In his Commentary on Plato＇s Phaedo, Damascius establishes a close relation between destination （lexis）, divine Justice, and life dignity （kat＇aian） of every soul. Among several meanings of destination, the most...In his Commentary on Plato＇s Phaedo, Damascius establishes a close relation between destination （lexis）, divine Justice, and life dignity （kat＇aian） of every soul. Among several meanings of destination, the most relevant one is related to the condition of the soul after death. Consequently, the purpose of this paper is to consider how this neoplatonic term is conceived in Dionysius Areopagite. For that purpose, the author will analyze such term widely used in the chapter 7 of Ecclesiastic Hierarchy in which Dionysius deals with the funerary rite and in which the notes of the dionysian eschatology are found. In other words, Dionysius＇ use of this term combines a spiritual and a metaphysic perspective. The former is part of the representation of the dionysian universe in which even the angels receive the name of lexeis and are distinguished by their never ending movement around the Thearchia; the latter is present among humans as a call to imitate such angelic condition. Such imitation is not possible without the effort needed to behave in agreement with an honorable lifestyle （kat＇axian, neoplatonic expression also used by Dionysius） that opens the door to a condition or rank granted to man after death.展开更多
For a graph, its boxicity is the minimum dimension k such that G is representable as the intersection graph of axis-parallel boxes＇in the k-dimension space. When the boxes are restricted to be axis-parallel k-dimensi...For a graph, its boxicity is the minimum dimension k such that G is representable as the intersection graph of axis-parallel boxes＇in the k-dimension space. When the boxes are restricted to be axis-parallel k-dimension cube＇s, the minimum k required to represent G is called the cubicity of G. In this paper, a special graph .called unit-interval graph. IG[X, Y] is given, then 2n such graphs which have the same vertices as V（FQn） are constructed, where FQ, is the n-dimension folded hypercube. Thanks to the specia] structure of IG[X, Y], the result that cubicity（FQn）≤ 2n is proved.展开更多
文摘In his Commentary on Plato＇s Phaedo, Damascius establishes a close relation between destination （lexis）, divine Justice, and life dignity （kat＇aian） of every soul. Among several meanings of destination, the most relevant one is related to the condition of the soul after death. Consequently, the purpose of this paper is to consider how this neoplatonic term is conceived in Dionysius Areopagite. For that purpose, the author will analyze such term widely used in the chapter 7 of Ecclesiastic Hierarchy in which Dionysius deals with the funerary rite and in which the notes of the dionysian eschatology are found. In other words, Dionysius＇ use of this term combines a spiritual and a metaphysic perspective. The former is part of the representation of the dionysian universe in which even the angels receive the name of lexeis and are distinguished by their never ending movement around the Thearchia; the latter is present among humans as a call to imitate such angelic condition. Such imitation is not possible without the effort needed to behave in agreement with an honorable lifestyle （kat＇axian, neoplatonic expression also used by Dionysius） that opens the door to a condition or rank granted to man after death.
文摘For a graph, its boxicity is the minimum dimension k such that G is representable as the intersection graph of axis-parallel boxes＇in the k-dimension space. When the boxes are restricted to be axis-parallel k-dimension cube＇s, the minimum k required to represent G is called the cubicity of G. In this paper, a special graph .called unit-interval graph. IG[X, Y] is given, then 2n such graphs which have the same vertices as V（FQn） are constructed, where FQ, is the n-dimension folded hypercube. Thanks to the specia] structure of IG[X, Y], the result that cubicity（FQn）≤ 2n is proved.
