• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.165-171
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• 2021

The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton (Mn, g, f, λ) with constant scalar curvature admitting a non-homothetic conformal vector field V leaving the potential vector field invariant. We show that in such manifolds the potential function f is constant and the scalar curvature of g is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field V, without constant scalar curvature assumption, we show that g has constant curvature and determines the potential function f explicitly.

• International Journal of Aeronautical and Space Sciences
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• v.6 no.2
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• pp.56-63
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• 2005

Some methods have been presented to avoid collisions among satellites for satellite formation flying mission. The potential function method based on Lyapunov's theory is known as a powerful tool for collision avoidance in the robotic system because of its robustness and flexibility. During the last decade, a potential function has also been applied to UAV's and spacecraft operations, which consists of repulsive and attractive potential. In this study, the controller is designed using a potential function via sliding mode technique for the configuration of satellite formation flying. The strategy is based on enforcing the satellite to move along the gradient of a given potential function. The new scalar velocity function is introduced such that all satellites reach the goal points simultaneously. Simulation results show that the controller drives the satellite toward the desired point along the gradient of the potential function and is robust against external disturbances.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.639-645
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• 2023

An almost Yamabe soliton is a generalization of the Yamabe soliton. In this article, we deduce some results regarding almost gradient Yamabe solitons. More specifically, we show that a compact almost gradient Yamabe soliton having non-negative Ricci curvature is trivial. Again, we prove that an almost gradient Yamabe soliton with a non-negative potential function and scalar curvature bound admitting an integral condition is trivial. Moreover, we give a characterization of a compact almost gradient Yamabe solitons.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1189-1208
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• 2017

In this paper, we study vanishing properties for $L^2$ harmonic 1-forms on a gradient shrinking Ricci soliton. We prove that if (M, g, f) is a complete oriented noncompact gradient shrinking Ricci soliton with potential function f, then there are no non-trivial $L^2$ harmonic 1-forms which are orthogonal to df. Second, we show that if the scalar curvature of the metric g is greater than or equal to (n - 2)/2, then there are no non-trivial $L^2$ harmonic 1-forms on (M, g). We also show that any multiplication of the total differential df by a function cannot be an $L^2$ harmonic 1-form unless it is trivial. Finally, we derive various integral properties involving the potential function f and $L^2$ harmonic 1-forms, and handle their applications.

• Geophysics and Geophysical Exploration
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• v.24 no.1
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• pp.1-5
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• 2021

The closed-form expressions of the vector gravity and gravity gradient tensor due to a circular disk are derived. The gravity potential due to a circular disk with a constant density is defined for a cylindrical system. Then, the vector gravity is derived by differentiating the gravity potential with respect to cylindrical coordinates. The radial component of the vector gravity in the cylindrical system is converted into horizontal gravity components in the Cartesian system. Finally, the gravity gradient tensor due to a circular disk is obtained by differentiating the vector gravity with respect to the Cartesian coordinates.

• Korean Journal of Mathematics
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• v.24 no.4
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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.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.547-554
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• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• Journal of the Korea Institute of Military Science and Technology
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• v.14 no.2
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• pp.205-212
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• 2011

In this paper, we have proposed a method for quantization of the stratification strength in the sea water and analysing the distributions of the maximum stratification depths calculated by the method at the seas near the Korean peninsular. For calculating the stratification strength, modified and applied the potential energy anomaly formular which was suggested by Simpson in 1977. The data had been collected by NFRDI from 1971 to 2008 were used to determine the maximum vertical density gradient depth and the relative potential energy anomaly at that depth. In the East Sea, the stratification depth has become deepened about 20m in February and April since 1971. In Yellow-South Sea, the maximum density gradient depth has been deepened about 10m only in December during the same period and the difference of the stratification depth between summer and winter has been enlarged. These trends of variation of stratification strength and depth near the Korean peninsular should be investigated more carefully and continuously. And the results of these studies could be adopted for the more efficient operation of underwater weapon and detection systems.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.10a
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• pp.454-456
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• 2017

Current and capacitance-voltage characteristics of tunnel field effect transistor (TFET) with various quantum models were investigated. Density gradient, Bohm quantum potential (BQP), and Vandort quantum correction are used with calibrating against Schrodinger-Poisson model. Drive-currents in all models. are decreased. When only BQP is used, SS and $V_{onset}$ are fixed but drive-current is decreased 3 times more than those of no quantum model. And When BQP with Vandort and density gradient are used, SS increased more than 40 mV./dec and $V_{onset}$ shifted as 0.07 eV.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.16 no.2
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• pp.121-129
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• 2002

The present paper describes a technique for installing an effective grounding grids, the major objective is forced on the experimental evaluation of the performance and characteristics with the arrangement and installation method for grounding grids consisting of the means to protect electric shock, electronics and computerized facilities against lightning, switching and ground fault surges. The study is oriented on two major areas: (1) the analysis of the ground surface potential gradient with the arrangement of grounding grids, (2) the control of the dangerous ground surface potential rise. The experiments wee carried out with the impulse currents as a function of the installation method or arrangement of grounding grids. An installation method of the inclined auxiliary grounding grid was proposed to overcome the drawbacks of equally spared grounding grids, i.e. an appropriate design concept far the installation of grounding grids was found out, It has been shown that the installation of the intwined auxiliary grounding grid can also result in a mere than 50% decrease in the maximum potential gradient on the ground surface and enhance the level of safety for persons and electronic equipments..