• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.401-430
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• 2023

In this paper, we prove L^p estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)² (𝕊^n-1 × 𝕊^m-1). Furthermore, we prove L^p estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

• Molecules and Cells
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• v.24 no.2
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• pp.294-300
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• 2007

The mammalian glycosylphosphatidylinositol (GPI) anchor consists of three mannoses attached to acylated GlcN-(acyl)PI to form $Man_3$-GlcN-(acyl)PI. The first of the three mannose groups is attached to an intermediate to generate Man-GlcN-(acyl)PI by the first mannosyltransferase (GPI-MT-I). Mammalian and protozoan GPI-MT-I have different substrate specificities. PIG-M encodes the mammalial GPI-MT-I which has 423 amino acids and multiple transmembrane domains. In this work we cloned PIG-M homologues from humans, Plasmodium falciparum (PfPIG-M), and Saccharomyces cerevisiae (GPI14), to test whether they could complement GPI-MT-I-deficient mammalian cells, since this biosynthetic step is likely to be a good target for selective screening of inhibitors against many pathogenic organisms. PfPIG-M partially restored cell surface expression of the GPI-anchored protein CD59 in PIG-M deficient mammalian cells, and first mannose transfer activity in vitro; however, this was not the case for GPI14.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.405-434
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• 2005

We establish appropriate $L^p$ estimates for a class of maximal operators $S_{\Omega}^{(\gamma)}$ on the product space $R^n\;\times\;R^m\;when\;\Omega$ lacks regularity and $1\;\le\;\gamma\;\le\;2.\;Also,\;when\;\gamma\;=\;2$, we prove the $L^p\;(2\;{\le}\;P\;<\;\infty)\;boundedness\;of\;S_{\Omega}^{(\gamma)}\;whenever\;\Omega$ is a function in a certain block space $B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ (for some q > 1). Moreover, we show that the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is nearly optimal in the sense that the operator $S_{\Omega}^{(2)}$ may fail to be bounded on $L^2$ if the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is replaced by the weaker conditions $\Omega\;{\in}\;B_q^{(0,\varepsilon)}(S^{n-1}\;\times\;S^{m-1})\;for\;any\;-1\;<\;\varepsilon\;<\;0.$

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.209-229
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• 2004

Let $\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha},\;z\;{\in}\;{\mathbb{C}}^n$ be a unimodular m-homogeneous polynomial in n variables (i.e. $$\mid$s_{\alpha}$\mid$\;=\;1$ for all multi indices $\alpha$), and let $R\;{\subset}\;{\mathbb{C}}^n$ be a (bounded complete) Reinhardt domain. We give lower bounds for the maximum modules $sup_{z\;{\in}\;R\;$\mid$\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha}$\mid$$, and upper estimates for the average of these maximum moduli taken over all possible m-homogeneous Bernoulli polynomials (i.e. $s_{\alpha}\;=\;{\pm}1$ for all multi indices $\alpha$). Examples show that for a fixed degree m our estimates, for rather large classes of domains R, are asymptotically optimal in the dimension n.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.93-96
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• 1997

An atomic integral domain R is a half-factorial domain (HFD) if whenever $\chi_1$… $\chi_{m}=y_1$…$y_n$ with each $\chi_{i},y_j \in R$ irreducible, then m = n. In this paper, we show that if R[X] is an HFD, then $Cl_{t}(R)$ $\cong$ $Cl_{t}$(R[X]), and if $G_1$ and $G_2$ are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) = $G_1\bigoplus\; G_2$.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.117-119
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• 1985

Let R be a commutative noetherian ring with 1.neq.0, denoting by .nu.(I) the cardinality of a minimal basis of the ideal I. Let A be a polynomial ring in n>0 variables with coefficients in R, and let M be a maximal ideal of A. Generally it is shown that .nu.(M $A_{M}$).leq..nu.(M).leq..nu.(M $A_{M}$)+1. It is well known that the lower bound is not always satisfied, and the most classical examples occur in nonfactional Dedekind domains. But in many cases, (e.g., A is a polynomial ring whose coefficient ring is a field) the lower bound is attained. In [2] and [3], the conditions when the lower bound is satisfied is investigated. Especially in [3], it is shown that .nu.(M)=.nu.(M $A_{M}$) if M.cap.R=p is a maximal ideal or $A_{M}$ (equivalently $R_{p}$) is not regular or n>1. Hence the problem of determining whether .nu.(M)=.nu.(M $A_{M}$) can be studied when p is not maximal, $A_{M}$ is regular and n=1. The purpose of this note is to provide some conditions in which the lower bound is satisfied, when n=1 and R is a regular local ring (hence $A_{M}$ is regular)./ is regular).

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.111-114
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• 1995

A C$\^$$\infty$/ manifold is a pair (M, C) where a) M is a Hausdorff topological space such that every point $\chi$$\in$M has a neighborhood homeomorphic to an open subset of R$^n$. b) C is a collection of these homeomorphisms whose domains cover M. If ø, $\psi$ $\in$ C then ø o $\psi$$\^$-1/ is C$\^$$\infty$/. c) C is maximal with respect to (b).(omitted)

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.10 no.3
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• pp.151-159
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• 2012

The potential repository domains for A-KRS (Advanced Korean Reference Disposal System for High Level Wastes) in geological characteristics of KURT (KAERI Underground Research Tunnel) facility site were proposed to develop a repository system design and to perform the safety assessment. The host rock of KURT facility site is one of major Mesozoic plutonic rocks in Korean peninsula, two-mica granite, which was influenced by hydrothermal alteration. The topographical features control the flow lines of surface and groundwater toward south-easterly and all waters discharge to Geum River. Fracture zones distributed in study site are classified into order 2 magnitude and their dominant orientations are N-S and E-W strike. From the geological features and fracture zones, the potential repository domains for A-KRS were determined spatially based on the following conditions: (1) fracture zone must not cross the repository; and (2) the repository must stay away from the fracture zones greater than 50 m. The western region of the fracture zones in the N-S direction with a depth below 200 m from the surface was sufficient for A-KRS repository. Because most of the fracture zones in N-S direction were inclined toward the east, we expected to find a homogeneous rock mass in the western region rather than in the eastern region. The lower left domain of potential domains has more suitable geological and hydrogeological conditions for A-KRS repository.

• Journal of Magnetics
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• v.14 no.4
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• pp.147-149
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• 2009

We report the exchange bias in antiferromagnet/ferrimagnet $Cr_2O_3/Fe_3O_4$ core/shell nanoparticles. The magnetic field hysteresis curve for $Cr_2O_3/Fe_3O_4$ nanoparticles after field-cooling (FC) clearly showed both horizontal ($H_{EB}{\sim}$610 Oe) and vertical (${\Delta}M{\sim}$5.6 emu/g) shifts at 5 K. These shifts disappeared as the temperature increased toward the Neel temperature of $Cr_2O_3\;(T_N{\sim}$307 K). The $H_{EB}\;and\;{\Delta}M$ values were sharply decreased between the $1^{st}\;and\;the\;2^{nd}$ magnetic field cycles, and then slowly decreased with further cycling. These results are discussed in terms of the formation of single domains with pinned, uncompensated, antiferromagnetic spin and their evolution into multi-domains with cycling.

• Journal of Microbiology and Biotechnology
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• v.16 no.9
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• pp.1416-1421
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• 2006

We identified a gene encoding the N-acetylmuramoyl L-alanine amidase (amiB) of Vibrio anguillarum, which catalyzes the degradation of peptidoglycan in bacteria. The entire open reading frame (ORF) of the amiB gene was composed of 1,722 nucleotides and 573 amino acids. The deduced amino acid sequence of AmiB showed a modular structure with two main domains; an N-terminal region exhibiting an Ami domain and three highly conserved, continuously repeating LysM domains in the C-terminal portion. An amiB mutant was constructed by homologous recombination to study the biochemical function of the AmiB protein in V. anguillarum. Transmission electron microscopy (TEM) revealed morphological differences, and that the mutant strain formed trimeric and tetrameric unseparated cells, suggesting that this enzyme is involved in the separation of daughter cells after cell division. Furthermore, inactivation of the amiB gene resulted in a marked increase of sensitivity to oxidative stress and organic acids.