• 대한수학회논문집
• /
• 제10권2호
• /
• pp.357-363
• /
• 1995

We study non-existence of $L^2$-harmonic p-forms on a complete, non-compact Riemannian manifold without boundary as extension of results of K. Yano in the case of compact.

• 대한수학회지
• /
• 제55권5호
• /
• pp.1103-1129
• /
• 2018

In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

• 대한수학회지
• /
• 제53권3호
• /
• pp.583-595
• /
• 2016

In the present note, we deal with $L^2$ harmonic 1-forms on complete submanifolds with weighted $Poincar{\acute{e}}$ inequality. By supposing submanifold is stable or has sufficiently small total curvature, we establish two vanishing theorems for $L^2$ harmonic 1-forms, which are some extension of the results of Kim and Yun, Sang and Thanh, Cavalcante Mirandola and $Vit{\acute{o}}rio$.

• 한국전기전자재료학회:학술대회논문집
• /
• 한국전기전자재료학회 2002년도 춘계합동학술대회 논문집
• /
• pp.117-120
• /
• 2002

Electrical power system has very complexity problem that it is plan measurement system to achieve Harmonic State Estimation (HSE). This complexity problem depends on discord of necessary accuracy, certainty of noise that exist in data communication damage and converter, adaptability of network modification and minimum of expense size of system, estimated monitering. Also, quantity of available measurement equipment for harmonic measurement has been limited. Therefore, systematic method that choose measurement location for harmonic state estimation. This paper is that see proposed HSE that use Observability Analysis(OA) for harmonic state estimation of electrical power system. OA depends on measurement number, measurement location and measurement form here, it is analysis method that depend on network form and admittance of the system. OA used achieve harmonic state estimation that it is Applied to New Zealand electrical power system to prove validity of HSE algorithm that propose. This study result about harmonic state estimation of electrical power system displayed very economical and effective method by OA.

• 대한수학회보
• /
• 제59권2호
• /
• pp.469-479
• /
• 2022

In this paper, we obtain some vanishing theorems for p-harmonic 1-forms on locally conformally flat Riemannian manifolds which admit an integral pinching condition on the curvature operators.

• 대한수학회보
• /
• 제59권3호
• /
• pp.709-723
• /
• 2022

In this note, we revise some vanishing and finiteness results on hypersurfaces with finite index in ℝⁿ⁺¹. When the hypersurface is stable minimal, we show that there is no nontrivial L^2p harmonic 1-form for some p. The our range of p is better than those in [7]. With the same range of p, we also give finiteness results on minimal hypersurfaces with finite index.

• 대한수학회보
• /
• 제46권6호
• /
• pp.1213-1219
• /
• 2009

Let M$^n$ be a complete oriented non-compact minimally immersed submanifold in a complete Riemannian manifold N$^{n+p}$ of nonnegative curvature. We prove that if M is super-stable, then there are no non-trivial L$^2$ harmonic one forms on M. This is a generalization of the main result in [8].

• 대한수학회논문집
• /
• 제31권3호
• /
• pp.625-635
• /
• 2016

In this paper, we study certain doubly-warped products which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form $g=dx^2_1+p(x_1)^2dx^2_2+h(x_1)^2\;{\tilde{g}}$ on ${\mathbb{R}}^2{\times}N$, where $x_1$, $x_2$ are the local coordinates on ${\mathbb{R}}^2$ and ${\tilde{g}}$ is an Einstein metric on the manifold N. We obtained a full description of all the possible local gradient Ricci solitons.

• Kyungpook Mathematical Journal
• /
• 제48권1호
• /
• pp.15-24
• /
• 2008

Let $N{\geq}1$ and p > 1. Let ${\Omega}$ be a domain of $\mathbb{R}^N$. In this article we shall establish Kato's inequalities for quasilinear degenerate elliptic operators of the form $A_pu$ = divA(x,$\nabla$u) for $u{\in}K_p({\Omega})$, ), where $K_p({\Omega})$ is an admissible class and $A(x,\xi)\;:\;{\Omega}{\times}\mathbb{R}^N{\rightarrow}\mathbb{R}^N$ is a mapping satisfying some structural conditions. If p = 2 for example, then we have $K_2({\Omega})\;= \;\{u\;{\in}\;L_{loc}^1({\Omega})\;:\;\partial_ju,\;\partial_{j,k}^2u\;{\in}\;L_{loc}^1({\Omega})\;for\;j,k\;=\;1,2,{\cdots},N\}$. Then we shall prove that $A_p{\mid}u{\mid}\;\geq$ (sgn u) $A_pu$ and $A_pu^+\;\geq\;(sgn^+u)^{p-1}\;A_pu$ in D'(${\Omega}$) with $u\;\in\;K_p({\Omega})$. These inequalities are called Kato's inequalities provided that p = 2. The class of operators $A_p$ contains the so-called p-harmonic operators $L_p\;=\;div(\mid{{\nabla}u{\mid}^{p-2}{\nabla}u)$ for $A(x,\xi)={\mid}\xi{\mid}^{p-2}\xi$.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2003년도 ICCAS
• /
• pp.2283-2286
• /
• 2003

This paper presents conservation of electrical energy in building with harmonics analysis and compensation which occur in electrical system. We use load controlling and management system in order to adjust load factor of system.The maximum demand limiting and controlling are used ,then the system can acquire the prediction and compare it to the maximum demand set point.The electrical signal analysis based on FFT technique. The harmonics are compensated by using harmonic filters.This system consists computer which works as controller, processor , analysis and database unit together with digital power meter in form of multidrop network through serial communication via RS-485.The load control system uses PLC to control load via serial communication RS-485. The A/D converter is used for sampling the electrical signals via parallel port of computer.The harmonic filters are controlled by a computer.The data of measurement such as voltage, current, power, power factor, total harmonic distortion, energy, etc., can be saved as database and analysis. The load factor is adjusted by limiting and controlling maximum demand. The load factor adjustment can reduce the cost of electric consumption and energy generation together with harmonics compensation in order to increase high efficiency of electrical system.