We study a natural generalization of the noncrossing relation between pairs of elements in [n] to k-tuples in [n]. We show that the flag simplicial complex on ( [n] k ) induced by this relation is a regular, unimodular and flag triangulation of the order polytope of the poset given by the product [k]× [n− k] of two chains, and it is the join of a simplex and a sphere (that is, it is a Gorenstei...

In this paper, we introduce the notion θ -Euclidean k–fuzzy ideal in semirings and to study the properties of the image and pre image of a θ -Euclidean k–fuzzy ideal in a semirings under epimorphism. Keywords—semiring, fuzzy ideal, k–fuzzy ideal,θ -Euclidean Lfuzzy ideal, θ -Euclidean fuzzy k–ideal, θ -Euclidean k-fuzzy ideal. 2000 AMS Classification: 16Y60, 13E05, 03G25.

For integers k and n with k ≤ n a vector x ∈ R is said to be weakly k-majorized by a vector q ∈ R if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1, . . . , k. For a given q the set of vectors weakly k-majorized by q defines a polyhedron P (q; k). We determine the vertices of both P (q; k) and its integer hull Q(q; k). Furthermore a ...

For a full semi-AFL K, B(K) is defined as the family of languages generated by all K-extended basic macro grammars, while H(K) 5 B(K) is the smallest full hyper-AFL containing K, a full basic-AFL is a full AFL K such that B(K) = K (hence every full basic-AFL is a full hyper-AFL). For any full semi-AFL K, K is a full basic-AFL if and only if B(K) is substitution closed if and only if H(K) is a f...

K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semiAFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type...

Representation-based classification methods such as sparse representation-based classification (SRC) and linear regression classification (LRC) have attracted a lot of attentions. In order to obtain the better representation, a novel method called projection representation-based classification (PRC) is proposed for image recognition in this paper. PRC is based on a new mathematical model. This ...