• 대한수학회보
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• 제61권1호
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• pp.217-227
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• 2024

Let G be an infinite countable group and A be a finite set. If Σ ⊆ A^G is a strongly irreducible subshift of finite type and 𝓖 is the local conjugacy equivalence relation on Σ. We construct a decreasing sequence 𝓡 of unital C^*-subalgebras of C(Σ) and a sequence of faithful conditional expectations E defined on C(Σ), and obtain a Toeplitz algebra 𝓣 (𝓡, 𝓔) and a C^*-algebra C^*(𝓡, 𝓔) for the pair (𝓡, 𝓔). We show that C^*(𝓡, 𝓔) is *-isomorphic to the reduced groupoid C^*-algebra C^*_r(𝓖).

• Kyungpook Mathematical Journal
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• 제64권2호
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• pp.311-335
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• 2024

The fundamental quandle is a powerful invariant of knots, links and spatial graphs, but it is often difficult to determine whether two quandles are isomorphic. One approach is to look at quotients of the quandle, such as the n-quandle defined by Joyce [8]; in particular, Hoste and Shanahan [5] classified the knots and links with finite n-quandles. Mellor and Smith [12] introduced the N-quandle of a link as a generalization of Joyce's n-quandle, and proposed a classification of the links with finite N-quandles. We generalize the N-quandle to spatial graphs, and investigate which spatial graphs have finite N-quandles. We prove basic results about N-quandles for spatial graphs, and conjecture a classification of spatial graphs with finite N-quandles, extending the conjecture for links in [12]. We verify the conjecture in several cases, and also present a possible counterexample.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제28권2호
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• pp.255-279
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• 2014

본 연구는 오답원인 자기평가와 유사 문제에 관련된 선행 연구를 바탕으로, 학생들이 자신의 학습 과정을 반성할 수 있는 하나의 방안으로 오답원인 자기평가를 실시하고 유사한 문제들을 해결하는 과정을 통해 학생들의 인지적, 정의적 영역의 변화를 살펴보고자 한다. 이를 위하여, 본 연구에서는 고등학교 1학년에 재학 중인 네 명의 학생들을 대상으로 근원 문항 3개를 제시하고 각각에 대한 유사 문항들을 유형별로 제시하여 오답원인 자기평가를 작성하게 하고, 이와 더불어 사전 면담과 사후 면담, 그리고 두 차례의 비공식 면담을 실시하였다. 한 마디로, 본 연구에서는 연구 대상자들로 하여금 오답원인 자기평가지를 이용하여 유사 문항들을 해결하고 오류 원인을 점검하는 반성 활동을 거치면서 자신의 문제점을 스스로 판단하며 문제 풀이 과정의 변화와 수학 학습 태도의 변화를 살펴보고자 한다.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.109-123
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• 2003

A tree is called starlike if it has exactly one vertex of degree greate. than two. In [4] it was proved that two starlike trees G and H are cospectral if and only if they are isomorphic. We prove here that there exist no two non-isomorphic Laplacian cospectral starlike trees. Further, let G be a simple graph of order n with vertex set V(G) : {1,2, …, n} and let H = {$H_1$, $H_2$, …, $H_{n}$} be a family of rooted graphs. According to [2], the rooted product G(H) is the graph obtained by identifying the root of $H_{i}$ with the i-th vertex of G. In particular, if H is the family of the paths $P_k_1,P_k_2,...P_k_2$ with the rooted vertices of degree one, in this paper the corresponding graph G(H) is called the sunlike graph and is denoted by G($k_1,k_2,...k_n$). For any $(x_1,x_2,...,x_n)\;\in\;{I_*}^n$, where $I_{*}$ = : {0,1}, let G$(x_1,x_2,...,x_n)$ be the subgraph of G which is obtained by deleting the vertices $i_1,i_2,...i_j\;\in\;V(G)\;(O\leq j\leq n)$, provided that $x_i_1=x_i_2=...=x_i_j=o.\;Let \;G[x_1,x_2,...x_n]$ be characteristic polynomial of G$(x_1,x_2,...,x_n)$, understanding that G[0,0,...,0] $\equiv$1. We prove that $G[k_1,k_2,...,k_n]-\sum_{x\in In}[{\prod_{\imath=1}}^n\;P_k_i+x_i-2(\lambda)](-1)...G[x_1,x_2,...,X_n]$ where x=($x_1,x_2,...,x_n$);G[$k_1,k_2,...,k_n$] and $P_n(\lambda)$ denote the characteristic polynomial of G($k_1,k_2,...,k_n$) and $P_n$, respectively. Besides, if G is a graph with $\lambda_1(G)\;\geq1$ we show that $\lambda_1(G)\;\leq\;\lambda_1(G(k_1,k_2,...,k_n))<\lambda_1(G)_{\lambda_1}^{-1}(G}$ for all positive integers $k_1,k_2,...,k_n$, where $\lambda_1$ denotes the largest eigenvalue.

• 대한수학회논문집
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• 제10권3호
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• pp.499-518
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• 1995

In this paper we consider more systematically the centralizer C(S) of the set $S = {f_a $\mid$ f_a : X \to X ; x \longmapsto x * a, a \in X}$ with respect to the semigroup End(X) of all endomorphisms of an implicative BCK-algebra X with the condition (S). We obtain a series of interesting results. The main results are stated as follows : (1) C(S) with repect to a binary operation * defined in a certain way forms a bounded implicative BCK-algebra with the condition (S). (2) X can be imbedded in C(S) such that X is an ideal of C(S)/ (3) If X is not bounded, it can be imbedded in a bounded subalgebra T of C(S) such that X is a maximal ideal of T. (4) If $X (\neq {0})$ is semisimple, C(S) is BCK-isomorphic to $\prod_{i \in I}{A_i}$ in which ${A_i}_{i \in I}$ is simple ideal family of X.

• ALGAE
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• 제26권1호
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• pp.51-60
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• 2011

Similar to other species of Gigartinaceae Chondrus crispus has an alternation of perennial, isomorphic gametophytic and sporophytic generations. As these two generations co-exist independently within populations and obtain their resources in a similar manner, intraspecific competition is expected. In populations within the southern Gulf of St. Lawrence, fronds of both generations of C. crispus occur in similar numbers. This equivalency can be related to substratum instability, where the population is dynamic with a high turn-over rate of genets. These observations support a stochastic hypothesis to account for distribution of gametophytes and sporophytes in this area. Along the Atlantic coast of Nova Scotia, where the substratum is stable, gametophytes are overwhelmingly predominant. Gametophytic predominance is greatest in the lower littoral zone where C. crispus is abundant and space is limited. Under the fucoid canopy where "free-space" exists, the gametophyte to sporophyte ratio is lower. Gametophytic and sporophytic fronds are distributed equally among different size-classes and size-distribution is not considered a competitive factor. Previous studies have shown that sporophytic fronds of C. crispus are more susceptible to infections by endophytic algae and other pathogens, and are more heavily grazed by herbivores than are gametophytic fronds. Thus, mechanistic factors are strongly implied in the selection of gametophytes in the Atlantic population.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2003년도 춘계종합학술대회논문집
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• pp.406-410
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• 2003

B.M. Schen([2])은 함수의 합성 "${\circ}$" 과 차집합 연산 "-"에 대하여 닫혀있는 함수들의 집합 ${\Phi}$에서의 대수적 구조인 subtraction semigroup (${\Phi}$; ${\circ}$,-)를 정의하였다. 이 구조에서 (${\Phi}$; ${\circ}$)는 semgroup, (${\Phi}$; -)는 [1]에서 정의한 subtraction algebra를 이룬다. B.M. Schen은 [2]에서 모든 subtraction semigroup은 invertible function들의 difference semigroup과 동형이라는 사실을 밝혔다. 본 논문에서는 이 subtraction semigroup의 일반화로써 near subtraction semigroupd을 정의하고 이의 한 특수한 형태인 strong near subtraction semigroup의 개념을 정의하여 이들의 일반적인 성질과 ideal의 특성을 조사하고 이들의 응용도를 조사하고자 한다.

• 한국멀티미디어학회논문지
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• 제6권3호
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• pp.549-555
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• 2003

LFSR보다 CA가 랜덤성이 우수한 패턴들을 효율적으로 생성함이 알려지면서 그 응용분야가 점차적으로 확대되고 있다. 특히 Nongroup CA는 해쉬함수의 생성, 암호알고리즘, 이미지 압축 등에 응용되고 있다. 본 논문에서는 TPNCA의 성질들을 분석하고, 선형 TPNCA의 0-트리의 기본경로와 순환상태의 사이클 구조를 이용하여 선형 TPNCA의 상태 전이그래프의 정확한 구조를 파악하는데 사용되던 기존의 행렬의 곱셈 연산 방법을 덧셈 연산으로 대체할 수 있음을 보였다. 또한 선형 TPNCA C의 0-트리의 비순환 상태를 여원벡터로 갖는 여원 TPNCA C'은 C와 그 구조가 동형임을 밝힘으로써 선형 TPNCA로부터 여원 TPNCA의 상태들의 위치를 정확하게 파악하여, CA를 이용하는 알고리즘을 개발하는데 있어 선행되어야 하는 CA의 상태를 분석하는 시간을 효과적으로 줄였다.

• 대한수학회지
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• 제52권5호
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• pp.991-1001
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• 2015

In this work we obtain conditions for nonspecial line bundles on general ${\kappa}$-gonal curves failing to be normally generated. Let L be a nonspecial very ample line bundle on a general ${\kappa}$-gonal curve X with ${\kappa}{\geq}4$ and $deg\mathcal{L}{\geq}{\frac{3}{2}}g+{\frac{g-2}{{\kappa}}}+1$. If L fails to be normally generated, then L is isomorphic to $\mathcal{K}_X-(ng^1_{\kappa}+B)+R$ for some $n{\geq}1$, B and R satisfying (1) $h^0(R)=h^0(B)=1$, (2) $n+3{\leq}degR{\leq}2n+2$, (3) $deg(R{\cap}F){\leq}1$ for any $F{\in}g^1_k $. Its converse also holds under some additional restrictions. As a corollary, a very ample line bundle $\mathcal{L}{\simeq}\mathcal{K}_X-g^0_d+{\xi}^0_e$ is normally generated if $g^0_d{\in}X^{(d)}$ and ${\xi}^0_e{\in}X^{(e)}$ satisfy $d{\leq}{\frac{g}{2}}-{\frac{g-2}{\kappa}}-3$, supp$(g^0_d{\cap}{\xi}^0_e)={\phi}$ and deg$(g^0_d{\cap}F){\leq}{\kappa}-2$ for any $F{\in}g^1_k$.

• 대한수학회지
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• 제49권5호
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• pp.1031-1051
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• 2012

In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set $T(M)^*$ makes up the vertices of the corresponding torsion graph, ${\Gamma}(M)$, with any two distinct vertices forming an edge if $[x:M][y:M]M=0$. We prove that, if ${\Gamma}(M)$ contains a cycle, then $gr({\Gamma}(M)){\leq}4$ and ${\Gamma}(M)$ has a connected induced subgraph ${\overline{\Gamma}}(M)$ with vertex set $\{m{\in}T(M)^*{\mid}Ann(m)M{\neq}0\}$ and diam$({\overline{\Gamma}}(M)){\leq}3$. Moreover, if M is a multiplication R-module, then ${\overline{\Gamma}}(M)$ is a maximal connected subgraph of ${\Gamma}(M)$. Also ${\overline{\Gamma}}(M)$ and ${\overline{\Gamma}}(S^{-1}M)$ are isomorphic graphs, where $S=R{\backslash}Z(M)$. Furthermore, we show that, if ${\overline{\Gamma}}(M)$ is uniquely complemented, then $S^{-1}M$ is a von Neumann regular module or ${\overline{\Gamma}}(M)$ is a star graph.