• Communications of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.39-46
• /
• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Asian Pacific Journal of Cancer Prevention
• /
• v.15 no.23
• /
• pp.10181-10185
• /
• 2015

Background: MicroRNAs, small noncoding RNA molecules, can regulate mammalian cell growth, apoptosis and differentiation by controlling the expression of target genes. The aim of this study was to investigate the function of miR-323-5p in the glioma cell line, U251. Materials and Methods: After over-expression of miR-323-5p using miR-323-5p mimics, cell growth, apoptosis and migration were tested by MTT, flow cytometry and cell wound healing assay, respectively. We also assessed the influence of miR-323-5p on the mRNA expression of IGF-1R by quantitative real-time reverse transcriptase PCR (qRT-PCR), and on the protein levels by Western blot analysi. In addition, dual-luciferase reporter assays were performed to determine the target site of miR-323-5p to IGF-1R 3'UTR. Results: Our findings showed that over-expression of miR-323-5p could promote apoptosis of U251 and inhibit the proliferation and migration of the glioma cells. Conclusions: This study demonstrated that increased expression of miR-323-5p might be related to glioma progression, which indicates a potential role of miR-323-5p for clinical therapy.

• Kyungpook Mathematical Journal
• /
• v.63 no.2
• /
• pp.235-250
• /
• 2023

Let 1 ≤ p, q < ∞ be fixed, and let R = [r_jk] be an infinite scalar matrix such that 1 ≤ r_jk < ∞ and sup_j,k r_jk < ∞. Let 𝓑(𝑙_p, 𝑙_q) be the set of all bounded linear operator from 𝑙_p into 𝑙_q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space S^R_p,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on S^R_p,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, sup_j,k r_jk}. The existance of S^R_p,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.6
• /
• pp.1041-1050
• /
• 2009

Let R be a ring and ${\alpha}$ a monomorphism of R. We study the skew Laurent polynomial rings R[x, x$^{-1}$; ${\alpha}$] over an ${\alpha}$-skew Armendariz ring R. We show that, if R is an ${\alpha}$-skew Armendariz ring, then R is a Baer (resp. p.p.-)ring if and only if R[x, x$^{-1}$; ${\alpha}$] is a Baer (resp. p.p.-) ring. Consequently, if R is an Armendariz ring, then R is a Baer (resp. p.p.-)ring if and only if R[x, x$^{-1}$] is a Baer (resp. p.p.-)ring.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.1
• /
• pp.13-30
• /
• 2007

In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $$du(x,\;t)\;=\;f(x,\;t,\;u_t)dt\;+\;g(x,\;t,\;u_t)dB(t),\;t\;>\;0$$ with initial data $u(x,\;0)\;=\;u_0(x)\;=\;{\xi}\;{\in}\;L^p_{F_0}\;([-{\tau},0];\;R^n)$. Here $x\;{\in}\;R^n$, ($R^n$ is the ${\nu}\;-\;dimenional$ Euclidean space), $f\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^n,\;g\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^{n{\times}m},\;u(x,\;t)\;{\in}\;R^n$ for each $t,\;u_t\;=\;u(x,\;t\;+\;{\theta})\;:\;-{\tau}\;{\leq}\;{\theta}\;{\leq}\;0\;{\in}\;C([-{\tau},\;0];\;R^n)$, and B(t) is an m-dimensional Brownian motion.

• The Plant Pathology Journal
• /
• v.23 no.3
• /
• pp.219-222
• /
• 2007

A total of the 261 Phytophthora infestans isolates collected from 2003 to 2005 in Korea were investigated for their physiological race composition. Among the isolates, we detected 18 physiological races and the dominant races were R0.1.3.5.6.10.11 and R0.1.3.5.6.7.10.11 with frequencies of 18.4% and 11.4%, respectively. All of the P. infestans races carried multiple virulence genes and showed virulence to the potato resistance genes R1, R3, R5, R6, R7, R10 and R11, but not to R8 and R9. Therefore, it is likely that the physiological races of P. infestans were diverse in Korea.

• East Asian mathematical journal
• /
• v.25 no.4
• /
• pp.433-440
• /
• 2009

Let R be a ring with unity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will consider some group actions on X by G, the left (resp. right) regular action and the conjugate action. In this paper, by investigating these group actions we can have some results as follows: First, if E(R), the set of all nonzero nonunit idempotents of a unit-regular ring R, is commuting, then $o_{\ell}(x)\;=\;o_r(x)$, $o_c(x)\;=\;\{x\}$ for all $x\;{\in}\;X$ where $o_{\ell}(x)$ (resp. $o_r(x)$, $o_c(x)$) is the orbit of x under the left regular (resp. right regular, conjugate) action on X by G and R is abelian regular. Secondly, if R is a unit-regular ring with unity 1 such that G is a cyclic group and $2\;=\;1\;+\;1\;{\in}\;G$, then G is a finite group. Finally, if R is an abelian regular ring such that G is an abelian group, then R is a commutative ring.

• Journal of Korea Water Resources Association
• /
• v.36 no.1
• /
• pp.13-21
• /
• 2003

The purpose of this study is to estimate Z-R relationships of between radar reflectivity and rainfall rate. The Z-R relationships estimated that rainfall events are selected at Yeongchun water level station where the discharge recorded from 1,000cms to 8,519cms in chungju dam basin. The result of Z-R relationship distributed at thirty two raingage sites, the constant values of A and $\beta$ are distributed between 26.4 and 7.4, 0.9 and 1.56 respectively. The correlation coefficients of standard Z-R relationships(Z=200Rl.6)shows that 0.63 lower than each other raingage sites(0.65~0.748).

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1187-1198
• /
• 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/$R{\leq}1$.

• Journal of Dental Rehabilitation and Applied Science
• /
• v.16 no.3
• /
• pp.197-210
• /
• 2000

Surface roughness is one of implant surface topography and it's found that surface roughness characterizations, such as surface energy, oxide layer thickness and its chemical composition, are closely correlated if the roughness is changed. Several studies showed the importance of analyzing surface structure so the surface structure of thread implant was analyzed to measure the implant quality exactly. In this study, surface roughness of 4 implants - MK $II^{(R)}$(Nobel Biocare), $RBM^{(R)}$(Life-Core, USA), $Osseotite^{(R)}$(3i, USA), $TPS^{(R)}$(Life-Core, USA) - were measured using $Accura^{(R)}$ and 40 implants were installed into 4 sets of ten bovine ribs based on the parameters from the measurements. From this test, the following conclusions for the initial stability were drawn by measuring and comparing RFA, Periotest Value (PTV), Removal Torgue Value (RTV). 1. $R_a$ value in surface roughness measurement was increasing by the order of $MKII^{(R)}$, $Osseotite^{(R)}$, $RBM^{(R)}$, $TPS^{(R)}$ and $R_q$ value was the same order. 2. $R_q$ value in each section was observed to increase by the order of $MKII^{(R)}$, $Osseotite^{(R)}$, $RBM^{(R)}$, $TPS^{(R)}$ in top and $MKII^{(R)}$, $RBM^{(R)}$, $Osseotite^{(R)}$, $TPS^{(R)}$ in mid-section but the value of $MKII^{(R)}$ bottom was the lowest, followed by $Osseotite^{(R)}$, $RBM^{(R)}$ and $TPS^{(R)}$. 3. RFA increased by the order of $RBM^{(R)}$(7042Hz), $MKII^{(R)}$(7047Hz), $Osseotite^{(R)}$(7076Hz), $TPS^{(R)}$(7168Hz) and there was no significance between each group. 4. PTV was increasing by the order of $MKII^{(R)}$(-1.62), $TPS^{(R)}$(-1.92), $Osseotite^{(R)}$ & $RBM^{(R)}$(-2.08) and there was no significance, either. 5. Removal torque in RTV measurement showed the increasing order of $MKII^{(R)}(5.31kgf{\cdot}cm)$, $Oeeotite^{(R)}(5.71kgf{\cdot}cm)$, $TPS^{(R)}(5.92kgf{\cdot}cm)$ and $RBM^{(R)}(7.24kgf{\cdot}cm)$ and there was no significance among groups. Above observations explains that surface roughness does not make any impact on the initial stability of implants installation.