• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.853-866
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• 2014

Constacyclic codes of length $p^s$ over $R=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}$ are precisely the ideals of the ring $\frac{R[x]}{<x^{p^s}-1>}$. In this paper, we investigate constacyclic codes of length $p^s$ over R. The units of the ring R are of the forms ${\gamma}$, ${\alpha}+u{\beta}$, ${\alpha}+u{\beta}+u^2{\gamma}$ and ${\alpha}+u^2{\gamma}$, where ${\alpha}$, ${\beta}$ and ${\gamma}$ are nonzero elements of $\mathbb{F}_{p^m}$. We obtain the structures and Hamming distances of all (${\alpha}+u{\beta}$)-constacyclic codes and (${\alpha}+u{\beta}+u^2{\gamma}$)-constacyclic codes of length $p^s$ over R. Furthermore, we classify all cyclic codes of length $p^s$ over R, and by using the ring isomorphism we characterize ${\gamma}$-constacyclic codes of length $p^s$ over R.

• International Journal of Oral Biology
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• v.44 no.2
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• pp.62-70
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• 2019

Xylitol is well-known to have an anti-caries effect by inhibiting the replication of cariogenic bacteria. In addition, xylitol enhances saliva secretion. However, the precise molecular mechanism of xylitol on saliva secretion is yet to be elucidated. Thus, in this study, we aimed to investigate the stimulatory effect of xylitol on saliva secretion and to further evaluate the involvement of xylitol in muscarinic type 3 receptor (M3R) signaling. For determining these effects, we measured the saliva flow rate following xylitol treatment in healthy individuals and patients with dry mouth. We further tested the effects of xylitol on M3R signaling in human salivary gland (HSG) cells using real-time quantitative reverse-transcriptase polymerase chain reaction, immunoblotting, and immunostaining. Xylitol candy significantly increased the salivary flow rate and intracellular calcium release in HSG cells via the M3R signaling pathway. In addition, the expressions of M3R and aquaporin 5 were induced by xylitol treatment. Lastly, we investigated the distribution of M3R and aquaporin 5 in HSG cells. Xylitol was found to activate M3R, thereby inducing increases in $Ca^{2+}$ concentration. Stimulation of the muscarinic receptor induced by xylitol activated the internalization of M3R and subsequent trafficking of aquaporin 5. Taken together, these findings suggest a molecular mechanism for secretory effects of xylitol on salivary epithelial cells.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.113-117
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• 1993

Good yield synthetic routes for the production of new B-alkyl-dithiaborane clusters are reported. The syntheses of the B-alkyl-dithiaboranes are based on the use of Fischer-type carbene reagents to activate the B-H bonds of dithiaborane for alkyl-addition reactions and are the first examples of transition-mediated reactions of dithiaborane to be reported. Thus, reactions employing arachno-$S_2B_7H_8$- and $(CO)_5M{C(R_1)R_2}$ (M = Cr, W; $R_1 = CH_3,\;C_6H_5;\; R_2 = OCH_3,\;SC_6H_5)$ were found to yield the intermidiate anions I, $[(CO)_5M{C(R_1)R_2S_2B_7H_8}]^-$, which upon protonation gave the corresponding neutral, air-sensitive cluster arachno-4-$RCH_2-6,8-S_2B_7H_8(R=CH_3,\;IIa;\;C_6H_5,\;IIb)$ range from 30 to 35% yield. Complexes IIa and IIb are isoelectronic with arachno-6,8-$S_2B_7H_9$ and, on the basis of the spectroscopic data, are proposed to adopt a similar arachno cage geometry in which an $RCH_2$ units are substituted to 4 position boron atom of the arachno-6,8-$S_2B_7H_9$.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.483-494
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• 2010

Let R be a non-commutative prime ring and I a non-zero left ideal of R. Let U be the left Utumi quotient ring of R and C be the center of U and k, m, n, r fixed positive integers. If there exists a generalized derivation g of R such that $[g(x^m)x^n,\;x^r]_k\;=\;0$ for all x $\in$ I, then there exists a $\in$ U such that g(x) = xa for all x $\in$ R except when $R\;{\cong}\;=M_2$(GF(2)) and I[I, I] = 0.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.885-902
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• 2016

In this paper we begin the study of $L_k$-2-type hypersurfaces of a hypersphere ${\mathbb{S}}^{n+1}{\subset}{\mathbb{R}}^{n+2}$ for $k{\geq}1$ Let ${\psi}:M^3{\rightarrow}{\mathbb{S}}^4$ be an orientable $H_k$-hypersurface, which is not an open portion of a hypersphere. Then $M^3$ is of $L_k$-2-type if and only if $M^3$ is a Clifford tori ${\mathbb{S}}^1(r_1){\times}{\mathbb{S}}^2(r_2)$, $r^2_1+r^2_2=1$, for appropriate radii, or a tube $T^r(V^2)$ of appropriate constant radius r around the Veronese embedding of the real projective plane ${\mathbb{R}}P^2({\sqrt{3}})$.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.1-14
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• 1998

In this short note we study the torsion theories over a commutative ring R and discuss a relative dimension related to such theories for R-modules. Let ${\sigma}$ be a torsion functor and (T, F) be its corresponding partition of Spec(R). The concept of ${\sigma}$-Cohen Macaulay (abbr. ${\sigma}$-CM) module is defined and some of the main points concerning the usual Cohen-Macaulay modules are extended. In particular it is shown that if M is a non-zero ${\sigma}$-CM module over R and S is a multiplicatively closed subset of R such that, for all minimal element of T, $S{\cap}p={\emptyset}$, then $S^{-1}M$ is a $S^{-1}{\sigma}$-CM module over $S^{-1}$R, where $S^{-1}{\sigma}$ is the direct image of ${\sigma}$ under the natural ring homomorphism $R{\longrightarrow}S^{-1}R$.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.621-626
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• 2001

Let { $A_{>o}$ t= exp(M log t)} $_{t}$ be a dilation group where M is a real n$\times$n matrix whose eigenvalues has strictly positive real part, and let $\rho$be an $A_{t}$ -homogeneous distance function defined on ( $R^{n}$ ). Suppose that K is a function defined on ( $R^{n}$ ) such that /K(x)/$\leq$ (No Abstract.see full/text) for a decreasing function defined on (t) on R+ satisfying where wo(x)=│log│log (x)ll. For f$\in$ $L_{1}$ ( $R^{n}$ ), define f(x)=sup t>0 Kt*f(x)=t-v K(Al/tx) and v is the trace of M. Then we show that \ulcorner is a bounded operator of $L_{-{1}( $R^{n}$ ) into $L^1$,$\infty$( $R^{n}$).

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.9 no.3
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• pp.276-283
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• 1997

The nucleate boiling heat transfer experiments are performed using a ternary refrigerant R407C which is a candidate of alternatives of HCFC 22. The boiling phenomena for R-32, R-125, and R-134a which are the constituent refrigerants of R407C are also investigated to give the foundation of theoretical research for the mixture component boiling. The nucleate boiling heat transfer coefficients of R407C is less than those of HCFC 22 which has the similar physical and transport properties. Since the experimental results show the deterioration of boiling heat transfer coefficients of ternary mixture refrigerants R407C, the boiling heat transfer coefficients of R407C cannot be obtained by the linear combination of boiling heat transfer coefficients from its constituent components R-32, R125, and R134a.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.12
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• pp.6139-6144
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• 2012

Aims: Mammalian target of rapamycin (mTOR) is master regulator of the PI3K/Akt/mTOR pathway and plays an important role in NSCLCs. Here we characterized mRNA and protein expression levels of mTOR and its functional associated molecules including PTEN, IGF-1R and 4EBP1 in surgically resected NSCLCs. Methods: Fifty-four patients with NSCLCs who underwent pulmonary resection were included in current study. mRNA levels of mTOR, PTEN, IGF-1R, and 4EBP1 were evaluated by RT-PCR and protein expression of mTOR, PTEN, and IGF-1R by immunohistochemistry (IHC). Association of expression of the relevant molecules with clinical characteristics, as well as correlations between mTOR and PTEN, 4EBP1 and IGF-1R were also assessed. Results: The results of RT-PCR showed that in NSCLCs, the expression level of mTOR increased, while PTEN, 4EBP1 and IGF-1R decreased. Statistical analysis indicated high IGF-1R expression was correlated with advanced clinical stage (stage III) and PTEN expression was reversely associated with tumor size (P=0.16). The results of IHC showed mTOR positive staining in 51.8% of cases, while IGF-1R positive staining was found in 83.3% and loss of PTEN in 46.3%. Protein expression of mTOR was correlated with its regulators, PTEN and IGF-1R, to some extent. Conclusions: Abnormal activation of mTOR signaling, high expression of IGF-1R, and loss of PTEN were observed in resected NSCLC specimens. The poor expression agreement of mTOR with its regulators, PTEN, and IGF-1R, implied that combination strategy of mTOR inhibitors with other targets hold significant potential for NSCLC treatment.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.35-43
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• 2009

We say that an isometric immersed hypersurface x : $M^n\;{\rightarrow}\;{\mathbb{R}}^{n+1}$ is of $L_k$-finite type ($L_k$-f.t.) if $x\;=\;{\sum}^p_{i=0}x_i$ for some positive integer p < $\infty$, $x_i$ : $M{\rightarrow}{\mathbb{R}}^{n+1}$ is smooth and $L_kx_i={\lambda}_ix_i$, ${\lambda}_i\;{\in}\;{\mathbb{R}}$, $0{\leq}i{\leq}p$, $L_kf=trP_k\;{\circ}\;{\nabla}^2f$ for $f\;{\in}\'C^{\infty}(M)$, where $P_k$ is the kth Newton transformation, ${\nabla}^2f$ is the Hessian of f, $L_kx\;=\;(L_kx^1,\;{\ldots},\;L_kx^{n+1})$, $x=(x^1,\;{\ldots},\;x^{n+1})$. In this article we study the following(hyper)surfaces in ${\mathbb{R}}^{n+1}$ from the view point of $L_1$-finiteness type: totally umbilic ones, generalized cylinders $S^m(r){\times}{\mathbb{R}}^{n-m}$, ruled surfaces in ${\mathbb{R}}^{n+1}$ and some revolution surfaces in ${\mathbb{R}}^3$.