• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1733-1757
• /
• 2017

Let $R={\oplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be an integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$, ${\bar{R}}$ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of $f{\in}R_H$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. Let $R_H$ be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if $Q=fR_H{\cap}R$ for some $f{\in}R$ and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of $R_{N(H)}$ is extended from a homogeneous ideal of R, if and only if ${\bar{R}}_{H{\backslash}Q}$ is a graded-$Pr{\ddot{u}}fer$ domain for all homogeneous maximal t-ideals Q of R, if and only if ${\bar{R}}_{N(H)}$ is a $Pr{\ddot{u}}fer$ domain, if and only if R is a UMT-domain.

• BMB Reports
• /
• v.35 no.3
• /
• pp.343-347
• /
• 2002

The human protein tyrosine kinase-6 (PTK6) polypeptide that is deduced from the cDNA sequence contains a Src homology (SH) 3 domain, SH2 domain, and catalytic domain of tyrosine kinase. We initiated biochemical and NMR characterization of PTK6 SH3 domain in order to correlate the structural role of the PTK6 using circular dichroism and heteronuclear NMR techniques. The circular dichroism data suggested that the secondary structural elements of the SH3 domain are mainly composed of $\beta$-sheet conformations. It is most stable when the pH is neutral based on the pH titration data. In addition, a number of cross peaks at the low-field area of the proton chemical shift of the NMR spectra indicated that the PTK6 SH3 domain retains a unique and folded conformation at the neutral pH condition. For other pH conditions, the SH3 domain became unstable and aggregated during NMR measurements, indicating that the structural stability is very sensitive to pH environments. Both the NMR and circular dichroism data indicate that the PTK6 SH3 domain experiences a conformational instability, even in an aqueous solution.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.1041-1057
• /
• 2019

Let ${\Gamma}$ be a nonzero commutative cancellative monoid (written additively), $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}$ $R_{\alpha}$ be a ${\Gamma}$-graded integral domain with $R_{\alpha}{\neq}\{0\}$ for all ${\alpha}{\in}{\Gamma}$, and $S(H)=\{f{\in}R{\mid}C(f)=R\}$. In this paper, we study homogeneously divisorial domains which are graded integral domains whose nonzero homogeneous ideals are divisorial. Among other things, we show that if R is integrally closed, then R is a homogeneously divisorial domain if and only if $R_{S(H)}$ is an h-local $Pr{\ddot{u}}fer$ domain whose maximal ideals are invertible, if and only if R satisfies the following four conditions: (i) R is a graded-$Pr{\ddot{u}}fer$ domain, (ii) every homogeneous maximal ideal of R is invertible, (iii) each nonzero homogeneous prime ideal of R is contained in a unique homogeneous maximal ideal, and (iv) each homogeneous ideal of R has only finitely many minimal prime ideals. We also show that if R is a graded-Noetherian domain, then R is a homogeneously divisorial domain if and only if $R_{S(H)}$ is a divisorial domain of (Krull) dimension one.

• Phonetics and Speech Sciences
• /
• v.3 no.4
• /
• pp.71-81
• /
• 2011

This paper investigated how prosodic position and word type affect the phonetic structure of Korean coronal stops. Initial segments of prosodic domains were known to be more strongly articulated and longer relative to prosodic domain-medial segments. However, there are few studies examining whether the properties of prosodic domain-initial segments are affected by the information content of words (real vs. nonsense words). In addition, since the scope of domain-initial effect was known to be local to the initial consonant and the effects on the following vowel have been found to be limited, it is thus worth examining whether the prosodic domain-initial effect extends into the vowel after the initial consonant in a systematic way across different prosodic domains. The acoustic properties of Korean coronal stops (lenis /t/, aspirated /$t^h$/, and tense /t'/) were compared across Intonational Phrase, Phonological Phrase and Word-initial positions both in real and nonsense words. The durational intervals such as VOT and CV duration were cumulatively lengthened for /t/ and /$t^h$/ in the higher prosodic domain-initial positions. However, tense stop /t'/ did not show any variation as a function of prosodic position and word type. The domain-initial lenis stop showed significantly longer duration in nonsense words than in real words. But the prosodic domain-initial effect was not found in the properties of F0 and [H1-H2] of the vowel after initial stops. The present study provided evidence that speakers tend to enhance speech clarity when there is less contextual information as in prosodic domain-initial position and in nonsense words.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1969-1980
• /
• 2017

Let ${\Gamma}$ be a nonzero torsionless commutative cancellative monoid with quotient group ${\langle}{\Gamma}{\rangle}$, $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be a graded integral domain graded by ${\Gamma}$ such that $R_{{\alpha}}{\neq}\{0\}$ for all ${\alpha}{\in}{\Gamma},H$ be the set of nonzero homogeneous elements of R, C(f) be the ideal of R generated by the homogeneous components of $f{\in}R$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. In this paper, we introduce the notion of graded t-almost Dedekind domains. We then show that R is a t-almost Dedekind domain if and only if R is a graded t-almost Dedekind domain and RH is a t-almost Dedekind domains. We also show that if $R=D[{\Gamma}]$ is the monoid domain of ${\Gamma}$ over an integral domain D, then R is a graded t-almost Dedekind domain if and only if D and ${\Gamma}$ are t-almost Dedekind, if and only if $R_{N(H)}$ is an almost Dedekind domain. In particular, if ${\langle}{\Gamma}{\rangle}$ isatisfies the ascending chain condition on its cyclic subgroups, then $R=D[{\Gamma}]$ is a t-almost Dedekind domain if and only if R is a graded t-almost Dedekind domain.

• Korean Journal of Mathematics
• /
• v.32 no.1
• /
• pp.97-107
• /
• 2024

Let A ⊆ B be an extension of integral domains with characteristic zero. Let H(A, B) and h(A, B) be rings of composite Hurwitz series and composite Hurwitz polynomials, respectively. We simply call H(A, B) and h(A, B) composite Hurwitz rings of A and B. In this paper, we study when H(A, B) and h(A, B) are unique factorization domains (resp., GCD-domains, finite factorization domains, bounded factorization domains).

• Korean Journal of Mathematics
• /
• v.19 no.3
• /
• pp.255-261
• /
• 2011

Let D be an integral domain, S be a torsion-free grading monoid such that the quotient group of S is of type (0, 0, 0, ${\ldots}$), and D[S] be the semigroup ring of S over D. We show that D[S] is an H-domain if and only if D is an H-domain and each maximal t-ideal of S is a $v$-ideal. We also show that if $\mathbb{R}$ is the eld of real numbers and if ${\Gamma}$ is the additive group of rational numbers, then $\mathbb{R}[{\Gamma}]$ is not an H-domain.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.205-211
• /
• 2012

Let R be a graded Noetherian domain and A a graded Krull overring of R. We show that if h-dim $R\leq2$, then A is a graded Noetherian domain with h-dim $A\leq2$. This is a generalization of the well-know theorem that a Krull overring of a Noetherian domain with dimension $\leq2$ is also a Noetherian domain with dimension $\leq2$.

• Proceedings of the KIEE Conference
• /
• 2006.10c
• /
• pp.145-147
• /
• 2006

Image resizing is to change an image size by upsampling or downsampling of a digital image. Most still images and video frames are given in a compressed domain on digital media. Image resizing of a compressed image can be performed in a spatial domain via decompression or recompression. In general, resizing of a compressed image in a compressed domain is much faster than that in a spatial domain. In this paper, we propose an approach to resize images in the integer discrete cosine transform (DCT) domain, which exploits the multiplication-convolution property of DCT.

• Journal of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.449-464
• /
• 2011

We show that, if R is a graded Noetherian ring and I is a proper ideal of R generated by n homogeneous elements, then any prime ideal of R minimal over I has h-height ${\leq}$ n, and that if R is a graded Noetherian domain with h-dim R ${\leq}$ 2, then the integral closure R' of R is also a graded Noetherian domain with h-dim R' ${\leq}$ 2. We also present a short improved proof of the result that, if R is a graded Noetherian domain, then the integral closure of R is a graded Krull domain.