• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.625-631
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• 2018

Let R be a commutative ring with identity and let R[x] be the collection of polynomials with coefficients in R. There are a lot of multiplications in R[x] such that together with the usual addition, R[x] becomes a ring that contains R as a subring. These multiplications are from a class of functions ${\lambda}$ from ${\mathbb{N}}_0$ to ${\mathbb{N}}$. The trivial case when ${\lambda}(i)=1$ for all i gives the usual polynomial ring. Among nontrivial cases, there is an important one, namely, the case when ${\lambda}(i)=i!$ for all i. For this case, it gives the well-known Hurwitz polynomial ring $R_H[x]$. In this paper, we completely determine the Krull dimension of $R_H[x]$ when R is a $Pr{\ddot{u}}fer$ domain. Let R be a $Pr{\ddot{u}}fer$ domain. We show that dim $R_H[x]={\dim}\;R+1$ if R has characteristic zero and dim $R_H[x]={\dim}\;R$ otherwise.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1225-1236
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• 2016

Let R be a commutative ring with $1{\neq}0$ and n a positive integer. In this article, we introduce the n-Krull dimension of R, denoted $dim_n\;R$, which is the supremum of the lengths of chains of n-absorbing ideals of R. We study the n-Krull dimension in several classes of commutative rings. For example, the n-Krull dimension of an Artinian ring is finite for every positive integer n. In particular, if R is an Artinian ring with k maximal ideals and l(R) is the length of a composition series for R, then $dim_n\;R=l(R)-k$ for some positive integer n. It is proved that a Noetherian domain R is a Dedekind domain if and only if $dim_n\;R=n$ for every positive integer n if and only if $dim_2\;R=2$. It is shown that Krull's (Generalized) Principal Ideal Theorem does not hold in general when prime ideals are replaced by n-absorbing ideals for some n > 1.

• Asian-Australasian Journal of Animal Sciences
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• v.24 no.5
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• pp.610-615
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• 2011

We examined the correlations between lactation curve shape, including persistency and changes in body condition score (BCS) during early-stage (0 to 30 days in milk (DIM)), nadir-stage (31 to 90 DIM), and late-stage (91 to 240 DIM) lactation in 191 first-lactation cows. Data used were first-parity BCS records, scored twice every month after calving, and daily milk yields. Individual lactation curves were depicted by the Wilmink function. Lactation persistency was defined as the difference in estimated milk yields between 240 DIM and 60 DIM. Changes in BCSs in the early and late stages were defined as linear regression coefficients. There were no significant correlations between traits for lactation curve shape and change in BCS in early-stage lactation. Peak yield and total milk yield were negatively correlated with BCSs in nadir- and late-stage lactation and with BCS change in late-stage lactation, suggesting that cows with high lactation yields had low body reserves and health status in mid- to late lactation and had delayed recovery of body reserves. Lactation persistency was positively correlated with change in BCS in late-stage lactation, suggesting that cows with high lactation persistency tended to be healthy and to recover their body reserves well in late lactation.

• Asian-Australasian Journal of Animal Sciences
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• v.31 no.10
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• pp.1542-1549
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• 2018

Objective: Because lactation periods in dairy cows lengthen with increasing total milk production, it is important to predict individual productivities after 305 days in milk (DIM) to determine the optimal lactation period. We therefore examined whether the random regression (RR) coefficient from 306 to 450 DIM (M2) can be predicted from those during the first 305 DIM (M1) by using a RR model. Methods: We analyzed test-day milk records from 85,690 Holstein cows in their first lactations and 131,727 cows in their later (second to fifth) lactations. Data in M1 and M2 were analyzed separately by using different single-trait RR animal models. We then performed a multiple regression analysis of the RR coefficients of M2 on those of M1 during the first and later lactations. Results: The first-order Legendre polynomials were practical covariates of RR for the milk yields of M2. All RR coefficients for the additive genetic (AG) effect and the intercept for the permanent environmental (PE) effect of M2 had moderate to strong correlations with the intercept for the AG effect of M1. The coefficients of determination for multiple regression of the combined intercepts for the AG and PE effects of M2 on the coefficients for the AG effect of M1 were moderate to high. The daily milk yields of M2 predicted by using the RR coefficients for the AG effect of M1 were highly correlated with those obtained by using the coefficients of M2. Conclusion: Milk production after 305 DIM can be predicted by using the RR coefficient estimates of the AG effect during the first 305 DIM.

• The Korean Journal of Physiology and Pharmacology
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• v.27 no.5
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• pp.493-511
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• 2023

Hippo/YAP signaling hinders cancer progression. Inactivation of this pathway contributes to the development of esophageal cancer by activation of Akt. However, the possible interaction between Akt and Hippo/YAP pathways in esophageal cancer progression is unclear. In this study, we found that ursolic acid (UA) plus 3'3-diindolylmethane (DIM) efficiently suppressed the oncogenic Akt/Gsk-3β signaling pathway while activating the Hippo tumor suppressor pathway in esophageal cancer cells. Moreover, the addition of the Akt inhibitor LY294002 and the PI3K inhibitor 3-methyladenine enhanced the inhibitory effects of UA plus DIM on Akt pathway activation and further stimulated the Hippo pathway, including the suppression of YAP nuclear translocation in esophageal cancer cells. Silencing YAP under UA plus DIM conditions significantly increased the activation of the tumor suppressor PTEN in esophageal cancer cells, while decreasing p-Akt activation, indicating that the Akt signaling pathway could be down-regulated in esophageal cancer cells by targeting PTEN. Furthermore, in a xenograft nude mice model, UA plus DIM treatment effectively diminished esophageal tumors by inactivating the Akt pathway and stimulating the Hippo signaling pathway. Thus, our study highlights a feedback loop between the PI3K/Akt and Hippo signaling pathways in esophageal cancer cells, implying that a low dose of UA plus DIM could serve as a promising chemotherapeutic combination strategy in the treatment of esophageal cancer.

• Journal of Photoscience
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• v.9 no.2
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• pp.364-366
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• 2002

Photoadaptation of Chlorobium (Cb.) phaeobacteroides was investigated under dim and strong light intensity. Absorption spectra of these whole cellIs were different each other. The Soret band intensity and the Qy bandwidth of BChl e in c디l grown under dim light intensity were smaller and more broadened than those under strong light intensity. From HPLC analysis of the pigments, total carotenoid (Car) / bacterochorolphyll (BChl) e ratio of cell increased wi1h increase of light intensities. But camposition of BChl e hamologs almost unchanged. Cb. phaeobacteroides contains 11 kinds of Car including isorenieratene and beta-isorenieratene as major Car. The campositions of Car were different for cells grown under dim and strong light intensities. In conclusion, Cb. phaeobacteroides changes total amount and canposition of Car to adapt various light intensities, while homolog canposition of BChle unchange.

• 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).

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1007-1012
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• 2018

Let R be an integral domain. We prove that the power series ring R[[X]] is a Krull domain if and only if R[[X]] is a generalized Krull domain and t-dim $R{\leq}1$, which improves a well-known result of Paran and Temkin. As a consequence we show that one of the following statements holds: (1) the concepts "Krull domain" and "generalized Krull domain" are the same in power series rings, (2) there exists a non-t-SFT domain R with t-dim R > 1 such that t-dim R[[X]] = 1.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.115-119
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• 2007

Let R be a Krull ring with the unique regular maximal ideal M. We show that R has a regular prime element and reg-$dimR=1{\Leftrightarrow}R$ is a factorial ring and reg-$dim(R)=1{\Rightarrow}M$ is invertible ${\Leftrightarrow}R{\varsubsetneq}[R:M]{\Leftrightarrow}M$ is divisorial ${\Leftrightarrow}$ reg-$htM=1{\Rightarrow}R$ is a rank one discrete valuation ring. We also show that if M is generated by regular elements, then R is a rank one discrete valuation ring ${\Rightarrow}$ R is a factorial ring and reg-dim(R)=1.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.779-791
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• 2016

Transfer of homological properties under base change is a classical field of study. Let $R{\rightarrow}S$ be a ring homomorphism. The relations of Gorenstein projective (or Gorenstein injective) dimensions of unbounded complexes between $U{\otimes}^L_RX$(or $RHom_R(X,U)$) and X are considered, where X is an R-complex and U is an S-complex. In addition, some sufficient conditions are given under which the equalities $G-dim_S(U{\otimes}^L_RX)=G-dim_RX+pd_SU$ and $Gid_S(RHom_R(X,U))=G-dim_RX+id_SU$ hold.