• 대한수학회지
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• 제49권4호
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• pp.687-701
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• 2012

Let $R$ be a ring and $nil(R)$ the set of all nilpotent elements of $R$. For a subset $X$ of a ring $R$, we define $N_R(X)=\{a{\in}R{\mid}xa{\in}nil(R)$ for all $x{\in}X$}, which is called a weak annihilator of $X$ in $R$. $A$ ring $R$ is called weak zip provided that for any subset $X$ of $R$, if $N_R(Y){\subseteq}nil(R)$, then there exists a finite subset $Y{\subseteq}X$ such that $N_R(Y){\subseteq}nil(R)$, and a ring $R$ is called weak symmetric if $abc{\in}nil(R){\Rightarrow}acb{\in}nil(R)$ for all a, b, $c{\in}R$. It is shown that a generalized power series ring $[[R^{S,{\leq}}]]$ is weak zip (resp. weak symmetric) if and only if $R$ is weak zip (resp. weak symmetric) under some additional conditions. Also we describe all weak associated primes of the generalized power series ring $[[R^{S,{\leq}}]]$ in terms of all weak associated primes of $R$ in a very straightforward way.

• Korean Journal of Mathematics
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• 제11권2호
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• pp.127-136
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• 2003

In this paper we obtain some properties of the weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and introduce the concepts of several types of $weak^*$ smooth compactness in smooth topological spaces and investigate some of their properties.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.233-240
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• 2006

In this paper we introduce the concepts of several types of $weak^*$ quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and investigate some of their properties.

• 대한수학회논문집
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• 제23권3호
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• pp.333-342
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• 2008

We introduce weak Armendariz ideals which are a generalization of ideals have the weakly insertion of factors property (or simply weakly IFP) and investigate their properties. Moreover, we prove that, if I is a weak Armendariz ideal of R, then I[x] is a weak Armendariz ideal of R[x]. As a consequence, we show that, R is weak Armendariz if and only if R[x] is a weak Armendariz ring. Also we obtain a generalization of [8] and [9].

• 대한한방소아과학회지
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• 제18권1호
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• pp.77-91
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• 2004

Objective: The purpose of this study were to examine the growth pattern of weak children by measurement according to the five weak symptoms (respiratory, digestive, psycho-neurological, neuromotor, urogenital symptom). Five weak symptoms are common etiology of short stature in childhood and oriental medicine therapy is used as a treatment in short stature but the effects on height are not conclusive. Methods: This clinical study had been carried out with the 166 case (male 74, female 92) of the children aged 3 to 18 years old who visited in growth clinic of Pediatrics, Dongguk university Bundang Oriental Hospital. They were divided into 3 groups by age (3-10, 11-14, 15-18 years group) Five weak symptoms were studied to determine the association with growth stature among children by comparison with the growth stature of weak children group and normal group Results: The distribution of age showed the highest in 11-14 years(58.4%), followed by I 3-10 years (26.5%), over 15years(15%) in order. In case of male, the distribution of five weak symptoms showed the highest respiratory weak symptom(68.9%), followed by digestive(52.7%), psycho-neurological(43.2%), neuromotor(24.3%), urogenital weak symptom (143.5%) and digestive weak children's Height SDS were lower than normal children in all age groups and respiratory weak children's Height SDS were lower than normal children in age group of 3-10. In case of female, the distribution of five weak symptoms showed the highest digestive weak symptom(59.8%), followed by respiratory(52.5%), psycho-neurological(51.5%), neuromotor (35.9%), urogenital weak symptom (25%) and digestive weak children's Height SDS were lower than normal children in age group of 3-14. Other weak children Height SDS were no significant difference from normal group. Conclusions: From the above result, it was suggested that weak symptoms is cause in short stature. These data indicate that the height was correlated with respiratory, digestive weak symptom and a way to improve the weakness increased significantly height in children growth stature. Growth stature should be investigated as a new field of oriental medical treatment and more controlled, long term studies are required to classify benefits of Oriental medicine therapy in short stature.

• 대한수학회지
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• 제55권6호
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• pp.1389-1421
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• 2018

In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to a semidualizing bimodule $_SC_R$, where R and S are arbitrary associative rings. We show that an iteration of the procedure used to define $G_C$-weak injective modules yields exactly the $G_C$-weak injective modules, and then give the Foxby equivalence in this setting analogous to that of C-Gorenstein injective modules over commutative Noetherian rings. Finally, some applications are given, including weak co-Auslander-Buchweitz context, model structure and dual pair induced by $G_C$-weak injective modules.

• 대한수학회보
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• 제43권1호
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• pp.141-148
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• 2006

Fuzzy (weak) implicative hyper K-ideals are introduced, and relations among fuzzy weak implicative hyper K-ideals, fuzzy implicative hyper K-ideals and fuzzy hyper K-ideals are discussed.

• 충청수학회지
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• 제31권2호
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• pp.239-246
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• 2018

In this paper, we define a concept of weak co-T-cofibration which is a generalization of weak H'-cofibration, and study some properties of weak co-T-cofibration and relations between the weak co-T-cofibration and the homology decomposition for a cofibration.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.12.2-12
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• 2003

미분 가능한 함수가 독립변수의 각 점에서 미분계수를 가지듯이 가장 일반화된 Cantor집합의 각 점에서 weak local dimension 을 갖는다. 이러한 weak local dimension 은 두 가지가 있는데 weak lower local dimension 과 weak upper local dimension 이 있다 weak lower local dimension 은 국소적인 의미로 perturbed Cantor 집합의 lower Cantor dimension 이고 Hausdorff dimension 과 관련이 있다. weak upper local dimension 은 국소적인 의미로 perturbed Cantor 집합의 upper Cantor dimension 이고 packing dimension 과 관련이 있다. 이때 각 점에 대응하는 유관한 측도는 quasi-self-similar measure 이며 그 점의 weak lower local dimension 이 s 이면 그 점의 s-차원 quasi-self-similar measure 의 lower local dimension 이 s 가 된다. 마찬가지로 그 점의 weak upper local dimension 이 s 이면 그 점의 s-차원 quasi-self-similar measure 의 upper local dimension 이 s 가 된다. 따라서 이와 같은 사실을 이용하면 가장 일반화된 Cantor집합의 각 점에서의 weak local dimension 을 이용하여 그 집합의 Hausdorff 또는 packing 차원의 정보를 얻을 수 있을 뿐 더러 weak local dimension 을 이용한 spectrum 을 또한 구할 수 있다. 한편 weak local dimension 과 유관한 quasi-self-similar measure 는 집합의 spectrum을 생성하며 이 spectrum 을 이루는 각 부분집합의 차원에 대하여 보다 좋은 정보를 주는 transformed dimension 과 또 다른 관련을 갖게 된다.

• 한국농촌건축학회논문집
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• 제15권4호
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• pp.17-24
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• 2013

Rural community in Korea being changed to aging community, declining population and income loss by the industrialization and the urbanization. The weak class in rural is confronted with more poorly environment. So it is needed to check the quality of the weak class's house in rural. Basically proposes of this paper is to find ways about rural housing improving and the vitality of rural community. This paper contents rural housing problems through the paper review and house repair characteristics for the weak class. Data for statics analysis were obtained from house repair support program for the weak class in Jeonnam province from 2011 to 2012. The results of this paper are as follow: First, house repair items ranking for the weak class in rural was insulation & heating, toilet, structure, indoor environment, electricity, outside and kitchen & waterproof. This result was reflected that weak class's energy bills is high ratio compared with income. Second, health facilities were improved for the socially disadvantaged's convenience in considering that most of weak class is a senior. Last, most of houses for weak class in rural are old clay wall and block wall. So these houses are reinforced the wall for structural safety.