• 충청수학회지
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• 제33권2호
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• pp.219-226
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• 2020

In this paper, we consider gradient Ricci solitons and gradient Yamabe solitons in the warped product spaces. Also we study warped product space with harmonic curvature related to gradient Ricci solitons and gradient Yamabe solitons. Consequently some theorems are generalized and we derive differential equations for a warped product space to be a gradient Ricci soliton.

• 한국우주과학회:학술대회논문집(한국우주과학회보)
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• 한국우주과학회 2011년도 한국우주과학회보 제20권1호
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• pp.26.3-27
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• 2011

Formation of a steep plasma density gradient in the middle-latitude ionosphere during geomagnetic storms and the latitudinal migration of its location depending on the storm phase are suggested to be associated with the ionospheric signature of the plasmapause. We test this idea by using the satellite and ground observation data during the 11 April 2001 storm. The locations of the steep plasma density gradient identified by TOPEX/Poseidon (2001 LT) and DMSP (1800 and 2130 LT) satellites coincide with the ionospheric footprints of the plasmapause identified by the IMAGE satellite. This observation may support the dependence of the middle-latitude plasma density gradient location on the plasmapause motion, but does not explain why the steep density gradient whose morphology is largely different from the morphology of the middle-latitude ionization trough during quiet period is formed in association with the plasmapause. The ionospheric disturbances in the total electron content (TEC) maps shows that the steep TEC gradient is formed at the boundary of the positive ionospheric storm in low-middle latitudes and the negative ionospheric storm in middle-high latitudes. We interpret that the thermospheric neutral composition disturbance in the dayside is confined within the middle-high latitude ionospheric convection zone. The neutral composition latitudes and, therefore, the locations of the steep plasma density gradient coincide with the footprints of the plasmapause. The TEC maps show that the appearance of the steep plasma density gradient in the pre-midnight sector during the recovery phase is related to the co-rotation of the gradient that is created during the main phase.

• Journal of Astronomy and Space Sciences
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• 제16권2호
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• pp.91-104
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• 1999

We use BV CCD images to investigate the reality of the color gradient within a King type globular cluster NGC 7089. Surface photometry shows that there is a strong radial color gradient in the central region of the cluster in the sense of bluer center with the amplitude of ~0.39 $\pm$ 0.07 mag/$arcsec^2$ in (B - V). In the outer region of the cluster, however, the radial color gradient shows a reverse case, i.e., redder toward the center. (B - V) color profile which was derived from resolved stars in VGC 7089 field also shows a significant color gradient in the central region of the clusters, indicating that lights from the combination of red giant stars and blue horizontal branch stars cause the radial color gradient. Color gradient of the outer region of NGC 7089 may be due to the unresolved background of the cluster. Similar color gradients in the central area of clusters have been previously observed exserved exclusively in highly concentrated systems classified as post core collapse clusters. We caution, however, to confirm the reality of the color gradient from resolved stars, we need more accurate imaging data of the cluster with exceptional seeing condition because the effect of completeness correlates with local density of stars.

• Investigative Magnetic Resonance Imaging
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• 제13권1호
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• pp.15-21
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• 2009

목적 : 나선 주사 영상에서 경사자계시스템의 회로 모델을 기반으로 실제 경사 자계를 추정하여 재구성에 사용함으로써 재구성 영상을 개선하는 방법을 제안하였다. 대상 및 방법 : 자기공명영상장치의 경사자계 시스템은 저항 성분과 자체 인덕턴스, magnet 시스템과의 상호 인덕턴스, 커패시턴스 성분 등을 가지고 있어서 경사자계 증폭기에 인가하는 입력 경사자계 파형과 실제 만들어지는 경사자계 사이에는 시간적인 지연과 함께 파형에도 차이가 있다. 나선주사 영상에서 실제 만들어진 경사자계 파형 및 k-space 궤적은 재구성 과정에서 매우 중요한 역할을 한다. 본 논문에서는 경사자계시스템을 회로 소자로 모델링하였고, 입력 전압 파형에 대한 출력 전류 파형을 구함으로써 실제 얻어지는 경사자계파형을 유도하였다. 모델링에서 사용한 R-L-C 값은 재구성영상의 화질로부터 얻을 수 있는 방법을 제시하였다. 결과 : 1.5 Tesla MRI 시스템에서 경사자계 시스템의 입력 전압 파형에 대하여 실제 얻어지는 경사자계 파형을 추정할 수 있었다. 경사자계파형을 적분함으로써 얻어진 나선 궤적을 재구성에 적용한 결과 재구성 영상의 균일도가 개선되었고, edge 부근에서 overshoot 가 줄어들었으며, 해상도가 향상된 영상을 얻을 수 있었다. 결론 : R-L-C 회로 모델을 이용하여 경사자계시스템을 성공적으로 모델링할 수 있었고, 입력 전압 파형에 대하여 실제 얻어지는 경사자계(전류) 파형을 추정할 수 있었다. 이로부터 얻은 kspace 나선 궤적을 이용하여 월등히 개선된 재구성영상을 얻을 수 있었다.

• 대한의용생체공학회:의공학회지
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• 제17권1호
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• pp.93-98
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• 1996

The purpose of this paper is to propose a new localized imaging method of reduced imaging time luting a locally-linear gradient. Since most fast MR(Magnetic Resonance) imaging methods need the whole $\kappa$-space(Spatial frequency space) data corresponding to the whole imaging area, there are limitstions in reducing the minimum imaging time. The imaging method proposed in this paper uses a specially-made gradient coil generating a local ramp-shape field and uniform field outside of the imaging areal Conventional imaging sequences can be used without any RF/gradient pulse sequence modifiestions except the change in the number of encoding steps and the field of view.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.627-636
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• 2016

In this paper, we study Ricci solitons, gradient Ricci solitons in the warped product spaces and gradient Yamabe solitons in the Riemannian product spaces. We obtain the necessary and sufficient conditions for the Riemannian product spaces to be Ricci solitons. Moreover we classify the warped product space which admit gradient Ricci solitons under some conditions of the potential function.

• 대한수학회지
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• 제60권2호
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• pp.341-358
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• 2023

Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with 𝛽-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with 𝛽-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with 𝛽-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either ψ∖T^k × M^2n+1-k or gradient 𝜂-Yamabe soliton.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.715-728
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• 2022

The aim of this article is to study the h-almost Ricci solitons and h-almost gradient Ricci solitons on generalized Sasakian-space-forms. First, we consider h-almost Ricci soliton with the potential vector field V as a contact vector field on generalized Sasakian-space-form of dimension greater than three. Next, we study h-almost gradient Ricci solitons on a three-dimensional quasi-Sasakian generalized Sasakian-space-form. In both the cases, several interesting results are obtained.

• 대한수학회논문집
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• 제34권4호
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• pp.1315-1328
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• 2019

The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.

• 대한수학회보
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• 제51권1호
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• pp.213-219
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• 2014

We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form $\mathbb{S}^3$, $\mathbb{H}^3$, $\mathbb{R}^3$ (Gaussian soliton); or a product space $\mathbb{R}{\times}\mathbb{S}^2$, $\mathbb{R}{\times}\mathbb{H}^2$, where the potential function depends only on the nullity.