• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.623-643
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• 2016

In this paper, we study piecewise Noetherian (resp., piecewise w-Noetherian) properties in several settings including flat (resp., t-flat) overrings, Nagata rings, integral domains of finite character (resp., w-finite character), pullbacks of a certain type, polynomial rings, and D + XK[X] constructions.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.863-872
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• 2007

Let D be an integral domain with quotient field K, A a nonempty set of height-one maximal t-ideals of D, F$({\Lambda})={I{\subseteq}D|I$ is an ideal of D such that $I{\subseteq}P$ for all $P{\in}A}$, and $D_F({\Lambda})={x{\in}K|xA{\subseteq}D$ for some $A{\in}F({\Lambda})}$. In this paper, we prove that if each $P{\in}A$ is the radical of a finite type v-ideal (resp., a principal ideal), then $D_{F({\Lambda})}$ is a weakly Krull domain (resp., generalized weakly factorial domain) if and only if the intersection $D_{F({\Lambda})}={\cap}_{P{\in}A}D_P$ has finite character, if and only if $F({\Lambda})$ is a t-splitting set of ideals, if and only if $F({\Lambda})$ is v-finite.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.487-494
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• 2021

In this paper, we study rings with Noetherian spectrum, rings with locally Noetherian spectrum and rings with t-locally Noetherian spectrum in terms of the polynomial ring, the Serre's conjecture ring, the Nagata ring and the t-Nagata ring. In fact, we show that a commutative ring R with identity has Noetherian spectrum if and only if the Serre's conjecture ring R[X]_U has Noetherian spectrum, if and only if the Nagata ring R[X]_N has Noetherian spectrum. We also prove that an integral domain D has locally Noetherian spectrum if and only if the Nagata ring D[X]_N has locally Noetherian spectrum. Finally, we show that an integral domain D has t-locally Noetherian spectrum if and only if the polynomial ring D[X] has t-locally Noetherian spectrum, if and only if the t-Nagata ring $D[X]_{N_v}$ has (t-)locally Noetherian spectrum.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.191-205
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• 2011

It is well known that for a Krull domain R, the divisor class group of R is a torsion group if and only if every subintersection of R is a ring of quotients. Thus a natural question is that under what conditions, for a non-Krull domain R, every (t-)subintersection (resp., t-linked overring) of R is a ring of quotients or every (t-)subintersection (resp., t-linked overring) of R is at. To address this question, we introduce the notions of *-compact packedness and *-coprime packedness of (an ideal of) an integral domain R for a star operation * of finite character, mainly t or w. We also investigate the t-theoretic analogues of related results in the literature.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.507-514
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• 2015

Let D be an integral domain, t be the so-called t-operation on D, and S be a (not necessarily saturated) multiplicative subset of D. In this paper, we study the Nagata ring of S-Noetherian domains and locally S-Noetherian domains. We also investigate the t-Nagata ring of t-locally S-Noetherian domains. In fact, we show that if S is an anti-archimedean subset of D, then D is an S-Noetherian domain (respectively, locally S-Noetherian domain) if and only if the Nagata ring $D[X]_N$ is an S-Noetherian domain (respectively, locally S-Noetherian domain). We also prove that if S is an anti-archimedean subset of D, then D is a t-locally S-Noetherian domain if and only if the polynomial ring D[X] is a t-locally S-Noetherian domain, if and only if the t-Nagata ring $D[X]_{N_v}$ is a t-locally S-Noetherian domain.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.169-180
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• 2009

A discontinuous Galerkin method with interior penalty terms is presented for linear Sobolev equation. On appropriate finite element spaces, we apply a symmetric interior penalty Galerkin method to formulate semidiscrete approximate solutions. To deal with a damping term $\nabla{\cdot}({\nabla}u_t)$ included in Sobolev equations, which is the distinct character compared to parabolic differential equations, we choose special test functions. A priori error estimate for the semidiscrete time scheme is analyzed and an optimal $L^\infty(L^2)$ error estimation is derived.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.02a
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• pp.176-177
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• 2013

Surface plasmon polaritons (SPPs) have attracted the attention of scientists and engineers involved in a wide area of research, microscopy, diagnostics and sensing. SPPs are waves that propagate along the surface of a conductor, usually metals. These are essentially light waves that are trapped on the surface because of their interaction with the free electrons of conductor. In this interaction, the free electrons respond collectively by oscillating in resonance with the light wave. The resonant interaction between the surface charge oscillation and the electromagnetic field of the light constitutes the SPPs and gives rise to its unique properties. In this papers, we studied theoretical and experimental extraordinary transmittance (T) and reflectance (R) of 2 dimensional metal hole array (2D-MHA) on GaAs in consideration of the diffraction orders. The 2d-MHAs was fabricated using ultra-violet photolithography, electron-beam evaporation and standard lift-off process with pitches ranging from 1.8 to $3.2{\mu}m$ and diameter of half of pitch, and was deposited 5-nm thick layer of titanium (Ti) as an adhesion layer and 50-nm thick layer of gold (Au) on the semiinsulating GaAs substrate. We employed both the commercial software (CST Microwave Studio: Computer Simulation Technology GmbH, Darmstadt, Germany) based on a finite integration technique (FIT) and a rigorous coupled wave analysis (RCWA) to calculate transmittance and reflectance. The transmittance was measured at a normal incident, and the reflectance was measured at variable incident angle of range between $30^{\circ}{\sim}80^{\circ}$ with a Nicolet Fourier transmission infrared (FTIR) spectrometer with a KBr beam splitter and a MCT detector. For MHAs of pitch (P), the peaks ${\lambda}$ max in the normal incidence transmittance spectra can be indentified approximately from SP dispersion relation, that is frequency-dependent SP wave vector (ksp). Shown in Fig. 1 is the transmission of P=2.2 um sample at normal incidence. We attribute the observation to be a result of FTIR system may be able to collect the transmitted light with higher diffraction order than 0th order. This is confirmed by calculations: for the MHAs, diffraction efficiency in (0, 0) diffracted orders is lower than in the (${\pm}x$, ${\pm}y$) diffracted orders. To further investigate the result, we calculated the angular dependent transmission of P=2.2 um sample (Fig. 2). The incident angle varies from 30o to 70o with a 10o increment. We also found the splitting character on reflectance measurement. The splitting effect is considered a results of SPPs assisted diffraction process by oblique incidence.