• 대한수학회보
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• 제49권6호
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• pp.1241-1250
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• 2012

We prove the maximum principle and the comparison principle of $p$-harmonic functions via $p$-harmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of $p$-harmonic functions via $p$-harmonic boundary of graphs.

• 대한수학회논문집
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• 제32권4호
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• pp.1025-1031
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• 2017

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

• 대한수학회논문집
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• 제10권2호
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• pp.357-363
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• 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
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• 제35권4호
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• pp.831-841
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• 1998

We shall discuss on some vanishing theorems of harmonic sections of a Riemannian vector bundle over a compact Riemannian manifold with boundary. In relating the results of H. Donnelly - P. Li ([4]), for special case of harmonic forms satisfying absolute or relative boundary problem, our results improve the vanishing results of T. Takahashi ([9]).

• 대한수학회보
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• 제47권2호
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• pp.423-432
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• 2010

We describe the asymptotic behavior of functions of the Royden p-algebra in terms of p-extremal length. We also prove that each bounded $\cal{A}$-harmonic function with finite energy on a complete Riemannian manifold is uniquely determined by the behavior of the function along p-almost every curve.

• Kyungpook Mathematical Journal
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• 제16권2호
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• pp.189-197
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• 1976

• 전기전자학회논문지
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• 제21권4호
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• pp.416-419
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• 2017

본 논문에서는 고속 DDR3/DDR4 SDRAM을 위한 새로운 디지털 지연고정루프 (delay-locked loop: DLL)를 제안한다. 제안하는 디지털 DLL은 디지털 지연라인의 boundary switching 문제에 의한 jitter 증가 문제를 제거하기 위하여 위상보간 (phase interpolation) 방식의 파인지연라인 (fine delay line)을 채택하였다. 또한, 제안하는 디지털 DLL은 harmonic lock 문제를 제거하기 위하여 새로운 점진직 검색 (gradual search) 알고리즘을 사용한다. 제안하는 디지털 DLL은 1.1V, 38-nm CMOS DRAM 공정으로 설계되었으며, 0.25-2.0 GHz의 주파수 동작 영역을 가진다. 2.0 GHz에서 1.1 ps의 피크-투-피크 (p-p) 지터를 가지며, 약 13 mW의 전력소모를 가진다.

• 충청수학회지
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• 제21권2호
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.

• Structural Engineering and Mechanics
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• 제22권4호
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• pp.483-510
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• 2006

The dynamic instability characteristics of laminated composite stiffened shell panels subjected to in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters like shell geometry, lamination scheme, stiffening scheme, static and dynamic load factors and boundary conditions, on the dynamic instability behaviour of laminated composite stiffened panels subjected to in-plane harmonic loads along the boundaries. The results of free vibration and buckling of the laminated composite stiffened curved panels are also presented.

• Structural Engineering and Mechanics
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• 제58권5호
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• pp.887-903
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• 2016

This study analyses the seismic response of a three-dimensional (3-D) rigid massless square foundation resting or embedded in a viscoelastic soil limited by rigid bedrock. The foundation is subjected to harmonic oblique seismic waves P, SV, SH and R. The key step is the characterization of the soil-foundation interaction by computing the impedance matrix and the input motion matrix. A 3-D frequency boundary element method (BEM) in conjunction with the thin layer method (TLM) is adapted for the seismic analysis of the foundation. The dynamic response of the rigid foundation is solved from the wave equations by taking into account the soil-foundation interaction. The solution is formulated using the frequency BEM with the Green's function obtained from the TLM. This approach has been applied to analyze the effect of soilstructure interaction on the seismic response of the foundation as a function of the kind of incident waves, the angles of incident waves, the wave's frequencies and the embedding of foundation. The parametric results show that the non-vertical incident waves, the embedment of foundation, and the wave's frequencies have important impact on the dynamic response of rigid foundations.