• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.349-355
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• 1995

Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

• BMB Reports
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• v.52 no.3
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• pp.214-219
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• 2019

The role of tumor-proximal factors in tumor plasticity during chemoresistance and metastasis following chemotherapy is well studied. However, the role of endothelial cell (EC) derived paracrine factors in tumor plasticity, their effect on chemotherapeutic outcome, and the mechanism by which these paracrine factors modulate the tumor microenvironment are not well understood. In this study, we report a novel mechanism by which endothelial miR-125a and let-7e-mediated regulation of interleukin-6 (IL-6) signaling can manipulate vasculogenic mimicry (VM) formation of MDA-MB-231 breast cancer cells. We found that endothelial IL-6 levels were significantly higher in response to cisplatin treatment, whereas levels of IL-6 upon cisplatin exposure remained unchanged in MDA-MB-231 breast cancer cells. We additionally found an inverse correlation between IL-6 and miR-125a/let-7e expression levels in cisplatin treated ECs. Interestingly, IL-6, IL-6 receptor (IL-6R), and signal transducer and activator of transcription 3 (STAT3) genes in the IL-6 pathway are closely regulated by miR-125a and let-7e, which directly target its 3' untranslated region. Functional analyses revealed that endothelial miR-125a and let-7e inhibit IL-6-induced adhesion of monocytes to ECs. Furthermore, conditioned medium from cisplatin treated ECs induced a significantly higher formation of VM in MDA-MB-231 breast cancer cells as compared to that from intact ECs; this effect of cisplatin treatment was abrogated by concurrent overexpression of miR-125a and let-7e. Overall, this study reveals a novel EC-tumor cell crosstalk mediated by the endothelial miR-125a/let-7e-IL-6 signaling axis, which might improve chemosensitivity and provide potential therapeutic targets for the treatment of cancer.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.819-826
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• 1998

The purpose of this paper is to prove the following results; (1) Let R be a prime ring of char $(R)\neq 2$ and I a nonzero left ideal of R. The existence of a nonzero symmetric bi-derivation D : $R\timesR\;\longrightarrow\;$ such that d is sew-commuting on I where d is the trace of D forces R to be commutative (2) Let m and n be integers with $m\;\neq\;0.\;or\;n\neq\;0$. Let R be a noncommutative prime ring of char$ (R))\neq \; 2-1\; p_1 \;n_1$ where p is a prime number which is a divisor of m, and I a nonzero two-sided ideal of R. Let $D_1$ ; $R\;\times\;R\;\longrightarrow\;and\;$ $D_2\;:\;R\;\times\;R\;longrightarrow\;R$ be symmetric bi-derivations. Suppose further that there exists a symmetric bi-additive mapping B ; $R\;\times\;R\;\longrightarrow\;and\;$ such that $md_1(\chi)\chi ＋ n\chi d_2(\chi)=f(\chi$) holds for all $\chi$$\in$I, where $d_1 \;and\; d_2$ are the traces of $D_1 \;and\; D_2$ respectively and f is the trace of B. Then we have $D_1=0 \;and\; D_2=0$.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.351-366
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• 2007

Let R be a commutative ring and let M be an R-module. Let X = Spec(M) be the prime spectrum of M with Zariski topology. Our main purpose in this paper is to specify the topological dimensions of X, where X is a Noetherian topological space, and compare them with those of topological dimensions of $Supp_{R}$(M). Also we will give a characterization for the irreducibility of X and we obtain some related results.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.235-250
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• 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
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• v.57 no.3
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• pp.709-737
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• 2020

Let R be a prime ring of characteristic different from 2. Suppose that F, G, H and T are generalized derivations of R. Let U be the Utumi quotient ring of R and C be the center of U, called the extended centroid of R and let f(x₁, …, x_n) be a non central multilinear polynomial over C. If F(f(r₁, …, r_n))G(f(r₁, …, r_n)) - f(r₁, …, r_n)T(f(r₁, …, r_n)) = H(f(r₁, …, r_n)²) for all r₁, …, r_n ∈ R, then we describe all possible forms of F, G, H and T.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.617-622
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• 2021

Let R be a commutative ring with identity, R[X] the polynomial ring over R and S a multiplicative subset of R. Let U = {f ∈ R[X] | f is monic} and let N = {f ∈ R[X] | c(f) = R}. In this paper, we show that if S is an anti-Archimedean subset of R, then R is an S-Noetherian ring if and only if R[X]_U is an S-Noetherian ring, if and only if R[X]_N is an S-Noetherian ring. We also prove that if R is an integral domain and R[X]_U is an S-principal ideal domain, then R is an S-principal ideal domain.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.99-104
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• 1994

Let R be a left Artinian ring with identity 1 and let G be the group of units of R. It is shown that if G is finite, then R is finite. It is also shown that if 2.1 is a unit in R, then G is abelian if and only if R is commutative.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.207-213
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• 1995

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$-algebras of F. If $r > 0$, let $J = [-r,0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert = sup_{s \in J}$\mid$\gamma(s)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E,F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.731-737
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• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.