• 대한수학회보
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• 제32권1호
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• pp.45-56
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• 1995

D. H. Gottlieb [1, 2] studied the subgroups $G_n(X)$ of homotopy groups $\pi_n(X)$. In [5, 7, 10], the authors introduced subgroups $G_n(X, A)$ and $G_n^{Rel}(X, A) of \pi_n(X)$ and $\pi_n(X, A)$ respectively and showed that they fit together into a sequence $$ \cdots \to G_n(A) \longrightarrow^{i_*} G_n(X, A) \longrightarrow^{j_*} G_n^{Rel}(X, A) \longrightarrow^\partial $$ $$ \cdots \to G_1^{Rel}(X, A) \to G_0(A) \ to G_0(X, A) $$ where $i_*, j_*$ and \partial$ are restrictions of the usual homomorphisms of the homotopy sequence $$ \cdot \to^\partial \pi_n(A) \longrightarrow^{i_*} \pi_n(X) \longrightarrow^{j_*} \pi_n(X, A) \to \cdot \to \pi_0(A) \to \pi_0(X) $$.

• 대한수학회보
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• 제49권4호
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.437-448
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• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• Animal Systematics, Evolution and Diversity
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• nspc8호
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• pp.1-176
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• 2010

Siphonostomatoid copepods associated with marine invertebrates are described from tropical waters of the West Indies and Madagascar. They belong to the families Asterocheridae (7 new genera and 39 new species), Dinopontiidae (one new species), and Nanaspididae (one new species). New taxa of the Asterocheridae are 14 species of Asterocheres (Asterocheres unioviger n. sp., A. trisetatus n. sp., A. bahamensis n. sp., A. tricuspis n. sp., A. plumosus n. sp., A. peniculatus n. sp., A. oricurvus n. sp., A. planus n. sp., A. sensilis n. sp., A. indivisus n. sp., A. nudicoxus n. sp., A. tenuipes n. sp., A. galeatus n. sp., and A. fastigatus n. sp.); 3 species of Hetairosynella n. gen. (Hetairosynella bifurcata n. sp.; H. angulata n. sp.; H. aculeata n. sp.); 15 species of Asteropontius (Asteropontius capillatus n. sp., A. membranulatus n. sp., A. plumatus n. sp., A. parvipes n. sp., A. humesi n. sp., A. angulatus n. sp., A. latioriger n. sp., A. magnisetiger n. sp., A. pinnatus n. sp., A. trifilis n. sp., A. orcafer n. sp., A. bilinguis n. sp., A. dentatus n. sp., A. minutisetiger n. sp., and A. bispinifer n. sp.); Collocherides minutus n. sp.; Cyclocheres sensilis n. gen. n. sp.; Stenomyzon edentatum n. gen. n. sp.; Cephalocheres flagellatus n. gen. n. sp.; Humesimyzon pusillum n. gen. n. sp.; Thermocheres validus n. gen. n. sp.; and Gascardama longisiphonata n. gen. n. sp. New taxa of the remaining two families are Stenopontius spinulatus n. sp. in the Dinopontiidae and Stephopontius ahni n. sp. in the Nanaspididae. Asterocheres crinoidicola Humes, Asteropontius genodon Stock, and Asteropontius ungellatus Stock are redescribed. Asteropontius gonioporae Kim is reported as a new record from Madagascar. A key to species of Asteropontius is provided.

• 대한수학교육학회지:학교수학
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• 제8권1호
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• pp.27-43
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• 2006

이 연구의 목적은 예비중등교사들의 실제적인 수학화 능력을 신장할 수 있도록 n-단체의 n-부피를 탐구하는 교수단원 를 설계하는 것이다. 이 교수단원에서는 2차원 도형인 삼각형의 넓이와 3차원 도형인 사면체의 부피를 n-단체의 n-부피로 일반화하는 것에 초점을 맞추고 있다. 이 일반화 과정에는 형식불역의 원리와 카발리에리의 원리가 적용된다. n-단체의 n-부피를 구하기 위해 n-직교삼각기둥을 정의하고, 그것의 n-부피를 공리적으로 탐색한다. 그리고 n-단체의 n-부피를 벡터와 행렬식을 이용하여 구한다. 이 교수단원을 통해 예비 중등교사들은 삼각형과 사면체의 일반화된 도형인 n-단체, 그리고 삼각형의 넓이와 사면체의 부피의 일반화된 n-단체의 부피를 이해하고 탐구할 수 있고, 학교수학과 학문수학의 자연스런 연결을 도모할 수 있다.

• Journal of Microbiology and Biotechnology
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• 제20권1호
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• pp.63-70
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• 2010

Novel influenza A (H1N1) is a newly emerged flu virus that was first detected in April 2009. Unlike the avian influenza (H5N1), this virus has been known to be able to spread from human to human directly. Although it is uncertain how severe this novel H1N1 virus will be in terms of human illness, the illness may be more widespread because most people will not have immunity to it. In this study, we compared the codon usage bias between the novel H1N1 influenza A viruses and other viruses such as H1N1 and H5N1 subtypes to investigate the genomic patterns of novel influenza A (H1N1). Totally, 1,675 nucleotide sequences of the hemagglutinin (HA) and neuraminidase (NA) genes of influenza A virus, including H1N1 and H5N1 subtypes occurring from 2004 to 2009, were used. As a result, we found that the novel H1N1 influenza A viruses showed the most close correlations with the swine-origin H1N1 subtypes than other H1N1 viruses, in the result from not only the analysis of nucleotide compositions, but also the phylogenetic analysis. Although the genetic sequences of novel H1N1 subtypes were not exactly the same as the other H1N1 subtypes, the HA and NA genes of novel H1N1s showed very similar codon usage patterns with other H1N1 subtypes, especially with the swine-origin H1N1 influenza A viruses. Our findings strongly suggested that those novel H1N1 viruses seemed to be originated from the swine-host H1N1 viruses in terms of the codon usage patterns.

• Journal of Astronomy and Space Sciences
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• 제9권1호
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• pp.11-29
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• 1992

In 1963, Toomre built up classes of mass models for the highly flattened galaxies which have free parameters n, $a_n$ and $C_n$. In order to keep the universal dimension, we adopt parameters $b_n({C_n}^2={a_n}^{2n}+^2{b_n}^2/(n-1)!)$ insteal of $C_n$. Series of the normalized Toomre's mass models (G = $V_{max}$ =$R_{max}$ = 1, n = 1 to 7) are derived and the normalized parameters $a_n$ and $b_n$ are determined by the iteration method. Replacing parameters $a_n$ and $b_n$ to ${a_n}^l(=a_nr_{max})$ and ${b_n}^l(=b_n\cdotV_{max}/r_{max})$, we can get the generalization of Toomre's mass model.

• 대한수학회논문집
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• 제38권4호
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• pp.1001-1017
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• 2023

Let R be a commutative graded ring with nonzero identity and n a positive integer. Our principal aim in this paper is to introduce and study the notions of graded n-irreducible and strongly graded n-irreducible ideals which are generalizations of n-irreducible and strongly n-irreducible ideals to the context of graded rings, respectively. A proper graded ideal I of R is called graded n-irreducible (respectively, strongly graded n-irreducible) if for each graded ideals I₁, . . . , I_n+1 of R, I = I₁ ∩ · · · ∩ I_n+1 (respectively, I₁ ∩ · · · ∩ I_n+1 ⊆ I ) implies that there are n of the I_i 's whose intersection is I (respectively, whose intersection is in I). In order to give a graded study to this notions, we give the graded version of several other results, some of them are well known. Finally, as a special result, we give an example of a graded n-irreducible ideal which is not an n-irreducible ideal and an example of a graded ideal which is graded n-irreducible, but not graded (n - 1)-irreducible.

• 정보처리학회논문지A
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• 제9A권3호
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• pp.333-340
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• 2002

임베딩은 어떤 상호연결망 G를 다른 상호연결망 H에 사상시키는 것으로 연결망 G에서 개발된 알고리즘을 다른 연결망 H에서 시뮬레이션 할 수 있게 한다. 본 논문에서는 먼저 Hierarchical Cubic Network HCN(n, n) and Hierarchical Folded-hypercube Network HFN(n, n) 사이의 임베딩 방법을 제시한다. HCN(n, n)과 HFN(n, n)은 하이퍼큐브에서 제안된 성질을 가지면서 하이퍼큐브의 망비용 (분지수$\times$지름)을 개선한 상호연결망이다. HCN(n, n)은 HFN(n, n)에 연장율 3, 밀집율 2로 임베딩되고 평균연장율이 2 이하임을 보인다. HFN（n, n）은 HCN（n, n）에 연장율 0(n)에 임베딩 되지만, 평균연장율이 2 이하임을 보인다. 마지막으로 HCN（n, n）의 고장허용도에 대해 논하고, HCN（n, n）이 최대 고장 허용도(maximally fault tolerant)를 가짐을 보인다.

• 대한수학회보
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• 제39권2호
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• pp.259-267
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• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.