• 대한수학회보
• /
• 제51권4호
• /
• pp.1195-1204
• /
• 2014

We newly define the volume integral means of harmonic functions to characterize the weighted harmonic Bergman spaces. It is based on Xiao and Zhu's results on holomorphic Bergman spaces [5].

• 대한수학회보
• /
• 제46권2호
• /
• pp.263-279
• /
• 2009

On the setting of the unit ball of ${\mathbb{R}}^n$, we consider a Banach space of harmonic functions motivated by the atomic decomposition in the sense of Coifman and Rochberg [5]. First we identify its dual (resp. predual) space with certain harmonic function space of (resp. vanishing) logarithmic growth. Then we describe these spaces in terms of boundedness and compactness of certain Toeplitz operators.

• Smart Structures and Systems
• /
• 제8권3호
• /
• pp.253-274
• /
• 2011

In this paper, the harmonic displacement response of a damaged square plate with all-over part-through damage parallel to one edge is utilized as the input signal function in wavelet analysis. The method requires the properties of the damaged plate, i.e., no information about the original undamaged structure is required. The location of damage is identified by sudden changes in the spatial variation of transformed response. The incurred damage causes a change in the stiffness or mass of the plate. This causes a localized singularity which can be identified by a wavelet analysis of the displacement response. In this study via numerical examples shown by using harmonic response is more versatile and effective compared with the static deflection response, specially in the presence of noise. In the light of the obtained results, suggestions for future work are presented and discussed.

• 대한수학회보
• /
• 제32권2호
• /
• pp.211-214
• /
• 1995

Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

• 대한전기학회논문지
• /
• 제34권9호
• /
• pp.361-367
• /
• 1985

A new injection method is proposed for active power filters to eliminate AC harmonics in ac input current of nonlinear loads such as rectifiers. By injecting the PWM current determined by the proposed injection method, all the harmonics up to order nn can be eliminated to exactly zero. This PWM injection current can be generated by sampling total harmonic wave at the rate of M and the sampled values are converted into the proposed PWM wave with N pulse-width variables and adjustable current magnitude Im. These variables are deetermined by solving a set of N nonlinear harmonic equations and the harmonic-elimination characteristics of the new injection are investigated through digital computer sinmulation. Also by comparing between the simulated results and the ones synthesized by data stored in EPROM, the possibility of the suggested injection method can be shown.

• 대한수학회지
• /
• 제44권4호
• /
• pp.941-947
• /
• 2007

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive scalar curvature. Let ${\mu}0$ be the least eigenvalue of the Laplacian acting on $L^2-functions$ on M. We show that if $Ric^M{\ge}-{\mu}0$ at all $x{\in}M$ and either $Ric^M>-{\mu}0$ at some point x0 or Vol(M) is infinite, then every harmonic morphism ${\phi}:M{\to}N$ of finite energy is constant.

• Journal of applied mathematics & informatics
• /
• 제8권1호
• /
• pp.27-44
• /
• 2001

A fast Poisson solver on irregular domains, based on bound-ary methods, is presented. The harmonic polynomial approximation of the solution of the associated homogeneous problem provides a good practical boundary method which allows a trivial parallel processing for solution evaluation or straightfoward computations of the interface values for domain decomposition/embedding. AMS Mathematics Subject Classification : 65N35, 65N55, 65Y05.

• 대한수학회보
• /
• 제39권2호
• /
• pp.327-332
• /
• 2002

In this paper we prove that if M is a J-invariant sub-manifold of codimension 2 in a complex projective space $P_{n+1}(C)$, and the second fundamental tensor is cyclic-parallel or M has harmonic curvature, then M is locally complex quadric Q$_n$(C) or P$_n$(C).

• 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].

• 대한수학회지
• /
• 제54권4호
• /
• pp.1189-1208
• /
• 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.