• Korean Journal of Mathematics
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• 제16권4호
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• pp.553-564
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• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권3호
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• pp.181-191
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• 2018

In the present paper, we investigate the action of generalized derivation G associated with a derivation g in a (semi-) prime ring R satisfying $(G([x,y])-[G(x),y])^n=0$ for all x, $y{\in}I$, a nonzero ideal of R, where n is a fixed positive integer. Moreover, we also examine the above identity in Banach algebras.

• 대한수학회보
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• 제42권4호
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• pp.671-678
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• 2005

Let R be a noncommutative semi prime ring. Suppose that there exists a derivation d : R $\to$ R such that for all x $\in$ R, either [[d(x),x], d(x)] = 0 or $\langle$$\langle(x),\;x\rangle,\;d(x)\rangle$ = 0. In this case [d(x), x] is nilpotent for all x $\in$ R. We also apply the above results to a Banach algebra theory.

• 대한수학회보
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• 제44권2호
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• pp.215-223
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• 2007

We in this note introduce the concept of NCI rings which is a generalization of NI rings. We study the basic structure of NCI rings, concentrating rings of bounded index of nilpotency and von Neumann regular rings. We also construct suitable examples to the situations raised naturally in the process.

• 대한수학회논문집
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• 제19권4호
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• pp.619-637
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• 2004

In this paper, a left module over an associative ring with identity is defined to be openly semiprimitive (strongly semiprimitive, respectively) by the zero intersection of all maximal open fully invariant submodules (all maximal open submodules which are fully invariant, respectively) of it. For any projective module, the openly semiprimitivity of the projective module is an equivalent condition of the semiprimitivity of endomorphism ring of the projective module and the strongly semiprimitivity of the projective module is an equivalent condition of the endomorphism ring of the projective module being a sub direct product of a set of subdivisions of division rings.

• Geomechanics and Engineering
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• 제18권3호
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• pp.299-313
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• 2019

This research investigated the nonlinear compressibility, permeability, the yielding due to structural degradation and their effects on consolidation behavior of structured soft soils. Based on oedometer and hydraulic conductivity test results of natural and reconstituted soft clays, linear log (1+e) ~ $log\;{\sigma}^{\prime}$ and log (1+e) ~ $log\;k_v$ relationships were developed to capture the variations in compressibility and permeability, and the yield stress ratio (YSR) was introduced to characterize the soil structure of natural soft clay. Semi-analytical solutions for one-dimensional consolidation of soft clay under time-dependent loading incorporating the effects of soil nonlinearity and soil structure were proposed. The semi-analytical solutions were verified against field measurements of a well-documented test embankment and they can give better accuracy in prediction of excess pore pressure compared to the predictions using the existing analytical solutions. Additionally, parametric studies were conducted to analyze the effects of YSR, compression index (${\lambda}_r$ and ${\lambda}_c$), and permeability index (${\eta}_k$) on the consolidation behavior of structured soft clays. The magnitude of the difference between degree of consolidation based on excess pore pressure ($U_p$) and that based on strain ($U_s$) depends on YSR. The parameter ${\lambda}_c/{\eta}_k$ plays a significant role in predicting consolidation behavior.

• 한국인터넷방송통신학회논문지
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• 제13권3호
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• pp.103-109
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• 2013

대표적인 소수판별법으로 밀러-라빈 방법이 적용되고 있다. 밀러-라빈 판별법은 카마이클 수 또는 반소수가 합성수임에도 불구하고 소수로 잘못 판별하는 단점이 있어 m=[2,n-1], (m,n)=1인 m을 k개 선택하여 소수 여부를 판별한다. 밀러-라빈 방법은 $n-1=2^sd$, $0{\leq}r{\leq}s-1$에 대해 $m^d{\equiv}1$(mod n) 또는 $m^{2^rd}{\equiv}-1$(mod n)로 소수를 판별한다. 본 논문은 m=2로 한정시켜 98.9%를 판별할 수 있는 알고리즘을 제안한다. 제안된 방법은 $n=6k{\pm}1$, $n_1{\neq}5$로 1차로 합성수 여부를 판별한다. 2차에서는 $2^{2^{s-1}d}{\equiv}{\beta}_{s-1}$(mod n)과 $2^d{\equiv}{\beta}_0$(mod n)로 판별하였으며, 3차에서는 ${\beta}_0$ >1이면 $1{\leq}r{\leq}s-2$에서 ${\beta}_r{\equiv}-1$ 존재 여부로, ${\beta}_0=1$이면 m=3,5,7,11,13,17을 순서대로 적용하였다. 제안된 알고리즘을 n=[101,1000]에 적용한 결과 ${\beta}_0$ >1은 26개로 3.0%, ${\beta}_0$ = 1은 0.55%만 수행되었으며, 96.55%는 초기에 판별할 수 있었다.

• Journal of Ecology and Environment
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• 제35권2호
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• pp.73-78
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• 2012

$Calotropis$ $procera$ L. is a perennial shrub distributed in saline areas of deserts of South Asia. Salt stress is a very challenging subject in arid and semi-arid areas. Germination stage is very sensitive and many plants do not germinate in saline soil. The objective of this study was identifying the salinity effect on seed germination of $Calotropis$ $procera$ L. The experimental design was a complete randomized block design with NaCl and $CaCl_2$ at five levels of isobar concentrations: 0.0, -0.01, -0.05, -0.1, and -0.15 MPa. Osmotic potential had significant effects ($P$ < 0.01) on germination percentage, germination rate, shoot length, root length, and seedling dry weight. All seedling characteristics decreased with decrease in osmotic potential. Shoot length and root length decreased more than the seedling characteristics. Germination was completely inhibited in -0.1 Mpa. Priming with NaCl and $CaCl_2$ (-0.1 MPa) for four days had significant effects ($P$ < 0.01) on the germination percentages. Priming improved the seedling characteristics in all samples, especially in -0.05 Mpa, but a decrease with decrease in osmotic potential.

• 대한수학회지
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• 제53권5호
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• pp.1167-1182
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• 2016

Let M be an R-module, where R is a commutative ring with identity 1 and let G(V,E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$. We show that M over R is finite if and only if the metric dimension of the graph $ann_f({\Gamma}(M_R))$ is finite. We further show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if M is a prime-multiplication-like R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if $$M{\sim_=}R$$. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 1998년도 가을 학술발표논문집 Vol.25 No.2 (3)
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• pp.9-11
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• 1998

본 논문에서는 '그룹화된 패리티를 갖는 소수 라운드 로빈({{{{ { PRP}_{gp } }}}}:Prime Round Robiin with Grouped Parties)' 방식에 대한 기존의 조합 모델을 이용한 신뢰도 분석 시에 문제가 됐던 결함복구율을 고려하지 못한 모델링에 대해서 미르코프 모델을 이용한 신뢰도 모델링을 바탕으로 결함복구율을 고려한 신뢰도를 계산한다. 또한 산출된 신뢰도를 근거로 반최적화된(semi-optimal) 패리트 그룹 나누기 알고리즘을 도출하고 동시에 두 개의 결함에 대한 분석을 수행한다. 마르코프 모델을 이용한 신뢰도 모델링을 통해서 결함발생율만을 고려한 경우에 신뢰도가 기존의 조합 모델의 신뢰도와 거의 일치하고 결함발생율과 결함복구율을 동시에 고려한 경우에 신뢰도가 결함발생율만을 고려했을 경우보다 더높다는 것을 보인다. 반최적화된 패리티 그룹 나누기 알고리즘을 사용할 경우에, 동시에 두 개의 결함에 대한 분석을 통해서 약 30% 이상의 경우에 대해서 저장된 패리티 정보를 이용한 복구가 가능하다.