• Nonlinear Functional Analysis and Applications
• /
• 제27권2호
• /
• pp.223-232
• /
• 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.

• 대한수학회논문집
• /
• 제32권2호
• /
• pp.447-456
• /
• 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
• /
• 제50권5호
• /
• pp.698-708
• /
• 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.

• 한국자기공명학회논문지
• /
• 제17권2호
• /
• pp.92-97
• /
• 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
• /
• 제26권2호
• /
• pp.347-371
• /
• 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.

• 한국방송∙미디어공학회:학술대회논문집
• /
• 한국방송공학회 1996년도 학술대회
• /
• pp.209-212
• /
• 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
• /
• 제8권1호
• /
• pp.55-66
• /
• 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.

• 한국자기학회지
• /
• 제22권3호
• /
• pp.73-78
• /
• 2012

본 연구에서는 Argyres-Sigel의 투영 연산자 방법을 단일 벽 탄소 나노튜브(SWNT)의 zigzag(10,0)에 직접 적용하여 이를 운동방정식의 형태로 만들어 선모양 함수를 구하는 방법을 사용하였다. 선모양 함수의 실수 부분인 선 너비는 저온 영역(T < 200K)에서 온도의 영향에 거의 무관한 것으로 조사되었다. 이는 온도에 관여하는 페르미-디랙 분포함수가 선모양 함수에 거의 영향을 작용하지 않기 때문인 것으로 생각된다. 고온 영역(T > 200K)에서는 선 너비가 다소 단조롭게 증가하는 것으로 나타났으며, 이는 음향 포논의 영향에 기인하는 것으로 보인다. 그리고 SWNT의 전자스핀이완 시간은 $1.4{\times}10^{-6}\;s$으로 계산되었다.

• 한국통신학회논문지
• /
• 제29권6C호
• /
• pp.815-823
• /
• 2004

색상(hue) 기반 주목연산자와 조합누적투영함수(combinational integral projection function: CIPF)를 제안하여 조명변화에 강건하게 정규화된 얼굴요소영역을 추출하였다. 살색 필터를 도입하여 얼굴후보영역들을 추출하고, 거기에 색상과 대칭성에 기반한 주목연산자를 적용하여 조명변화에 강건하게 두 눈의 위치를 정확히 검출할 수 있도록 하였으며, 색상기반 눈 분산 필터로 눈을 검증하여 얼굴영역을 확인하였다. 또한, 색상과 밝기 성분을 조합한 조합누적투영함수를 사용하여 두 눈의 위치를 기준으로 조명변화나 수염의 존재유무에 둔감하게 눈썹 및 입의 수직위치를 구하고, 이를 바탕으로 정규화된 얼굴영역 및 그 요소영역을 추출하였다. AR 얼굴 데이터베이스［8］에 제안한 색상기반 주목연산자를 적용한 결과 기존 명도기반 주목연산자에 비해 약 39.3%의 눈 검출 성능향상을 보임으로써 조명방향 변화에 강건하게 정규화된 얼굴 및 그 요소영역을 일관성 있게 추출할 수 있음을 확인하였다.

• 대한수학회지
• /
• 제33권3호
• /
• pp.513-525
• /
• 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 $<\cdot, \cdot>$.