• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.355-359
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• 1994

It would be interesting to know if energy minimizing harmonic maps between manifolds have symmetric properties when the manifolds under consideration have some. In this paper, we consider among others radial symmetry. A radially symmetric manifold M of dimension m is the one with a point, called a pole, and an O(m) action as an isometric rotation with respect to the pole, or more precisely a radially symmetric manifold M has a coordinate on which the metric is of the form $ds_{M}$$^2$ = d$r^2$ + m(r)$^2$d$\theta^2$ for some function m(r) depending only on r. Of course m(0) = 0, m'(0) = 1, and when m(r) = r, (M, $ds_{ M}$/$^2$) is the Euclidean space $R^2$.(omitted)

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.65-73
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• 2003

In this paper we seek a positive, radially symmetric and energy minimizing solution of an m-Laplacian equation, -div$($\mid${\nabla}u$\mid$^{m-2}$\mid${\nabla}u)\;=\;h(u)$. In the variational sense, the solutions are the critical points of the associated functional called the energy, $J(v)\;=\;\frac{1}{m}\;\int_{R^N}\;$\mid${\nabla}v$\mid$^m\;-\;\int_{R^N}\;H(v)dx,\;where\;H(v)\;=\;{\int_0}^v\;h(t)dt$. A positive, radially symmetric critical point of J can be obtained by solving the constrained minimization problem; minimize{$\int_{R^N}$\mid${\nabla}u$\mid$^mdx$\mid$\;\int_{R^N}\;H(u)d;=\;1$}. Moreover, the solution minimizes J(v).

• Journal of Biomedical Engineering Research
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• v.26 no.4
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• pp.215-221
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• 2005

We describe the development of a prototype multi-channel electrical impedance tomography (EIT) system. The EIT system can be equipped with either a single-ended current source or a balanced current source. Each current source can inject current between any chosen pair of electrodes. In order to reduce the data acquisition time, we implemented multiple digital voltmeters simultaneously acquiring and demodulating voltage signals. Each voltmeter measures a differential voltage between a fixed pair of adjacent electrodes. All voltmeters are configured in a radially symmetric architecture to optimize the routing of wires and minimize cross-talks. To maximize the signal-to-noise ratio, we implemented techniques such as digital waveform generation, Howland current pump circuit with a generalized impedance converter, digital phase-sensitive demodulation, tri-axial cables with both grounded and driven shields, and others. The performance of the EIT system was evaluated in terms of common-mode rejection ratio, signal-to-noise ratio, and reciprocity error. Future design of a more innovative EIT system including battery operation, miniaturization, and wireless techniques is suggested.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.387-398
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• 1998

We investigate the existence of radial nodal solutions of the elliptic equation $\Delta$u ＋ h($\mid$x$\mid$)f(u) = 0, in annular domains. It is proved that for each integer k $\geq$ 1, there exist at least one radially symmetric solution which has exactly k nodes.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1131-1145
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• 2021

In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for p ∈ (2, 6) which are radially symmetric. Here, p comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case p = 6.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1252-1255
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• 1987

In this paper an approach for the analysis of the transient field response of radially symmetric transducer due to a wideband ultrasonic pulse is presented, which is based on a development of Green's function and applies the linear system theory to obtain an analytic expression for the impulse response of an annulus with a planar or spherical geometry. For the focused annular array, the impulse responses of the indivisual annuli are convolved with the delayed excitation pulse, and then summed to obtain the resultant response of the array. This process is very effective in the study of the various focusing abilities of the annular array. For illustration, the field distribution of a five element annular array is treated in detail for several focusing system.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.501-515
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• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.699-707
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• 2006

In the paper, a direct method of solution of the Navier equation is presented. An orthotropic thick hollow cylinder under a one-dimensional steady-state temperature distribution and a uniform magnetic field with general types of thermal and mechanical boundary conditions is considered. The Navier equation in terms of displacement is derived and solved analytically by the direct method, and magnetothermoelastic responses and perturbation of the magnetic field vector in the orthotropic thick hollow cylinder is described. The present method is suitable for orthotropic thick hollow cylinders placed in an axial magnetic field with arbitrary thermal and mechanical boundary conditions. Finally, numerical examples are carried out and discussed.

• Korean Journal of Plant Resources
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• v.21 no.3
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• pp.226-229
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• 2008

We described and illustrated a rare species in Korea, Hypoxis aurea Lour. (Hypoxidaceae) which was rediscovered about 70 years after its first collection from Jeju island in Korea. The members of the family Hypoxidaceae R. Br. are distinguished from the plants of Amaryllidaceae J. St-Hill. by having grass-like leaves, an invisible stem which is modified into a corm or a rhizome, trimerous, and radially symmetric flowers with an inferior ovary developing into a capsule on scapes. Hypoxis aurea Lour. is readily distinguishable from Curculigo orchinoides Gsertn. in Japan by beakless ovary and capsular fruit. The number of somatic chromosome is 2n=54.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1449-1460
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• 2021

In this paper, we consider the following nonlocal fractional Laplacian equation with a singular nonlinearity (-∆)^su(x) = λu^β (x) + a₀u^-γ (x), x ∈ ℝⁿ, where 0 < s < 1, γ > 0, $1<{\beta}{\leq}\frac{n+2s}{n-2s}$, λ > 0 are constants and a₀ ≥ 0. We use a direct method of moving planes which introduced by Chen-Li-Li to prove that positive solutions u(x) must be radially symmetric and monotone increasing about some point in ℝⁿ.