirms the existence of real field situation with advection dominated condition and dispersion dominated condition simultaneously as well as the significance or advantage of the proposed approach in the real field problem.

• IEIE Transactions on Smart Processing and Computing
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• 제1권3호
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• pp.171-181
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• 2012

In the new video coding standard, called high efficiency video coding (HEVC), the coding unit (CU) is adopted as a basic unit of a coded block structure. Therefore, the rate control (RC) methods of H.264/AVC, whose basic unit is a macroblock, cannot be applied directly to HEVC. This paper proposes the largest CU (LCU) level RC method for hierarchical video coding in a HEVC. In the proposed method, the effective bit allocation is performed first based on the hierarchical structure, and the quantization parameters (QP) are then determined using the Cauchy density based rate-quantization (RQ) model. A novel method based on the linear rate model is introduced to estimate the parameters of the Cauchy density based RQ model precisely. The experimental results show that the proposed RC method not only controls the bitrate accurately, but also generates a constant number of bits per second with less degradation of the decoded picture quality than with the fixed QP coding and latest RC method for HEVC.

• 대한수학회보
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• 제45권1호
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• pp.111-118
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• 2008

Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)$$=f(x)+f(y)+2f(z), which was introduced and investigated in [2, 17]. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Furthermore, isometries and isometric isomorphisms in quasi-Banach algebras are studied.

• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.647-671
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• 2020

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using 𝜖-approximated solutions. Finally, we present examples to illustrate our main results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권1호
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• pp.93-101
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• 2008

In this article we shall characterize the Heinz-Kato-Furuta inequality in several ways, and the best bound for sharpening of the inequality is obtained by the method in [7].