In this paper we present an automatic method for extraction of synonyms of verbs from an explanatory dictionary based only on hyponym/hyperonym relations existing between the verbs defined and the genus used in their definitions. The set of pairs verb-genus can be considered as a directed graph, so we applied an algorithm to identify cycles in these kind of structures. We found that some cycles...

sueyoshi and sekitani in 2007 presented a paper that explores the measurement of returns to scale under a possible occurrence of multiple solution in a reference set and a supporting hyperplane. the occurrence ofmultiple solutions is classified into type i and type ii. type i is an occurrence of multiple solutions in a reference set. type ii is an occurrence of multiple solutions on a supportin...

In this paper, we investigate certain graded-commutative rings which are related to the reciprocal plane compactification of coordinate ring a complement hyperplane arrangement. We give presentation these by generators and defining relations. This was used Holler I. Kriz calculate $\mathbb{Z}$-graded coefficients localizations ordinary $RO((\mathbb{Z}/p)^n)$-graded equivariant cohomology at giv...

The polytope subalgebra of deformations a zonotope can be endowed with the structure module over Tits algebra corresponding hyperplane arrangement. We explore this construction and find relations between statistics on (signed) permutations in case (type B) generalized permutahedra. In type B, surprisingly reveals that any family generators (via signed Minkowski sums) for permutahedra B will con...

Defining all words in a Japanese dictionary by using a limited number of words (defining vocabulary) is helpful for Japanese children and second-language learners of Japanese. Although some English dictionaries have their own defining vocabulary, no Japanese dictionary has such vocabulary as of yet. As the first step toward building a Japanese defining vocabulary, we ranked Japanese words based...

The datum σ yields a measure dσ on the boundary ∂P—on each edge E we take dσ to be a constant multiple of the standard Lebesgue measure with the constant normalised so that the mass of the edge is σ(E). Equally, the datum σ specifies an affine-linear defining function λE for each edge E, i.e. the edge lies in the hyperplane λ E (0). We choose an inward-pointing normal vector v at a point of E w...

We construct finite complete rewriting systems for two large classes of Artin groups: those of finite type, and those whose defining graphs are based on trees. The constructions in the two cases are quite different; while the construction for Artin groups of finite type uses normal forms introduced through work on complex hyperplane arrangements, the rewriting systems for Artin groups based on ...

Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was made by Siegel, who proved that a nonsingular plane cubic equation has only finitely many integral solutions. Examples show that simple equations can have inordinately large integral solutions in comparison to the size...