Families by JU. Mike and K. McCluskey

Modified Quine-McCluskey Method

The digital gates are basic electronic component of any digital circuit. Digital circuit should be simplified in order to reduce its cost by reducing number of digital gates required to implement it. To achieve this, we use Boolean expression that helps in obtaining minimum number of terms and does not contain any redundant pair. Karnaugh map (K-map) and Quine-McCluskey (QM) methods are well kn...

Mike Nolan , Sue Davies and Gordon Grant Working with older people and their families

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Extreme k-families

Let P be a poset. A subset A of P is a k-family ii A contains no (k+1)-element chain. For i 1, let A i be the set of elements of A at depth i?1 in A. The k-families of P can be ordered by deening A B ii for all i, A i is included in the order ideal generated by B i. This paper examines minimal r-element k-families, deened as k-families A such that A = r and for every B < A, B < r. Minimal k-fam...

Families of k-derivations on k-algebras

Let A be an integral k-algebra of finite type over a field k of characteristic zero. Let F be a family of k-derivations on A and MF the A-module spanned by F . In this paper, we generalise a result due to A. Nowicki and construct an element ∂ of MF such that ker ∂ = ∩d∈Fker d. Such a derivation is called F-minimal. Then we establish a density theorem for F-minimal derivations in MF .

Mike Anderson