• Fisheries and Aquatic Sciences
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• v.1 no.2
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• pp.227-231
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• 1998

The teleosts represent ancient real-bony vertebrates in phylogeny and resemble major genetic patterns to higher vertebrates. In the present study, we have defined the single family of insulin-like growth factors (IGFs) from flounder (Paralichthys olivaceus), compared to the prototype of IGFs observed in the Agnathan hagfish. In flounder, IGFs are clearly diverged into two major types including type I and II, and they are structurally similar by displaying a multidomain structure consisting of five functional regions as previously found in other vertebrates. However, flIGF-I appears to be more basic (pI 8.03) than the flIGF-II (pI 5.34) in the fully processed form for the B to D domain region. The flIGF-I seems to contain an evolutionary conserved Asn-linked glycosylation in E domain, which is not found in flIGF­II. The most interesting feature is that flIGF-II appeared to be structurally close to hagfish IGF in secondary structures, particularly in Band D domains. This could tell us an idea on the molecular divergence of IGFs from the Agnatha to teleosts during the vertebrate phylogeny. It also support, in part, a notion regarding on how IGF-II is appeared as more embryonic during development. Nonetheless, the biologically active B to D domain region of flIGF-II shows significant sequence homology of $65.6\%$ to flIGF-Is and contains the evolutionary conserved insulin-family signature, as well as a reserved recognition site (Lys) in D domain, necessary to generate proteolytic cleavage for E-peptide. A significant structural difference was found in E domain in which flIGF-I possesses two potential alternative splicing donor site at $Val^{17,\;24}$ of E domain. Therefore, it seems so far that IGF-I sorely produces spliced variants due to the spliced E-peptide moiety while IGF-II appears to be maintained in a single type during evolution. IGF-II, however, may be also possible to transcribe unidentified variants, depending on the physiological conditions of tissues in vertebrates in vivo.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.81-87
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• 1992

Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.335-342
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• 2010

Let D be an integral domain with quotient field K,$\mathcal{I}(D)$ be the set of nonzero ideals of D, and $w$ be the star-operation on D defined by $I_w=\{x{\in}K{\mid}xJ{\subseteq}I$ for some $J{\in}\mathcal{I}(D)$ such that J is finitely generated and $J^{-1}=D\}$. The D is called a Pr$\ddot{u}$fer $v$-multiplication domain if $(II^{-1})_w=D$ for all nonzero finitely generated ideals I of D. In this paper, we show that D is a Pr$\ddot{u}$fer $v$-multiplication domain if and only if $(A{\cap}(B+C))_w=((A{\cap}B)+(A{\cap}C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $(A(B{\cap}C))_w=(AB{\cap}AC)_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $((A+B)(A{\cap}B))_w=(AB)_w$ for all $A,B{\in}\mathcal{I}(D)$, if and only if $((A+B):C)_w=((A:C)+(B:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with C finitely generated, if and only if $((a:b)+(b:a))_w=D$ for all nonzero $a,b{\in}D$, if and only if $(A:(B{\cap}C))_w=((A:B)+(A:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with B, C finitely generated.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1207-1218
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• 2011

Let * be a star-operation on an integral domain R, and let $\mathfrak{I}_*^+(R)$ be the semigroup of *-invertible integral *-ideals of R. In this article, we introduce the concept of a *-coatom, and we then characterize when $\mathfrak{I}_*^+(R)$ is a free semigroup with a set of free generators consisting of *-coatoms. In particular, we show that $\mathfrak{I}_*^+(R)$ is a free semigroup if and only if R is a Krull domain and each ${\upsilon}$-invertible ${\upsilon}$-ideal is *-invertible. As a corollary, we obtain some characterizations of *-Dedekind domains.

• 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.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.15-23
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• 2009

Let D be an integral domain, P be a nonzero prime ideal of D, $\{P_{\alpha}{\mid}{\alpha}{\in}{\mathcal{A}}\}$ be a nonempty set of prime ideals of D, and $\{I_{\beta}{\mid}{\beta}{\in}{\mathcal{B}}\}$ be a nonempty family of ideals of D with ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\neq}(0)$. Consider the following conditions: (i) If $P{\subseteq}{\cup}_{{\alpha}{\in}{\mathcal{A}}}P_{\alpha}$, then $P=P_{\alpha}$ for some ${\alpha}{\in}{\mathcal{A}}$; (ii) If ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\subseteq}P$, then $I_{\beta}{\subseteq}P$ for some ${\beta}{\in}{\mathcal{B}}$. In this paper, we prove that D satisfies $(i){\Leftrightarrow}D$ is a generalized weakly factorial domain of ${\dim}(D)=1{\Rightarrow}D$ satisfies $(ii){\Leftrightarrow}D$ is a weakly Krull domain of dim(D) = 1. We also study the t-operation analogs of (i) and (ii).

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

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.571-594
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• 2022

Let D be an integral domain with quotient field K, Pic(D) be the ideal class group of D, and X be an indeterminate. A polynomial overring of D means a subring of K[X] containing D[X]. In this paper, we study almost Dedekind domains which are polynomial overrings of a principal ideal domain D, defined by the intersection of K[X] and rank-one discrete valuation rings with quotient field K(X), and their ideal class groups. Next, let ℤ be the ring of integers, ℚ be the field of rational numbers, and 𝔊f be the set of finitely generated abelian groups (up to isomorphism). As an application, among other things, we show that there exists an overring R of ℤ[X] such that (i) R is a Bezout domain, (ii) R∩ℚ[X] is an almost Dedekind domain, (iii) Pic(R∩ℚ[X]) = $\oplus_{G{\in}G_{f}}$ G, (iv) for each G ∈ 𝔊f, there is a multiplicative subset S of ℤ such that RS ∩ ℚ[X] is a Dedekind domain with Pic(RS ∩ ℚ[X]) = G, and (v) every invertible integral ideal I of R ∩ ℚ[X] can be written uniquely as I = XnQe11···Qekk for some integer n ≥ 0, maximal ideals Qi of R∩ℚ[X], and integers ei ≠ 0. We also completely characterize the almost Dedekind polynomial overrings of ℤ containing Int(ℤ).

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.771-775
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• 2007

In this note we discussed the half-factoriality of Krull monoid domain D[S] whenever the monoid S has trivial divisor class group.

• Journal of Sasang Constitutional Medicine
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• v.19 no.3
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• pp.75-88
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• 2007

1. Objectives The purpose of this study was to objectively diagnose American male and female's production of two vowels /a, i/ by Sasang Constitution. 2. Methods It was analyzed the constitutional characteristics of the American adults voices with PSSC-2004. of 134 cases of vowels /a, i/ with a duration of $2.5{\sim}3$ seconds were inputted in PSSC-2004 and analyzed into 40 factors. 3. Results and Conclusions 1) APQ In the male group's production of vowel /a/, the Soyangin's APQ(l), APQ(3) and APQ(4) were significantly high compared with those of Taeumin and Soeumin. 2) Shimmer In the male group's production of vowel /a/, Soeumin's Octave1 Shimmer was significantly low compared with that of Taeumin and Soeumin. In the male group's production of vowel /i/, Soeumin's D-Shimmer was significantly low compared with that of Taeumin and Soeumin. In the female group's production of vowel /a/, the Soyangin's C-Shimmer was significantly high compared with that of Taeumin and Soeumin. 3) Octave In the male group's production of vowel /a/, the Soyangin's Octave3, Octave4, Octave5, Octave6 and Octave1 Ratio were significantly high compared with those of Taeumin and Soeumin. In the male group's production of vowels /a, i/, the Soyangin's Octave4 was significantly high compared with that of Taeumin and Soeumin. 4) Energy In the male group's production of vowel /a/, the Soyangin's Time Domain Total Sum /Time Domain Count, Freq Domain Total Sum /cnt(0), 0k-4k Total Sum, Dev., A(A#, C, E, D#, E, F#) tot E, and A(C,, D#, F#) Dev. were significantly high compared with those of Taeumin and Soeumin. In the male group's production of vowel /i/, the Soyangin's Time Domain Total Sum /Time Domain Count, Freq Domain Total Sum /cnt(0) and 0k-4k Total Sum, Dev. were significantly high compared with those of Taeumin and Soeumin. 5) Peak In the male group's production of vowels /a/ and /i/,, the Soyangin's Peak1 Ratio was significantly low compared with that of Taeumin and Soeumin. In the male group's production of vowels /a/ and /i/,, the Soyangin's Peak10 Ratio, Time Domain Peak Total/Total Energy Sum, Time Domain Peak Dev. and Total/Total Dev. Sum were significantly high compared with those of Taeumin and Soeumin. 6) It is necessary to expand the research of the acoustic analysis of American and Korean to other countries in the diagnosis of the Sasang Constitution by using the voice characteristics.