• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1485-1495
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• 2019

The purpose of this paper is to compute the number of semistar operations of certain classes of finite dimensional $Pr{\ddot{u}}fer$ domains. We prove that ${\mid}SStar(R){\mid}={\mid}Star(R){\mid}+{\mid}Spec(R){\mid}+ {\mid}Idem(R){\mid}$ where Idem(R) is the set of all nonzero idempotent prime ideals of R if and only if R is a $Pr{\ddot{u}}fer$ domain with Y -graph spectrum, that is, R is a $Pr{\ddot{u}}fer$ domain with exactly two maximal ideals M and N and $Spec(R)=\{(0){\varsubsetneq}P_1{\varsubsetneq}{\cdots}{\varsubsetneq}P_{n-1}{\varsubsetneq}M,N{\mid}P_{n-1}{\varsubsetneq}N\}$. We also characterize non-local $Pr{\ddot{u}}fer$ domains R such that ${\mid}SStar(R){\mid}=7$, respectively ${\mid}SStar(R){\mid}=14$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.1003-1019
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• 2021

In this paper, we introduce a class of maximal functions along twisted surfaces in ℝⁿ×ℝ^m of the form {(𝜙(|v|)u, 𝜑(|u|)v) : (u, v) ∈ ℝⁿ×ℝ^m}. We prove L^p bounds when the kernels lie in the space L^q (𝕊^n-1×𝕊^m-1). As a consequence, we establish the L^p boundedness for such class of operators provided that the kernels are in L log L(𝕊^n-1×𝕊^m-1) or in the Block spaces B^0,0_q (𝕊^n-1×𝕊^m-1) (q > 1).

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.409-421
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• 2018

Let X be a complex manifold of dimension n $n{\geqslant}2$ and let ${\Omega}{\Subset}X$ be a weakly q-convex domain with smooth boundary. Assume that E is a holomorphic line bundle over X and $E^{{\otimes}m}$ is the m-times tensor product of E for positive integer m. If there exists a strongly plurisubharmonic function on a neighborhood of $b{\Omega}$, then we solve the ${\bar{\partial}}$-problem with support condition in ${\Omega}$ for forms of type (r, s), $s{\geqslant}q$ with values in $E^{{\otimes}m}$. Moreover, the solvability of the ${\bar{\partial}}_b$-problem on boundaries of weakly q-convex domains with smooth boundary in $K{\ddot{a}}hler$ manifolds are given. Furthermore, we shall establish an extension theorem for the ${\bar{\partial}}_b$-closed forms.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1221-1241
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• 2008

Most of domains people have studied are convex bounded projective (or affine) domains. Edith $Soci{\acute{e}}$-$M{\acute{e}}thou$ [15] characterized ellipsoid in ${\mathbb{R}}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.991-1008
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• 2013

In this paper, we mainly discuss Gorenstein Dedekind do-mains (G-Dedekind domains for short) and their overrings. Let R be a one-dimensional Noetherian domain with quotient field K and integral closure T. Then it is proved that R is a G-Dedekind domain if and only if for any prime ideal P of R which contains ($R\;:_K\;T$), P is Gorenstein projective. We also give not only an example to show that G-Dedekind domains are not necessarily Noetherian Warfield domains, but also a definition for a special kind of domain: a 2-DVR. As an application, we prove that a Noetherian domain R is a Warfield domain if and only if for any maximal ideal M of R, $R_M$ is a 2-DVR.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1187-1198
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• 2019

Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1053-1066
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• 2010

In this paper, several properties of endomorphism rings of modules are investigated. A multiplication module M over a commutative ring R induces a commutative ring $M^*$ of endomorphisms of M and hence the relation between the prime (maximal) submodules of M and the prime (maximal) ideals of $M^*$ can be found. In particular, two classes of ideals of $M^*$ are discussed in this paper: one is of the form $G_{M^*}\;(M,\;N)\;=\;\{f\;{\in}\;M^*\;|\;f(M)\;{\subseteq}\;N\}$ and the other is of the form $G_{M^*}\;(N,\;0)\;=\;\{f\;{\in}\;M^*\;|\;f(N)\;=\;0\}$ for a submodule N of M.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.259-263
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• 1995

The following classical Oka-Weil approximation theorem on pseudoconvex domains in $C^n$ is well-known. Suppose that $M \subseteq C^n$ is pseudoconvex and that K is a compact subset of M with K = K, where K is the usual holomorphic hull of K in M. Then any function holomorphic in a neighborhood of K can be approximated uniformly on K by functions holomorphic on M (see [5], [6]).

• Journal of Magnetics
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• v.8 no.1
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• pp.13-17
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• 2003

The longitudinal magnetooptical Kerr effect was used to analyse magnetic domains in soft magnetic ${(Fe_{97}A1_3)}_{85}N_{15}$/$Al_{2}O_{3}$ multilayers in order to get microscopic understanding of interlayer exchange coupling. The measuring system consists of a Kerr microscope, a CCIR camera (with an 8-bit framegrabber), 16 bit digital camera and computer system for real-time image processing and to control external magnetic field and cameras. The strength of ferromagnetic (EM) coupling as a function of the spacer thickness of $Al_2O_3$ was investigated. It was found that strong FM-coupling, strong uniaxial anisotropy and coherent rotation of the magnetization have been observed for the spacer thickness in the range of 0.2 nm $\leq$ t $\leq$ 1 m, however, weak FM-coupling, patch domains and $360^{\circ}$-walls occur for the spacer thickness of t = 2.5 nm. At a spacer thickness of t $\geq$ 5 nm transition takes place from weak FM-coupling to the decoupled state where complex interlayer interactions and different types of the domain walls were observed.

• Steel and Composite Structures
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• v.24 no.2
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• pp.201-211
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• 2017

This study evaluates the reliability of present European codes in predicting the collapse load of columns made with perforated cold-formed steel (CFS) profiles under combined axial load and bending. To this aim, a series of experimental tests on slender open-section specimens have been performed at varying load eccentricity. Preliminarily, stub column tests have also been performed to calculate the effective section properties of the investigated profile. By comparison of experimental data with code-specified M-N strength domains, the authors demonstrate that present code formulations may underestimate the collapse load of thin-walled perforated open sections. The study is the first step of a wider experimental and numerical study aimed at better describing strength domains of perforated CFS open sections.