Let A be a basis for N0 of some order. By an essential subset of A one means a subset P such that A\P is no longer a basis (of any order) and such that P is minimal among all subsets of A with this property. In a recent paper, Deschamps and Farhi asked whether every basis of N0 possesses some such subset. We construct, for every integer h ≥ 2, a basis of order h with no essential subsets. We al...

This paper deals with the question of completing a monotone increasing family of subsets Γ of a finite set Ω to obtain the dependent sets of a matroid. Specifically, we provide several natural processes for transforming the clutter Λ of the inclusionminimal subsets of the family Γ into the set of circuits C(M) of a matroid M with ground set Ω. In addition, by combining these processes, we prove...

We characterize heirs of so called box types of a polynomially bounded o-minimal structure M . A box type is an n-type of M which is uniquely determined by the projections to the coordinate axes. From this, we deduce various structure theorems for subsets of M, definable in the expansion M of M by all convex subsets of the line. Moreover we obtain a model completeness result for M .

This paper studies the class of infinite sets that have minimal perfect hash functions­ one-to-one onto maps between the sets and E·-computable in polynomial time. We show that all standard NP-complete sets have polynomial-time computable minimal per­ fect hash functions, and give a structural condition sufficient to ensure that all infinite NP sets have polynomial-time computable minimal perfe...

although mohaghegh khorasani has raised the impossibility of replacement of certitude as to subject by authorized conjectural proof (amara) due to the impediment of conjunction in consideration; sheikh ansari, while rejecting the replacement of certitude as to attribute, has accepted the replacement of declaratory certitude. some islamic scholars believe in classification, according to the basi...

Radio Frequency Identification (RFID) systems have become popular for identifying not only objects but also persons. For example, in supply chain applications, the company can constantly track the movements of goods. Also, for Body Area Network or Personal Area Work, the tag is used for identifying a person. However, the movements and current locations of goods and a person’s activity profiles ...