• 한국산업정보학회논문지
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• 제5권1호
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• pp.1-15
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• 2000

In this paper, an efficient system for finding answers to a given path algebra expression in a directed acylic graph is discussed more particulary, in a multimedia presentration graph. Path algebra expressions are formulated using revised versions of operators next and until of temporal logic, and the connected operator. To evaluate queries with path algebra expressions, the node code system is proposed. In the node code system, the nodes of a presentation graph are assigned binary codes (node codes) that are used to represent nodes and paths in a presentation graph. Using node codes makes it easy to find parent-child predecessor-sucessor relationships between nodes. A pair of node codes for connected nodes uniquely identifies a path, and allows efficient set-at-a-time evaluations of path algebra expressions. In this paper, the node code representation of nodes and paths in multimedia presentation graphs are provided. The efficient algorithms for the evaluation of queries with path algebra expressions are also provided.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.21-43
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• 2020

We introduce the Leavitt path algebras of ultragraphs and we characterize their ideal structures. We then use this notion to introduce and study the algebraic analogy of Exel-Laca algebras.

• 대한수학회논문집
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• 제19권2호
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• pp.197-204
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• 2004

Every orthomodular lattice satisfying the loop lemma is the direct product of a Boolean algebra and an irreducible path-connected orthomodular lattice.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.199-209
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• 2012

For a locally compact higher rank graph ${\Lambda}$, we construct a two-sided path space ${\Lambda}^{\Delta}$ with shift homeomorphism ${\sigma}$ and its corresponding path groupoid ${\Gamma}$. Then we find equivalent conditions of aperiodicity, cofinality and irreducibility of ${\Lambda}$ in (${\Lambda}^{\Delta}$, ${\sigma}$), ${\Gamma}$, and the groupoid algebra $C^*({\Gamma})$.

• 대한수학회논문집
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• 제37권4호
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• pp.957-967
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• 2022

Recently, Brešar's Jordan {g, h}-derivations have been investigated on triangular algebras. As a first aim of this paper, we extend this study to an interesting general context. Namely, we introduce the notion of Jordan 𝒢_n-derivations, with n ≥ 2, which is a natural generalization of Jordan {g, h}-derivations. Then, we study this notion on path algebras. We prove that, when n > 2, every Jordan 𝒢_n-derivation on a path algebra is a {g, h}-derivation. However, when n = 2, we give an example showing that this implication does not hold true in general. So, we characterize when it holds. As a second aim, we give a positive answer to a variant of Lvov-Kaplansky conjecture on path algebras. Namely, we show that the set of values of a multi-linear polynomial on a path algebra KE is either {0}, KE or the space spanned by paths of a length greater than or equal to 1.

• 대한수학회지
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• 제33권2호
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• pp.217-225
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• 1996

An orthomodular lattice (abbreviated by OML) is an ortholattice L which satisfies the orthomodular law: if x $\leq$ y, then $y = x \vee (x' \wedge y)$ [5]. A Boolean algebra B is an ortholattice satisfying the distributive law : $x \vee (g \wedge z) = (x \vee y) \wedge (x \vee z) \forall x, y, z \in B$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권5호
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• pp.2346-2361
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• 2017

A major challenge in cloud infrastructure is the efficient allocation of virtual network elements on top of substrate network elements. Path algebra is a mathematical framework which allows the validation and convergence analysis of the mono-constraint or multi-constraint routing problems independently of the network topology or size. The present study proposes a new heuristic approach based on mathematical framework "paths algebra" to map virtual nodes and links to substrate nodes and paths in cloud. In this approach, we define a measure criterion to rank the substrate nodes, and map the virtual nodes to substrate nodes according to their ranks by using a greedy algorithm. In addition, considering multi-constraint routing in virtual link mapping stage, the used paths algebra framework allows a more flexible and extendable embedding. Obtained results of simulations show appropriate improvement in acceptance ratio of virtual networks and cost incurred by the infrastructure networks.

• 정보처리학회논문지D
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• 제8D권6호
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• pp.799-812
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• 2001

데이터 교환을 위한 표준 형식으로 XML 활용 증가에 따라 데이터베이스 분야에서 XML 처리의 중요성이 증가하고있다. 현재까지 XML 데이터모델과 정규표현 질의 같은 복잡한 질의처리를 위한 XML대수에 관한 연구가 수행되고 있지만 미디에이터 시스템처럼 XML질의 처리 시 기능이 제한적이다. 따라서 이 논문에서는 반 구조데이터 모델을 확장한 방향 그래프 기반 XML 모델을 설계하고 XML 질의를 위한 XML 대수 연산을 정의하며 그 구현기법을 제시한다. XML 대수 연산 구현을 위해 물리적 저장소인 RDBMS를 접근하기 위한 접근 메소드와 패스 인덱스를 이용하여 알고리즘을 구현한다. 아울러 제안 알고리즘의 효율성을 보이기 위하여 반 구조 특성을 가지는 EST유전체 서열에 대한 XML 문서를 대상으로 성능을 평가한다.

• 대한수학회논문집
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• 제34권3호
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• pp.701-718
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• 2019

In this paper we compute the U-projective resolution of kQ-modules where Q is quiver of type $A_n$ and ${\tilde{A}}_n$. The behavior of the sequence can be seen through its geometric representation.

• 대한수학회보
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• 제46권5호
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• pp.845-856
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• 2009

A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A $\cap$ B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A $\cap$ B| < $\infty$ for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [ComL]$\vee$ generated by the commutators of L is finite, then L is pathconnected.