• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.69-94
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• 2024

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature.

• 대한수학회지
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• 제42권5호
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• pp.975-1002
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• 2005

On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

• 한국항공우주학회지
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• 제38권6호
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• pp.570-576
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• 2010

본 논문은 GPS 항공항법에 사용될 수 있는 무결성 감시 알고리즘에 관한 연구로써, 평면상에 수평 투영된 의사거리 잔차와 이용하여 보다 위성 배치 (PDOP)에 따른 한계치를 생성하여, 고장 위성을 식별 및 제거할 수 있는 RAIM 알고리즘을 제시하고 있다. 고장위성의 수평 투영 잔차가 정상 위성의 수평 투영 잔차보다 크다는 점을 수학적으로 증명함으로써, 잔차 수평 투영 비교만으로 고장 가능성이 높은 위성을 식별할 수 있음을 보였다. 또한 성능 평가를 위해 의사거리에 일정한 크기의 바이어스 형태의 고장을 삽입하였고, 기존의 패리티 공간 기법과 성능 비교를 수행하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.913-920
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• 2000

The hall and the projection room of the multiplex cinema being constructed on the sixth and seventh floors at Jeonpo-dong market, Pusan, is composed of structural beams and decks considering the structures self weight problem, and the following problems are expected: - Vibration and noise generated on the floors by moving audiences may annoy the audiences in the other hall - Vibration and noise generate on the floor of the nearby hall as the audiences walk through the alley near the projection room - Vibration and noise generate on the floor of the hall nearby the projection room as the film drops This study measured and reviewed the vibration amount of the seven representative transferring routes that were selected for the halls and the alley near the projection room. Based on the analysis, the model hall was constructed and the vibration in the hall was estimated after cutting the deck. Also, this study constructed the steel stairs and investigated the vibration transferring characteristics to decide whether to construct the steel stairs in the building. Finally, the results were evaluated by actually using the stairs and reviewed the appropriateness of the measurement.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권2호
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• pp.83-94
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• 2003

Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements $x^*,\;y^*{\in}H$ such that $g(x^*),\;g(y^*){\in}K$ and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T: $H\;{\rightarrow}\;H$ is a relaxed $g-{\gamma}-r-cocoercive$ and $g-{\mu}-Lipschitz$ continuous nonlinear mapping on H and g: $H{\rightarrow}\;H$ is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권2호
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• pp.945-961
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• 2019

Tongue diagnosis is one of the most important diagnostic methods in Traditional Chinese Medicine (TCM). Tongue image segmentation aims to extract the image object (i.e., tongue body), which plays a key role in the process of manufacturing an automated tongue diagnosis system. It is still challenging, because there exists the personal diversity in tongue appearances such as size, shape, and color. This paper proposes an innovative segmentation method that uses image thresholding, gray projection and active contour model (ACM). Specifically, an initial object region is first extracted by performing image thresholding in HSI (i.e., Hue Saturation Intensity) color space, and subsequent morphological operations. Then, a gray projection technique is used to determine the upper bound of the tongue body root for refining the initial object region. Finally, the contour of the refined object region is smoothed by ACM. Experimental results on a dataset composed of 100 color tongue images showed that the proposed method obtained more accurate segmentation results than other available state-of-the-art methods.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제17권2호
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• pp.471-485
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• 2023

As data sharing increases explosively, such information encoded in QR code is completely public as private messages are not securely protected. This paper proposes a new 'PROMISE' framework for hiding information based on the QR code projection matrix by using image segmentation without modifying the essential QR code characteristics. Projection matrix mapping, matrix scrambling, fusion image segmentation and steganography with SEL(secret embedding logic) are part of the PROMISE framework. The QR code could be mapped to determine the segmentation site of the fusion image as a binary information matrix. To further protect the site information, matrix scrambling could be adopted after the mapping phase. Image segmentation is then performed on the fusion image and the SEL module is applied to embed the secret message into the fusion image. Matrix transformation and SEL parameters should be uploaded to the server as the secret key for authorized users to decode the private message. And it was possible to further obtain the private message hidden by the framework we proposed. Experimental findings show that when compared to some traditional information hiding methods, better anti-detection performance, greater secret key space and lower complexity could be obtained in our work.

• 대한수학회지
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• 제43권2호
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• pp.399-411
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• 2006

Let L be a subspace lattice on a Hilbert space H and X and Y be operators acting on a Hilbert space H. Let P be the projection onto $\frac\;{R(X)}$, where RX is the range of X. If PE = EP for each $E\;\in\;L$, then there exists an operator A in AlgL such that AX = Y if and only if $$sup\{{\parallel}E^{\bot}Yf{\parallel}/{\parallel}E^{\bot}Xf{\parallel}\;:\;f{\in}H,\; E{\in}L}=K\;<\;\infty$$ Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}A{\parallel} = K.$ Let x and y be vectors in H and let $P_x$ be the projection onto the singlely generated space by x. If $P_xE = EP_x$ for each $E\inL$, then the assertion that there exists an operator A in AlgL such that Ax = y is equivalent to the condition $$K_0\;:\;=\;sup\{{\parallel}E^{\bot}y{\parallel}/{\parallel}E^{\bot}x\;:\;E{\in}L}=<\;\infty$$ Moreover, we may choose an operator A such that ${\parallel}A{\parallel} = K_0$ whose norm is $K_0$ under this case.

• Structural Engineering and Mechanics
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• 제69권6호
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• pp.615-626
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• 2019

The 3-noded metric Timoshenko beam element with an offset of the internal node from the element centre is used here to demonstrate the best-fit paradigm using function space formulation under locking and mesh distortion. The best-fit paradigm follows from the projection theorem describing finite element analysis which shows that the stresses computed by the displacement finite element procedure are the best approximation of the true stresses at an element level as well as global level. In this paper, closed form best-fit solutions are arrived for the 3-noded Timoshenko beam element through function space formulation by combining field consistency requirements and distortion effects for the element modelled in metric Cartesian coordinates. It is demonstrated through projection theorems how lock-free best-fit solutions are arrived even under mesh distortion by using a consistent definition for the shear strain field. It is shown how the field consistency enforced finite element solution differ from the best-fit solution by an extraneous response resulting from an additional spurious force vector. However, it can be observed that when the extraneous forces vanish fortuitously, the field consistent solution coincides with the best-fit strain solution.

• 디지털융복합연구
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• 제11권8호
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• pp.331-340
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• 2013

초현실주의 대표적인 작가 르네마그리트가 주장한 데페이즈망 기법은 여러매체에 활용되어지고 응용되어 왔다. TV, CF, 광고등 다양한 매체를 통하여 데페이즈망의 기법들을 적용한 흔히 사용되어지는 소재들을 새로운 낯선 환경에 재배치되었을때 고정관념의 탈피와 시각적 충격을 통해 흥미를 부여하고자 하였다. 서로 다른 용도의 투명스크린과 오브제를 활용하여 프로젝션 맵핑의 매체에 접목하여 작품 '환영'에 데페이즈망 기법을 적용하여 낯선 환경을 통해 시각적 즐거움과, 새로운 미디어로써의 가능성과 투명스크린과 오브제를 활용한 프로젝션 맵핑의 기법을 제시하였다. 데페이즈망의 기법에서 대표적인 공간의 변조, 모순된 이미지의 결합, 물체의 변형과 변화 3가지 분류에 의해 표현방법과 효과를 적용하여 작품사례를 제시하였고, 레이아웃, 타이포그래피, 이미지, 컬러, 시간으로 분류하여 유형별 분석하였다. 작품 '환영'을 통해 프로젝션 맵핑과 데페이즈망 기법을 활용한 새로운 오브제와 매체의 특성을 적용하여 확장하였다.