• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.717-734
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• 2024

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of weakly (m, n)-prime ideals generalizing (m, n)-prime and weakly (m, n)-closed ideals. A proper ideal I of R is called weakly (m, n)-prime if for a, b ∈ R, 0 ≠ a^mb ∈ I implies either aⁿ ∈ I or b ∈ I. We justify several properties and characterizations of weakly (m, n)-prime ideals with many supporting examples. Furthermore, we investigate weakly (m, n)-prime ideals under various contexts of constructions such as direct products, localizations and homomorphic images. Finally, we discuss the behaviour of this class of ideals in idealization and amalgamated rings.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.57-71
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• 2019

Let R be an associative ring with identity, M a t.u.p. monoid with only one unit and ${\omega}:M{\rightarrow}End(R)$ a monoid homomorphism. Let R be a reversible, M-compatible ring and ${\alpha}=a_1g_1+{\cdots}+a_ng_n$ a non-zero element in skew monoid ring $R{\ast}M$. It is proved that if there exists a non-zero element ${\beta}=b_1h_1+{\cdots}+b_mh_m$ in $R{\ast}M$ with ${\alpha}{\beta}=c$ is a constant, then there exist $1{\leq}i_0{\leq}n$, $1{\leq}j_0{\leq}m$ such that $g_{i_0}=e=h_{j_0}$ and $a_{i_0}b_{j_0}=c$ and there exist elements a, $0{\neq}r$ in R with ${\alpha}r=ca$. As a consequence, it is proved that ${\alpha}{\in}R*M$ is unit if and only if there exists $1{\leq}i_0{\leq}n$ such that $g_{i_0}=e$, $a_{i_0}$ is unit and aj is nilpotent for each $j{\neq}i_0$, where R is a reversible or right duo ring. Furthermore, we determine the relation between clean and nil clean elements of R and those elements in skew monoid ring $R{\ast}M$, where R is a reversible or right duo ring.

• Journal of the Korea Society of Computer and Information
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• v.20 no.8
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• pp.29-33
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• 2015

This paper proposes a discrete logarithm algorithm that remarkably reduces the execution time of Pollard's Rho algorithm. Pollard's Rho algorithm computes congruence or collision of ${\alpha}^a{\beta}^b{\equiv}{\alpha}^A{\beta}^B$ (modp) from the initial value a = b = 0, only to derive ${\gamma}$ from $(a+b{\gamma})=(A+B{\gamma})$, ${\gamma}(B-b)=(a-A)$. The basic Pollard's Rho algorithm computes $x_i=(x_{i-1})^2,{\alpha}x_{i-1},{\beta}x_{i-1}$ given ${\alpha}^a{\beta}^b{\equiv}x$(modp), and the general algorithm computes $x_i=(x_{i-1})^2$, $Mx_{i-1}$, $Nx_{i-1}$ for randomly selected $M={\alpha}^m$, $N={\beta}^n$. This paper proposes 4-model Pollard Rho algorithm that seeks ${\beta}_{\gamma}={\alpha}^{\gamma},{\beta}_{\gamma}={\alpha}^{(p-1)/2+{\gamma}}$, and ${\beta}_{{\gamma}^{-1}}={\alpha}^{(p-1)-{\gamma}}$) from $m=n={\lceil}{\sqrt{n}{\rceil}$, (a,b) = (0,0), (1,1). The proposed algorithm has proven to improve the performance of the (0,0)-basic Pollard's Rho algorithm by 71.70%.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.9
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• pp.514-519
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• 2002

We are considering the following problem that can be used in the prediction of the structure of proteins. Given two length n arrays A, B with positive numbers and a positive number M, find all pairs of subarrays A[i]＋…A[j],$1{\leq}i{\leq}j{\leq}n$ such that A[i]＋…A[j]＋B[k]＋…B[l]=M. This paper presents an algorithm with $Ο(n^2log n+K)$ time using Ο(n) memory, where K is the number of pairs output. The previously best known one is with $Ο(n^2log +Klog n)$ time and Ο(n) memory.

• Journal of the Korea Computer Industry Society
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• v.2 no.7
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• pp.895-904
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• 2001

In this study, gain can be high because an active double balance mixer was used. Receiving system II was made with receiving system I of low IIP3, a passive double balance mixer which has low gain and high IIP3, and an intermediate frequency amplifier for enhancing the low gain. The result of simulating receiving parameter is as follows： the total NF of receiving system I was 6.4382dB, gain was 53.5dB, and IIP3 was -6.6352dB m. As for the receiving system II, the total NF was 9.70672dB, gain was 47dB, and IIP3 was 3.66729dB m.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.23-32
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• 2004

Let (B, $m_B$, ${\kappa}$) be a maximal commutative ${\kappa}$-subalgebra of a matrix algebra $M_n(\kappa)$. We will construct a maximal commutative ${\kappa}$-subalgebra (R, $m$, ${\kappa}$) of $M_n+3(\kappa)$ from the algebra B such that the algebra R has dimension greater than the dimension of B by 3. Moreover, we will show a $C_i$-construction doesn't imply a $C^3_2$-construction for $i=1,2$.

• Journal of Acupuncture Research
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• v.22 no.3
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• pp.155-167
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• 2005

Objectives : The purpose of this study was to investigate the anti-inflammatory effect of Cobrotoxin on binding affinity of cobrotoxin with P50, $IKK{\alpa}$ and $IKK{\beta}$, activities of NF-${\kappa}B$, Cell viability of astrocyte, expressions of protein molecules of NF-${\kappa}B$ such as P50, P-$1{kappa}B$, $1{\kappa}B$ and iflammation related genes such as Cox-2, iNOS, cPLA2 in the SNP or LPS induced Inflammatory pathway of Rats' astrocytes. Methods : In this study, The expression of cytosolic phospholipase A2, Nitric oxcide, Cyclooxygenase-2 and inducible nitrogen oxide synthase was determined by western blotting with corresponding antibodies, and the generation of NF-${\kappa}B$ was assayed by EMSA method in astrocytes of rats. The Cell viability of astrocytes was determined by MTT assay, and Binding affinity of Cobrotoxin with P50, $IKK{\alpha}$ and $IKK{\beta}$ was assayed by Surface plasmon resonance analysis, and NF-${\kappa}B$ dependent luciferase activity was determined by luciferase analysis, and Uptake of cobrotoxin in astrocytes was identified by Confocal laser scanning microscope Results : 1. Compared with control, LPS-induced NF-${\kappa}B$ DNA binding activity was decreased significantly by 0.1, $0.5{\mu}g/m{\ell}$ of Cobrotoxin in Astrocyte. 2. Compared with control, LPS-induced NF-kB dependent luciferase expression was decreased significantly by 0.1, 0.5 and $1{\mu}g/m{\ell}$ of Cobrotoxin in Astrocyte. 3. Compared with control, SNP induced P50, $I{\kappa}B$ expressions in astrocyte were decreased significantly by 0.1, 0.5 and $1{\mu}g/m{\ell}$ of Cobrotoxin and P-$1{\kappa}B$ expression was decreased significantly by 0.5 and $1{\mu}g/m{\ell}$ of Cobrotoxin. 4. Compared with control, LPS induced P50, $1{\kappa}B$ expressions in astrocyte were decreased significantly by 0.5 and $1{\mu}g/m{\ell}$ of Cobrotoxin. 5. Compared with control, SNP induced Cox-2, iNOS, CPLA2 expressions in astrocyte were decreased significantly by $1{\mu}g/m{\ell}$ of Cobrotoxin. 6. Compared with control, LPS induced Cox-2, cPLA2 expressions in astrocyte were decreased significantly by 0.1, 0.5, $1{\mu}g/m{\ell}$ of Cobrotoxin and iNOS expression was decreased significantly by 0.5, $1{\mu}g/m{\ell}$ of Cobrotoxin. 7. Compared with $0.5{\mu}g/m{\ell}$ of Cobrotoxin, SNP-induced NF-${\kappa}B$ DNA bindins activity in astrocyte was increased significantly by Cobrotoxin $0.5{\mu}g/m{\ell}$ with DTT 1mM and Cobrotoxin $0.5{\mu}g/m{\ell}$ with DTT 5mM. 8. Compared with $0.5{\mu}g/m{\ell}$ of Cobrotoxin, LPS-induced NF-${\kappa}B$ DNA binding activity in astrocyte was increased significantly by Cobrotoxin $0.5{\mu}g/m{\ell}$ with DTT 1mM, Cobrotoxin $0.5{\mu}g/m{\ell}$ with DTT 5mM, Cobrotoxin $0.5{\mu}g/m{\ell}$with GSH 1mM and Cobrotoxin $0.5{\mu}g/m{\ell}$ with GSH 5mM 9. Compared with $0.1{\mu}g/m{\ell}$ of cobrotoxin, SNP induced P50 expressions in astrocyte were increased significantly by Cobrotoxin $0.5{\mu}g/m{\ell}$ with DTT 1mM, Cobrotoxin $0.5{\mu}g/m{\ell}$ with DTT 5mM Cobrotoxin $0.5{\mu}g/m{\ell}$ with GSH 1mM and Cobrotoxin $0.5{\mu}g/m{\ell}$ with GSH 5mM. 10. The uptake of the labeled cobrotoxin into the cells was shown under a confocal laser scanning microscope. cobrotoxin was uptaken into the membrane and nucleus of astrocytes. Conclusions : In summary, the present results demonstrate that cobrotoxin directly binds to sulfhydryl group of p50 and IKKS resulting In the reduction of translocation of p50 and IkB release, thereby inhibits activation of NF-${\kappa}B$, and suggest that pico to nanomolar range of cobrotoxin could inhibit the expression of genes in the NF-${\kappa}B$ signal pathway.

• Asian Journal of Turfgrass Science
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• v.10 no.1
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• pp.31-40
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• 1996

The mechanical expresion provides for the use of Soil property reserves and permanent protec-tion or improvement of soil resources in accordance with measurable standards. If the functions I (initial soil property), E (soil erosion), R (soil renewal), and M. (minimum allowable value) are assumed to be integrable in region A, erosion tolerance over a region is leaded to ${\int}_A{\int}I(m, cl, re, ch, b)dA-{\int}_A{\int}{\{\int}_{to}^{\infty}[E(w, re, c, re, ch, b, t)-R(m, ch, re, b, t)]dt}\dA{\geqq}{\int}_A{\int}M_i(m, cl, re, ch, b)dA$ were variable factors are m=parent material of soil, cl=climate, re=relief or topography, ch=soil characteristics, r=rain or water, w=wind, b=biota, and t=time.

• Journal of Physiology & Pathology in Korean Medicine
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• v.24 no.2
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• pp.278-283
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• 2010

Inducible nitric oxide synthase (iNOS) are important inflammation enzyme and severe up-nitric oxide (NO) production by this enzyme has been intricate with pathogenesis of atopy dermatitis. The present study was designed in order to determine whether Lonicera japonica could inhibit atopy dermatitis through modulation of iNOS by NF-${\kappa}B$ suppression. We found that IKK mRNA and iNOS mRNA expression in RAW 264.7 macrophages stimulated with lipopolysaccharide dose-dependantly decreased by Lonicera japonica (0.4 - 1.0 mg/$m{\ell}$) and NO production decreased. The distribution of NF-${\kappa}B$ p65 and iNOS positive reacted cell in NC/Nga mice with atopy dermatitis were decreased by Lonicera japonica (45 mg/kg/day) and apoptosis were increased. These data likely indicate that Lonicera japonica may act as inflammatory regulator for atopy dermatitis through iNOS modulation by NF-${\kappa}B$B suppression and may be possible to develop useful agent for chemoprevention of NO intricate inflammatory diseases.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.