• Journal of Multimedia Information System
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• v.5 no.2
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• pp.87-90
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• 2018

Various approaches have been proposed to convert low dynamic range (LDR) to high dynamic range (HDR). Of these approaches, the Multi Scale Fusion (MSF) algorithm based on Laplacian pyramid decomposition is used in many applications and demonstrates its usefulness. However, the pyramid fusion technique has no means for controlling the luminance component because the total number of pixels decreases as the pyramid rises to the upper layer. In this paper, we extract the reflection light of the image based on the Retinex theory and generate the weight map by adjusting the reflection component. This weighting map is applied to achieve an MSF-like effect during image fusion and provides an opportunity to control the brightness components. Experimental results show that the proposed method maintains the total number of pixels and exhibits similar effects to the conventional method.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• Interaction and multiscale mechanics
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• v.3 no.2
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• pp.111-121
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• 2010

Dynamic analysis of nano/micro bio-sensors based on a multiscale atomistic/continuum theory is introduced. We use a generalized atomistic finite element method (GAFEM) to analyze a bio-sensor which has $3{\times}N_a{\times}N_p$ degrees of freedom, where $N_p$ is the number of representative unit cells and $N_a$ is the number of atoms per unit cell. The stiffness matrix is derived from interatomic potential between pairs of atoms. This work contains two studies: (1) the resonance analysis of nano bio-sensors with different amount of target analyte and (2) the dependence of resonance frequency on finite element mesh. We also examine the Courant-Friedrichs-Lewy (CFL) condition based on the highest resonance frequency. The CFL condition is the criterion for the time step used in the dynamic analysis by GAFEM. Our studies can be utilized to predict the performance of micro/nano bio-sensors from atomistic perspective.

• ETRI Journal
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• v.46 no.3
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• pp.367-378
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• 2024

We propose a number-theory-based quantized mathematical optimization scheme for various NP-hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization-based optimization proposal also depends on stochastic features (i.e., the white-noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization-based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.993-1008
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• 1996

The white noise analysis, initiated by Hida [3] in 1975, has been developed to an infinite dimensional distribution theory on Gaussian space $(E^*, \mu)$ as an infinite dimensional analogue of Schwartz distribution theory on Euclidean space with Legesgue measure. The mathematical framework of white noise analysis is the Gel'fand triple $(E) \subset (L^2) \subset (E)^*$ over $(E^*, \mu)$ where $\mu$ is the standard Gaussian measure associated with a Gel'fand triple $E \subset H \subset E^*$.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.263-271
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• 2012

We investigate the number of the solutions for the biharmonic boundary value problem with a variable coefficient nonlinear term. We get a theorem which shows the existence of $m$ weak solutions for the biharmonic problem with variable coefficient. We obtain this result by using the critical point theory induced from the invariant function and invariant linear subspace.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.173-187
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• 1998

Several aspects of pseudorandom number generators are investigated from the viewpoint of ergodic theory. An algorithm of generating pseudorandom numbers proposed and shown to behave reasonably well.

• Proceedings of the KIPE Conference
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• 1999.07a
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• pp.58-61
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• 1999

This paper describes the program of optimally choosing parameter in designing inductor, which applied by fuzzy theory, and verifies the reliability of program to use in design of power supply of electronic machine and information communication. It is available to find optimal value of complex and various parameter, such as core, winding, winding number, and air-gap, etc., needed on designing inductor. We expects to minimize time and cost of inductor design.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.669-690
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• 1998

In this paper we develop a new theory of adjoint and symmetric method in the class of general implicit one-step fixed-stepsize methods. These methods arise from simple and natral def-initions of the concepts of symmetry and adjointness that provide a fruitful basis for analysis. We prove a number of theorems for meth-ods having these properties and show in particular that only the symmetric methods possess a quadratic asymptotic expansion of the global error. In addition we give a very simple test to identify the symmetric methods in practice.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.333-341
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• 2012

We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.