• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.513-519
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• 1997

We show that each orthomodular lattice containing only atomic nonpath-connected blocks is a full subalgebra of an irreducible path-connected orthomodular lattice and there is a path-connected orthomodualr lattice L containing a weakly path-connected full subalgebra C(x) for some element x in L.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.31-37
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• 1999

We prove the following: every chain-finite OML is path-connected; every finite block of an OML L is path-connected with at least one other block in L; every OML with unifromly finite sites is path-connected.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.445-448
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• 2006

Let N be a normal subgroup of a path-connected topological group (G, $t$). In this paper, the authors consider the existence of path-connectedness in refined topologies in order to address the property of maximal path-connectedness in topological groups. In particular, refinements on $t$ and refinements on the quotient topology on G/N are studied. The preservation of path-connectedness in extending topologies and translation topologies is also considered.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.305-320
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• 2013

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.10
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• pp.539-554
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• 2007

In this Paper, we investigate conditions for proper interval graphs to have k-disjoint path covers of three types each: one-to-one, one-to-many, and many-to-many. It was proved that for $k{\geq}2$, a proper interval graph is one-to-one k-disjoint path coverable if and only if the graph is k-connected, and is one-to-many k-disjoint path coverable if and only if the graph is k+1-connected. For $k{\geq}3$, a Proper interval graph is (paired) many-to-many k-disjoint path coverable if and only if the graph is 2k-1-connected.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.285-292
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• 1995

Some nonpath-connected orthomodular lattices are given : Every infinite direct product of othomodular lattices containing infinitely many non-Boolean factors is a nonpath-connected orthomodular lattice. The orthomodular lattice of all closed subspaces of an infinite dimensional Hilbert space is a nonpath-connected orthomodular lattice.

• Journal of Korea Society of Industrial Information Systems
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• v.5 no.1
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.7
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• pp.671-678
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• 2006

This article proposes a smooth path generation and time scheduling method for general tasks defined by non-smooth path segments in industrial robotic applications. This method utilizes a simple 3rd order polynomial function for smooth interpolation between non-smooth path segments, so that entire task can effectively maintain constant line speed of operation. A predictor-corrector type numerical mapping technique, which correlates time based speed profile to the smoothed path in Cartesian space, is also provided. Finally simulation results show the feasibility of the proposed algorithm.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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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 : $x \vee (g \wedge z) = (x \vee y) \wedge (x \vee z) \forall x, y, z \in B$.