• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.447-456
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• 2017

The purpose of this paper is to introduce some strong convergence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.

• Nuclear Engineering and Technology
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• v.50 no.5
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• pp.698-708
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• 2018

This article introduces a methodology of designing a wavelet operator suitable for multiscale modeling. The operator matrix transforms states of a multivariable system onto projection space. In addition, it imposes a specific structure on the system matrix in a multiscale environment. To be specific, the article deals with a diagonalizing transform that is useful for decoupled control of a system. It establishes that there exists a definite relationship between the model in the measurement space and that in the projection space. Methodology for deriving the multirate perfect reconstruction filter bank, associated with the wavelet operator, is presented. The efficacy of the proposed technique is demonstrated by modeling the point kinetics nuclear reactor. The outcome of the multiscale modeling approach is compared with that in the single-scale approach to bring out the advantage of the proposed method.

• Journal of the Korean Magnetic Resonance Society
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• v.17 no.2
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• pp.92-97
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• 2013

We study the electron spin resonance line-width (ESRLW) of $Fe^{3+}$ in crystalline $LiNbO_3$ ; the ESRLW is obtained using the projection operator method (POM) developed by Argyres and Sigel. The ESRLW is calculated to be axially symmetric about the c-axis and is analyzed by the spin Hamiltonian with an isotopic g factor at a frequency of 9.5 GHz. The ESRLW increases exponentially as the temperature increases, and the ESRLW is almost constant in the high-temperature region (T>8000 K). This kind of temperature dependence of the ESRLW indicates a motional narrowing of the spectrum when $Fe^{3+}$ ions substitute the $Nb^{5+}$ ions in an off-center position. It is clear from this feature that there are two different regions in the graph of the temperature dependence of the ESRLW.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.347-371
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• 2021

A plethora of applications from mathematical programmings, such as minimax, mathematical programming, penalization and fixed point problems can be framed as variational inequality problems. Most of the methods that used to solve such problems involve iterative methods, that is why, in this paper, we introduce a new extragradient-like method to solve pseudomonotone variational inequalities in a real Hilbert space. The proposed method has the advantage of a variable step size rule that is updated for each iteration based on previous iterations. The main advantage of this method is that it operates without the previous knowledge of the Lipschitz constants of an operator. A strong convergence theorem for the proposed method is proved by letting the mild conditions on an operator 𝒢. Numerical experiments have been studied in order to validate the numerical performance of the proposed method and to compare it with existing methods.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1996.06a
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• pp.209-212
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• 1996

In this paper, we propose to re-size images using an oblique projection operator instead of the orthogonal one in order to obtain faster, simpler, and more general algorithms. The main advantage is that it becomes perfectly feasible to use higher order models(e.g., splines of degree n 3). We develop the theoretical background and present a simple and practical implementation procedure that uses B-splines. Experiments show that the proposed algorithm consistently outperforms the standard interpolation method and that it essentially provides the same performance as the optimal procedure (least squares solution) with considerably less computations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.55-66
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• 2004

First the notion of the A-monotonicity is applied to the approximation - solvability of a class of nonlinear variational inclusion problems, and then the convergence analysis is given based on a projection-like method. Results generalize nonlinear variational inclusions involving H-monotone mappings in the Hilbert space setting.

• Journal of the Korean Magnetics Society
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• v.22 no.3
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• pp.73-78
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• 2012

We calculated the electron spin resonance (ESR) line-profile function. The line-width of single-walled carbon nanotube (SWNT) was studied as a function of the temperature at a frequency of 9.5 GHz in the presence of external electromagnetic radiation. The temperature dependence of the line-widths is obtained with the projection operator method (POM) proposed by Argyres and Sigel. The scattering is little affected in the low-temperature region (T < 200 K). We conclude that the calculation process presented in this method is useful for optical transitions in SWNT.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.6C
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• pp.815-823
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• 2004

A hue-based attention operator and a combinational integral projection function(CIPF) are proposed to extract the normalized regions of face and facial features robustly against illumination variation. The face candidate regions are efficiently detected by using skin color filter, and the eyes are located accurately nil robustly against illumination variation by applying the proposed hue- and symmetry-based attention operator to the face candidate regions. And the faces are confirmed by verifying the eyes with the color-based eye variance filter. The proposed CIPF, which combines the weighted hue and intensity, is applied to detect the accurate vertical locations of the eyebrows and the mouth under illumination variations and the existence of mustache. The global face and its local feature regions are exactly located and normalized based on these accurate geometrical information. Experimental results on the AR face database［8］ show that the proposed eye detection method yields better detection rate by about 39.3% than the conventional gray GST-based method. As a result, the normalized facial features can be extracted robustly and consistently based on the exact eye location under illumination variations.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.513-525
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• 1996

Let the operator A be self-adjoint with domain, Dom(A), dense in $(H)$ which is a separable Hilbert space with norm $\left\$\mid$ \cdot \right\$\mid$$ and inner product $<\cdot, \cdot>$.