Cella caratteristica di un reticolo

Sunto è contenuto nel n. 1. A Enrico Bompiani in occasione del suo Giubileo scientifico.     

Sul modulo delle derivazioni integrabili in caratteristica positiva

Summary There are some inequalities concerning the module of derivations of a local ring which are true in characteristic0 and false in general in characteristic p≠0 (as it is well known); in the present paper we prove that such inequalities in char. p are true for the module of integrable derivations. Moreover we give some sufficient conditions for an associated prime ideal to be differentiable in char. p.

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Entrata in Redazione il 5 ottobre 1977.

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Lavoro eseguito nell'ambito della sezione no. 3 del G.N.S.A.G.A. del C.N.R.     

Switching Sets Regolari E Cubiche Rigate DiP G(5,q) Piani Di Tralsazione Ad Essi AssociatiG(5,q) Piani Di Tralsazione Ad Essi Associati

In a recent paper, the authors studied some algebraic hypersurfaces of the third order in the projective spacePG(5,q) and they called them ruled cubics, since they possess three systems of planes. Any two of these constitute a regular switching set and furthermore, if Σ is a given regular spread ofPG(5,q), one of the three systems is contained in Σ. The subject of this note is to prove, conversely, that every regular switching set (Φ, Φ′) with Φ ? Σ is a ruled cubic and to construct, for a generic choice of the projective reference system inP G(5,q), the quasifield which coordinatizes the translation plane Π associated with the spread (Σ ? Φ) ∪ Φ′. The planes Π, of orderq ³, are a generalization of the finite Hall planes.     

Un algoritmo per la scelta dell'origine e della scala nelle routines di tracciamento di grafici

Riassunto Viene proposto un algoritmo che, nelle routine di tracciamento automatico di grafici, opera la scelta della scala (lineare) più conveniente secondo criteri di opportunità non molto dissimili da quelli adottati da Giammo e Dixon-Kronmal. Sostanzialmente si ottiene una migliore utilizzazione dello spazio disponibile con la sola rinuncia al principio per cui l'origine dell'asse debba avere un valore multiplo del fattore di scala.

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Summary This paper provides an efficient computational procedure for providing scales for use in automatic plotting data. The ?reasonable? scale definition used is similar to that of Giammo and of Dixon-Kronmal, but space available for plotting is better utilized.

     

Switching Sets Regolari E Cubiche Rigate Di P G (5, q ) Piani Di Tralsazione Ad Essi Associati G (5, q ) Piani Di Tralsazione Ad Essi Associati

In a recent paper, the authors studied some algebraic hypersurfaces of the third order in the projective spacePG(5,q) and they called them ruled cubics, since they possess three systems of planes. Any two of these constitute a regular switching set and furthermore, if Σ is a given regular spread ofPG(5,q), one of the three systems is contained in Σ. The subject of this note is to prove, conversely, that every regular switching set (Φ, Φ′) with Φ ⊂ Σ is a ruled cubic and to construct, for a generic choice of the projective reference system inP G(5,q), the quasifield which coordinatizes the translation plane Π associated with the spread (Σ − Φ) ∪ Φ′. The planes Π, of orderq ³, are a generalization of the finite Hall planes.     

Constructing a 3-tree for a 3-connected matroid

In an earlier paper with Whittle, we showed that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid M. The purpose of this paper is to give a polynomial-time algorithm for constructing such a tree for M.     

Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5

For each surface Σ, we define Δ(Σ) = max{Δ(G)|Gis a class two graph of maximum degree Δ(G) that can be embedded in Σ}. Hence, Vizing's Planar Graph Conjecture can be restated as Δ(Σ) = 5 if Σ is a plane. In this paper, we show that Δ(Σ) = 9 if Σ is a surface of characteristic χ(Σ) = ?5. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:148‐168, 2011     

3-连通3-正则图生成树外的可去边

G是3-连通图，e是G中的一条边．若G-e是3-连通图的一个剖分，则称e是3-连通图的可去边．否则，e是G中不可去边．本给出3-连通3-正则图中生成树外可去边的分布情况及数目．     

Weak -property in Σ-products

It is shown that each Σ-product of paracompact p-spaces has the weak -property.