• 제목/요약/키워드: Gradient Vector Field

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The Geometry of 𝛿-Ricci-Yamabe Almost Solitons on Paracontact Metric Manifolds

  • Somnath Mondal;Santu Dey;Young Jin Suh;Arindam Bhattacharyya
    • Kyungpook Mathematical Journal
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    • 제63권4호
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    • pp.623-638
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    • 2023
  • In this article we study a 𝛿-Ricci-Yamabe almost soliton within the framework of paracontact metric manifolds. In particular we study 𝛿-Ricci-Yamabe almost soliton and gradient 𝛿-Ricci-Yamabe almost soliton on K-paracontact and para-Sasakian manifolds. We prove that if a K-paracontact metric g represents a 𝛿-Ricci-Yamabe almost soliton with the non-zero potential vector field V parallel to 𝜉, then g is Einstein with Einstein constant -2n. We also show that there are no para-Sasakian manifolds that admit a gradient 𝛿-Ricci-Yamabe almost soliton. We demonstrate a 𝛿-Ricci-Yamabe almost soliton on a (𝜅, 𝜇)-paracontact manifold.

RICCI SOLITONS AND RICCI ALMOST SOLITONS ON PARA-KENMOTSU MANIFOLD

  • Patra, Dhriti Sundar
    • 대한수학회보
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    • 제56권5호
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    • pp.1315-1325
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    • 2019
  • The purpose of this article is to study the Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold. First, we prove that if a para-Kenmotsu metric represents a Ricci soliton with the soliton vector field V is contact, then it is Einstein and the soliton is shrinking. Next, we prove that if a ${\eta}$-Einstein para-Kenmotsu metric represents a Ricci soliton, then it is Einstein with constant scalar curvature and the soliton is shrinking. Further, we prove that if a para-Kenmotsu metric represents a gradient Ricci almost soliton, then it is ${\eta}$-Einstein. This result is also hold for Ricci almost soliton if the potential vector field V is pointwise collinear with the Reeb vector field ${\xi}$.

*-CONFORMAL RICCI SOLITONS ON ALMOST COKÄHLER MANIFOLDS

  • Tarak Mandal;Avijit Sarkar
    • 대한수학회논문집
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    • 제38권3호
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    • pp.865-880
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    • 2023
  • The main intention of the current paper is to characterize certain properties of *-conformal Ricci solitons on non-coKähler (𝜅, 𝜇)-almost coKähler manifolds. At first, we find that there does not exist *-conformal Ricci soliton if the potential vector field is the Reeb vector field θ. We also prove that the non-coKähler (𝜅, 𝜇)-almost coKähler manifolds admit *-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist *-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.

3-Dimensional Trans-Sasakian Manifolds with Gradient Generalized Quasi-Yamabe and Quasi-Yamabe Metrics

  • Siddiqi, Mohammed Danish;Chaubey, Sudhakar Kumar;Ramandi, Ghodratallah Fasihi
    • Kyungpook Mathematical Journal
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    • 제61권3호
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    • pp.645-660
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    • 2021
  • This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.

모바일 벡터 그래픽을 위한 OpenVG 가속기 설계 (Design of Open Vector Graphics Accelerator for Mobile Vector Graphics)

  • 김영옥;노영섭
    • 한국멀티미디어학회논문지
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    • 제11권10호
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    • pp.1460-1470
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    • 2008
  • 최근 휴대용 기기의 성능이 향상되면서 다양한 형태의 메뉴 구성과, 메일 및 이차원 지도 등의 표현에 벡터 그래픽을 많이 도입하고 있다. 본 논문은 모바일 기기에서 많이 사용되고 여는 이차원 벡터의 처리 기술인 OpenVG (Open Vector Graphics)의 하드웨어 가속기를 제안했다. 제안된 하드웨어 가속기는 그래픽에서 처리가 빈번한 렌더링(rendering)의 각 기능을 분석하여 하드웨어 구현에 적합하도록 나누고, 그 알고리즘을 설계 및 검증하여 HDL (Hardware Description Language)로 FPGA (Field Programmable Gate Array)에 이식하여 구현되었으며, 알렉스 처리기에 비하여 약 4배의 빠른 처리속도를 보였다.

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Detection of View Reversal in a Stereo Video

  • Son, Ji Deok;Song, Byung Cheol
    • IEIE Transactions on Smart Processing and Computing
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    • 제2권5호
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    • pp.317-321
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    • 2013
  • This paper proposes a detection algorithm for view reversal in a stereoscopic video using a disparity map and motion vector field. We obtain the disparity map of a stereo image was obtained using a specific stereo matching algorithm and classify the image into the foreground and background. Next, the motion vector field of the image on a block basis was produced using a full search algorithm. Finally, the stereo image was considered to be reversed when the foreground moved toward the background and the covered region was in the foreground. The proposed algorithm achieved a good detection rate when the background was covered sufficiently by its moving foreground.

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이미지 기울기에서 선별된 포아송 모델을 이용한 이미지 재구성 (Image Reconstruction Using Poisson Model Screened from Image Gradient)

  • 김용길
    • 한국인터넷방송통신학회논문지
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    • 제18권2호
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    • pp.117-123
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    • 2018
  • 본 연구에서는 이미지 기울기 영역에서 포아송 방정식을 이용한 빠른 이미지 재구성 기법을 제안한다. 포아송 방정식을 사용하는 이 접근법에서, 유도된 벡터 필드는 제 1 단계에서 선택된 영역 내에서 원본과 대상 이미지를 사용함으로써 생성된다. 다음으로, 유도된 벡터는 결과 이미지를 생성하는데 사용된다. 우리는 원하는 기울기 집합과 데이터 항을 근사화하는 2차원 함수를 재구성하는 문제를 분석했다. 결합된 데이터와 기울기는 원본 이미지에 가깝게 머무르는 동안 이미지 기울기를 수정하는 것처럼 작동 할 수 있다. 이 공식으로부터 우리는 물리학에서 알려진 포아송 방정식을 찾아냈다. 이 방정식은 FFT 도메인의 문제에 대한 효율적인 해결책을 제시한다. 이것은 2차원으로 알려진 포아송 모델을 해결하고 기울기 비례축소는 라플라스를 확실하게 일반화하는 잘 정의된 선명한 필터임을 공간 필터에 잘 나타냅니다. 포아송 모델을 기반으로 이산 코사인 변환을 사용하여 결과를 확인할 수 있었다.

전기비저항탐사에서 음의 겉보기 비저항 (Negative Apparent Resistivity in Resistivity Method)

  • 조인기;김정호;정승환;서정희
    • 지구물리와물리탐사
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    • 제5권3호
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    • pp.199-205
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    • 2002
  • 전기비저항 탐사에서 측정되는 양은 두 전위전극 사이의 전위차이다. 이 전위차가 양일 경우에는 겉보기 비저항도 양의 값을 가지며, 음일 경우에는 겉보기 비저항도 음의 값을 나타낸다. 또한 측정되는 전위차의 부호는 전기장의 방향에 따라 좌우된다. 만약 측정방향과 전기장의 방향이 같다면, 전위차와 겉보기 비저항은 양의 값을 보이게 되며, 그 반대의 경우에는 음의 값을 나타낸다. 일반적으로 지표 전기비저항 탐사에는 측정방향과 1차 전기장의 방향이 같은 전극 배열을 사용하며, 이 방향의 1차 전기장은 2차 전기장에 비하여 항상 크다. 따라서 일반적인 전극배열을 사용하는 지표 전기비저항 탐사의 경우에는 지형이 평탄하고 잡음이 없다면 음의 겉보기 비저항은 나타나지 않는다. 그러나 시추공-시추공 전기비저항 탐사의 경우에는 1차 전기장의 방향과 측정방향이 일치하지 않으며, 경우에 따라서는 1차 전기장의 측정방향 성분이 2차 전기장의 측정방향 성분 보다 그 크기가 작을 수 있다. 이 경우 2차 전기장의 방향과 측정방향이 서로 반대일 경우에는 음의 겉보기 비저항이 나타날 수 있다. 따라서 음의 겉보기 비저항은 측정방향의 1차 전기장이 매우 작은 영역에서 발생할 가능성이 높다.

Data-Driven Modelling of Damage Prediction of Granite Using Acoustic Emission Parameters in Nuclear Waste Repository

  • Lee, Hang-Lo;Kim, Jin-Seop;Hong, Chang-Ho;Jeong, Ho-Young;Cho, Dong-Keun
    • 방사성폐기물학회지
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    • 제19권1호
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    • pp.75-85
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    • 2021
  • Evaluating the quantitative damage to rocks through acoustic emission (AE) has become a research focus. Most studies mainly used one or two AE parameters to evaluate the degree of damage, but several AE parameters have been rarely used. In this study, several data-driven models were employed to reflect the combined features of AE parameters. Through uniaxial compression tests, we obtained mechanical and AE-signal data for five granite specimens. The maximum amplitude, hits, counts, rise time, absolute energy, and initiation frequency expressed as the cumulative value were selected as input parameters. The result showed that gradient boosting (GB) was the best model among the support vector regression methods. When GB was applied to the testing data, the root-mean-square error and R between the predicted and actual values were 0.96 and 0.077, respectively. A parameter analysis was performed to capture the parameter significance. The result showed that cumulative absolute energy was the main parameter for damage prediction. Thus, AE has practical applicability in predicting rock damage without conducting mechanical tests. Based on the results, this study will be useful for monitoring the near-field rock mass of nuclear waste repository.

Mean fragmentation size prediction in an open-pit mine using machine learning techniques and the Kuz-Ram model

  • Seung-Joong Lee;Sung-Oong Choi
    • Geomechanics and Engineering
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    • 제34권5호
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    • pp.547-559
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    • 2023
  • We evaluated the applicability of machine learning techniques and the Kuz-Ram model for predicting the mean fragmentation size in open-pit mines. The characteristics of the in-situ rock considered here were uniaxial compressive strength, tensile strength, rock factor, and mean in-situ block size. Seventy field datasets that included these characteristics were collected to predict the mean fragmentation size. Deep neural network, support vector machine, and extreme gradient boosting (XGBoost) models were trained using the data. The performance was evaluated using the root mean squared error (RMSE) and the coefficient of determination (r2). The XGBoost model had the smallest RMSE and the highest r2 value compared with the other models. Additionally, when analyzing the error rate between the measured and predicted values, XGBoost had the lowest error rate. When the Kuz-Ram model was applied, low accuracy was observed owing to the differences in the characteristics of data used for model development. Consequently, the proposed XGBoost model predicted the mean fragmentation size more accurately than other models. If its performance is improved by securing sufficient data in the future, it will be useful for improving the blasting efficiency at the target site.