• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.265-277
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• 1995

In [9], we gave a very explicit description of the injective envelope of an arbitray simple module over a polynomial ring $K[X_1, \ldots, X_n]$ over a field K in indeterminates $X_1, \ldots, X_n$. This paper presents another approach to give a description.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.63-70
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• 1996

Let K be a field of characteristic 0 and G a Klein's four group. We find the idempotent elements and units of the group ring KG by using the basic group table matrix of G.

• Journal of Astronomy and Space Sciences
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• v.40 no.2
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• pp.91-92
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• 2023

• East Asian mathematical journal
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• v.37 no.1
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• pp.87-95
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• 2021

Let K be an imaginary quadratic field with ��K its ring of integers. For a positive integer N, let K(N) be the ray class field of K modulo N��K, and let ��N be the field of meromorphic modular functions of level N whose Fourier coefficients lie in the Nth cyclotomic field. For each h ∈ ��N, we construct a ray class invariant as its special value in terms of the extended form class group, and show that the invariant satisfies the natural transformation formula via the Artin map in the sense of Siegel and Stark. Finally, we establish an isomorphism between the extended form class group and Gal(K(N)/K) without any restriction on K.

• Korean Journal of Materials Research
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• v.23 no.8
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• pp.453-461
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• 2013

Controlling the stick and slip motions of the contact lines in a confined geometry comprised of a spherical lens with a flat substrate is useful for manufacturing polymer ring patterns. We used a sphere on a flat geometry, by which we could control the interfaces of the solution, vapor and substrate. By this method, hundreds of concentric ring-pattern formations of a linear conjugated polymer, poly [2-methoxy-5-(2-thylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV), were generated with excellent regularity over large areas after complete solvent evaporation. Subsequently, the MEH-PPV ring patterns played a role as a directed template to organize highly regular concentric rings of single-walled carbon nanotubes(SWCNTs); when a droplet of the SWCNT suspension in water was casted onto the prepared substrate, hydrophobic polymer patterns confined the water dispersed SWCNTs in between the hydrophilicized $SiO_2/Si$ substrate. As the solvent evaporated, SWCNT-rings were formed in between MEH-PPV rings with controlled density. Finally, we used a lift-off process to produce SWCNT patterns by the removal of a sacrificial polymer template with organic solvent. We also fabricated a field effect transistor using self-assembled SWCNT networks on a $SiO_2/Si$ substrate.

• Journal of Biomedical Engineering Research
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• v.32 no.4
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• pp.305-311
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• 2011

For effective stimulation with tDCS, spatial focality of induced electrical field(EF) and current density(CD) is one of the important factors to be considered. Recently, there have been some studies to improve the spatial focality via different types of electrodes and their new configurations: some improvements using ring electrodes were reported over the conventional pad electrodes. However, most of these studies assumed isotropic conductivities in the head. In this work, we have investigated the effect of tissue anisotropy on the spatial focality of tDCS with the 4 + 1 ring electrode configuration via a 3-D high-resolution finite element(FE) head model with anisotropic conductivities in the skull and white matter. By examining the profiles of the induced EF from the head models with isotropic and anisotropic conductivities respectively, we found that the spatial focality of the induced EF significantly drops and get diffused due to tissue anisotropy. Our analysis suggests that it is critical to incorporate tissue anisotropy in the effective stimulation of the brain via tDCS.

• Korean Journal of Optics and Photonics
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• v.2 no.1
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• pp.20-25
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• 1991

Using evanescent field coupling between single ($LP_{01}$) and double ($LP_{01}, LP_{11}$) mode optical fiber, we selected LPII mode beam. With a $LP_{11}$ mode beam from a double mode fiber. we fabricated $LP_{11}$ mode fiber optic resonant ring interferometer, and assured that the guided mode is $LP_{11}$ mode from a radiation beam coming through the prism output coupler. When an external perturbation applied to the signal arm of the $LP_{11}$ fiber optic resonant ring interferometer, we examined the change of radiation mode coming from a prism output coupler and an end of optical fiber. Using two photodiode, LPn mode beam converted to voltage. This two output voltages is applied to X and Y terminal of oscilloscope to display circular motion on oscilloscope.

• Korean Journal of Optics and Photonics
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• v.24 no.5
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• pp.217-223
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• 2013

White light MTF(Modulation Transter Function)s of biconvex trial lenses from 10 to 20 diopter (D) were represented as a function of angular frequency and visual acuity, and then they were compared with AIM(Aerial Image Modulation) curves. All of the biconvex trial lenses evaluated in on-axis mode had MTF performance that could resolve Landolt's ring up to visual acuity 2.0. However, in a half field angle of five degrees, the trial lens of 10 diopters was able to resolve Landolt's ring up to visual acuity 0.9, and that of 20 diopter only up to visual acuity 0.8. This means that the trial lenses in the case of a half field angle of five degrees do not have sufficient resolution to measure visual acuity by 1.0.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.05b
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• pp.25-29
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• 2004

Corona on polymer materials causes deterioration by the combined action of the discharge striking the surface and the action of certain chemical compounds that are formed by the discharges. In the design and manufacture of polymer insulators must be sufficiently large to avoid corona discharges, otherwise a shielding or corona ring (grading ring) needs to be installed on the insulator. To conduct this purpose, many researchers have investigated end-fitting of polymer insulator by voltage distribution simulation and electrical test. Grading rings are used to improve the performance of the insulator in multiple ways. They can reduce corona and associated audible noise and radio influence and television interference. The factors determining the uses of a grading ring are line voltage, geometry and dimensions of end fittings, geometry and dimensions of line hardware, and environmental conditions. In this paper, electrical property of polymer insulator with end-fitting design have been investigated by electrical field analysis, various end-fitting design, tracking wheel test, corona inception voltage and extinction voltage. Electrical field analysis is conducted by FEM program and various end-fitting is designed through this result. Designed end-fittings are manufactured and their performance is conducted by electrical performance test.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.581-600
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• 2017

A classical result of A. Cohn states that, if we express a prime p in base 10 as $$p=a_n10^n+a_{n-1}10^{n-1}+{\cdots}+a_110+a_0$$, then the polynomial $f(x)=a_nx^n+a_{n-1}x^{n-1}+{\cdots}+a_1x+a_0$ is irreducible in ${\mathbb{Z}}[x]$. This problem was subsequently generalized to any base b by Brillhart, Filaseta, and Odlyzko. We establish this result of A. Cohn in $O_K[x]$, K an imaginary quadratic field such that its ring of integers, $O_K$, is a Euclidean domain. For a Gaussian integer ${\beta}$ with ${\mid}{\beta}{\mid}$ > $1+{\sqrt{2}}/2$, we give another representation for any Gaussian integer using a complete residue system modulo ${\beta}$, and then establish an irreducibility criterion in ${\mathbb{Z}}[i][x]$ by applying this result.