• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.189-195
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• 2006

Let R be a prime ring with characteristics not 2 and ${\sigma},\;{\tau},\;{\alpha},\;{\beta}$ be auto-morphisms of R. Suppose that $d_1$ is a (${\sigma},\;{\tau}$)-derivation and $d_2$ is a (${\alpha},\;{\beta}$)-derivation on R such that $d_{2}{\alpha}\;=\;{\alpha}d_2,\;d_2{\beta}\;=\;{\beta}d_2$. In this note it is shown that; (1) If $d_1d_2$(R) = 0 then $d_1$ = 0 or $d_2$ = 0. (2) If [$d_1(R),d_2(R)$] = 0 then R is commutative. (3) If($d_1(R),d_2(R)$) = 0 then R is commutative. (4) If $[d_1(R),d_2(R)]_{\sigma,\tau}$ = 0 then R is commutative.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.471-477
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• 2019

Let (R, m) be a commutative Noetherian ring, I an ideal of R and M a non-zero finitely generated R-module. We show that if M and $H_0(I,M)$ are aCM R-modules and $I=(x_1,{\cdots},x_{n+1})$ such that $x_1,{\cdots},x_n$ is an M-regular sequence, then $H_i(I,M)$ is an aCM R-module for all i. Moreover, we prove that if R and $H_i(I,R)$ are aCM for all i, then R/(0 : I) is aCM. In addition, we prove that if R is aCM and $x_1,{\cdots},x_n$ is an aCM d-sequence, then depth $H_i(x_1,{\cdots},x_n;R){\geq}i-1$ for all i.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1253-1270
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• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.

• BMB Reports
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• v.55 no.9
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• pp.447-452
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• 2022

Neurogenic differentiation 1 (NeuroD1) is an essential transcription factor for neuronal differentiation, maturation, and survival, and is associated with inflammation in lipopolysaccharide (LPS)-induced glial cells; however, the concrete mechanisms are still ambiguous. Therefore, we investigated whether NeuroD1-targeting miRNAs affect inflammation and neuronal apoptosis, as well as the underlying mechanism. First, we confirmed that miR-30a-5p and miR-153-3p, which target NeuroD1, reduced NeuroD1 expression in microglia and astrocytes. In LPS-induced microglia, miR-30a-5p and miR-153-3p suppressed pro-inflammatory cytokines, reactive oxygen species, the phosphorylation of c-Jun N-terminal kinase, extracellular-signal-regulated kinase (ERK), and p38, and the expression of cyclooxygenase and inducible nitric oxide synthase (iNOS) via the NF-κB pathway. Moreover, miR-30a-5p and miR-153-3p inhibited the expression of NOD-like receptor pyrin domain containing 3 (NLRP3) inflammasomes, NLRP3, cleaved caspase-1, and IL-1β, which are involved in the innate immune response. In LPS-induced astrocytes, miR-30a-5p and miR-153-3p reduced ERK phosphorylation and iNOS expression via the STAT-3 pathway. Notably, miR-30a-5p exerted greater anti-inflammatory effects than miR-153-3p. Together, these results indicate that miR-30a-5p and miR-153-3p inhibit MAPK/NF-κB pathway in microglia as well as ERK/STAT-3 pathway in astrocytes to reduce LPS-induced neuronal apoptosis. This study highlights the importance of NeuroD1 in microglia and astrocytes neuroinflammation and suggests that it can be regulated by miR-30a-5p and miR-153-3p.

• East Asian mathematical journal
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• v.25 no.4
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• pp.441-447
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• 2009

Jat and Choudhari defined a near-ring R with left bipotent or right bipotent condition in 1979. Also, we can dene a near-ring R as subcommutative if aR = Ra for all a in R. From these above two concepts it is natural to investigate the near-ring R with the properties aR = $Ra^2$ (resp. $a^2R$ = Ra) for each a in R. We will say that such is a near-ring with (1,2)-potent condition (resp. a near-ring with (2,1)-potent condition). Thus, we can extend a general concept of a near-ring R with (m,n)-potent condition, that is, $a^mR\;=\;Ra^n$ for each a in R, where m, n are positive integers. We will derive properties of near-ring with (1,n) and (n,1)-potent conditions where n is a positive integer, any homomorphic image of (m,n)-potent near-ring is also (m,n)-potent, and we will obtain some characterization of regular near-rings with (m,n)-potent conditions.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.521-530
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• 2000

We find the values of numerical invariants col(R) and row (R) for R=k[te, te+1, t(e-1)e-1] where k is a field and e$\geq$4. We also show that col(R) = crs (R) and row (R) = drs(R), but they are strictly less than the reduction number of R plus 1.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.49-58
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• 2009

For $1{\leq}k{\leq}r$, let ${\sigma}$($K_{r,r}$ - ke, n) be the smallest even integer such that every n-term graphic sequence ${\pi}$ = ($d_1$, $d_2$, ..., $d_n$) with term sum ${\sigma}({\pi})$ = $d_1$ + $d_2$ + ${\cdots}$ + $d_n\;{\geq}\;{\sigma}$($K_{r,r}$ - ke, n) has a realization G containing $K_{r,r}$ - ke as a subgraph, where $K_{r,r}$ - ke is the graph obtained from the $r\;{\times}\;r$ complete bipartite graph $K_{r,r}$ by deleting k edges which form a matching. In this paper, we determine ${\sigma}$($K_{r,r}$ - ke, n) for even $r\;({\geq}4)$ and $n{\geq}7r^2+{\frac{1}{2}}r-22$ and for odd r (${\geq}5$) and $n{\geq}7r^2+9r-26$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.623-632
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• 2010

A holomorphic function F defined on the unit disc belongs to $A^{p,{\alpha}}$ (0 < p < $\infty$, 1 < ${\alpha}$ < $\infty$) if $\int\limits_U|F(z)|^p \frac{1}{1-|z|}(1+log)\frac{1}{1-|z|})^{-\alpha}$ dxdy < $\infty$. For boundedness of the composition operator defined by $C_{fg}=g{\circ}f$ mapping Blochs into $A^{p,{\alpha}$ the following (1) is a sufficient condition while (2) is a necessary condition. (1) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha}M_p(r,\lambda{\circ}f)^p\;dr$ < $\infty$ (2) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha+p}(1-r)^pM_p(r,f^#)^p\;dr$ < $\infty$.

• Journal of Life Science
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• v.14 no.1
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• pp.91-97
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• 2004

As a part of our study on the improvement of anticonvulsant, here we report the synthesis of N-acyl-$\alpha$-aminosuc-cinimides 1 and N-acyl-$\alpha$-aminoglutarimides 2. (R)-Benzoic acid 4-benzyloxycarbonylamino-2-oxo-pyrrolidin-1-ylester 6a, (R)-4-nifro-benzoic acid 4-benzyloxycarbonylamino-2- oxo-pyrrolidin-1-yl ester 6b, (R) -4-nitro-benzoic acid 4-benzyloxycarbonylamino-2-oxo-pyrrolidin-1-yl ester 6c, and (R)-propionic acid 4-benzyloxycarbonylamino-2-oxo-pyrrolidin-1-yl ester 6d were synthesized from (R)-2-benzyloxy carbonylamino-succinic acid 3 as a starting meterial. (R)-(3- Benzyloxycarbonylamino-2,6-dioxo-piperidin-1-yloxy)-acetic acid methyl ester 10a, (R)-(3-benzyloxycarbonylamino-2,6-dioxo-piperidin-1-yloxy)-acetic acid ethy1 ester 10b, an d (R)-2-(3-benzyloxycarbonylamino-2,6- diox o-piperidin-1-yl oxy)-propionic acid methyl ester l0c were synthesized from (R)- 3-carbobenzyloxy-amino-glutarmic acid 7 as a starting meterial. The yield, mp, IR, $^1H-NMR,\; and^{13}C$- NMR spectra of the products 6a, 6b, 6c, 6d, 10a, l0b, l0c are summarized in footnote. The biological studies of these compounds are in progress and will be reported in future.