S-内射模及S-内射包络

设R是环.设S是一个左R-模簇,E是左R-模.若对任何N∈S,有Ext_R~1(N,E)=0,则E称为S-内射模.本文证明了若S是Baer模簇,则关于S-内射模的Baer准则成立;若S是完备模簇,则每个模有S-内射包络;若对任何单模N,Ext_R~1(N,E)=0,则E称为极大性内射模;若R是交换环,且对任何挠模N,Ext_R~1(N,E)=0,则E称为正则性内射模.作为应用,证明了每个模有极大性内射包络.也证明了交换环R是SM环当且仅当T/R的正则性内射包e(T/R)是∑-正则性内射模,其中T=T(R)表示R的完全分式环,当且仅当每一GV-无挠的正则性内射模是∑-正则性内射模.     

On finite groups with a reducible permutability-graph

We characterize finite groups in which the permutability-graph has more than one connected component.Research partially supported by G.N.S.A.G.A. of C.N.R. and M.U.R.S.T. of Italy.     

Characterization of three types of planar spaces with invisible planes

In this paper we characterize a class of finite planar spaces whose planes have two sizes.Dedicato alla memoria dell'amico e Maestro Giuseppe TalliniWork supported by G.N.S.A.G.A. of C.N.R. and the projects M.U.R.S.T. 40 %     

Banach spaces in which Dunford-Pettis sets are relatively compact

Work performed under the auspices of G.N.A.F.A. of C.N.R. and partially supported by M.U.R.S.T. of Italy (40%)     

Free boundary problems in the theory of fluid flow through porous media: Existence and uniqueness theorems

Summary Elliptic free boundary problems in the theory of fluid flow through porous media are studied by a new method, which reduces the problems to variational inequalities: existence and uniqueness theorems are proved. Entrata in Redazione il 3 agosto 1972. Research supported by C.N.R. in the frame of the collaboration between L.A.N. of Pavia and E.R.A. 215 of C.N.R.S. and of Paris University. ? Laboratorio di Analisi Numerica del C.N.R. di Pavia ? and ? Università di Pavia ?. ? Università di Pavia ? and ? G.N.A.F.A. del C.N.R. ?.     

On the geometry of quadrics and their degenerations

members of G.N.S.A.G.A. of C.N.R.     

L 2·Curvature pinching

This work was partially supported by an N.S.E.R.C. Grant A7873 of Canada and N.S.F. Grant DMS-8601282 of the USA.     

A note on a Heegaard diagram of S3

In this work, we study via crystallizations some properties of the counterexample to the Whitehead's conjecture and to the algorithm of Volodin-Kuznetsov-Fomenko, introduced by Ochiai. Research performed under the auspices of the G.N.S.A.G.A.-C.N.R., and within the Project “Topologia e geometria”, supported by M.U.R.S.T. of Italy     

Su alcuni gruppi dellaK-teoria delle varietà affini

Lavoro eseguito nell'ambito della sezione n. 3 del G.N.S.A.G.A. del C.N.R.     

Stratifications et ensemble de non-cohérence d'un espace analytique réel

Sans résuméL'auteur est associé au groupe G.N.S.A.G.A. du C.N.R.     

Finite groups and subgroup-permutability

Subgrouppermutability in a finite group is studied, in order to distinguish between irreducible and reducible groups and to give a bound for the diameter. A simple nonabelian finite group is irreducible and its diameter is less or equal16 while a reducible group is forced to be soluble and the bound of the diameter of such a group is 4.Research partially supported by G.N.S.A.G.A. of C.N.R. and M.U.R.S.T. of Italy.     

Invariants,orbits and symmetric spaces

Lavoro svolto nell'ambito del G.N.S.A.G.A. del C.N.R. con contributo del M.P.I. fondi 40%.     

Minima of some non convex non coercive problems

We give here an existence result of minimizers for a class of one dimensional integrals of the Calculus of Variations with non convex, non coercive integrands.This work was performed as part of a national research project supported by M.U.R.S.T. (40%).Authors are members of G.N.A.F.A., C.N.R.     

On the non-polynomiality of the relaxation method for systems of linear inequalities

A class of linear programs is given in which the relaxation method for inequalities, under the same operating rules as Khacian's method, is not polynomial in the length of the input. This result holds for any value of the relaxation parameter.This research was supported in part by the D.G.E.S. (Quebec), the N.S.E.R.C. of Canada under grant A 4152, and the S.S.H.R.C. of Canada.     

On the Griffiths group of the cubic sevenfold

Partially supported by Science Project Geometry of Algebraic Varieties, n. 0-198-SC1, and by fundings from M.U.R.S.T. and G.N.S.A.G.A. (C.N.R.), Italy     

Essential coverings and triangulations

Sunto In questo lavoro si danno condizioni sufficienti per un ricoprimento di una varietà differenziabile V affinchè il suo nerbo abbia lo stesso tipo P.L. di V e si prova l'esistenza di una larga classe di siffatti ricoprimenti.

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The author is member of G.N.S.A.G.A. of the C.N.R. and partially supported by a N.A.T.O.-C.N.R. fellowship.     

Control subspaces of minimal dimension. Elementary introduction. Discotheca

In this paper there is introduced and studied the following characteristic of a linear operator A acting on a Banach space Χ: , where Cyc A=R∶R is a subspace of Χ, dim R<+∞. Spqn (AⁿR∶n?0)=χ. Always disc A ?μ_A=(the multiplicity of the spectrum of the operator (dim R∶R∈Cyc A), where (by definition) in each A-cyclic subspace there is contained a cyclic subspace of dimension ? disc A. For a linear dynamical system x(t)=Ax(t)+Bu,(t) which is controllable, the characteristic disc A of the evolution operator A shows how much the control space can be diminished without losing controllability. In this paper there are established some general properties ofdisc (for example, conditions are given under which disc(A⊕B))=max(discA, disc B); disc is computed for the following operators: S (S is the shift in the Hardy space H²); disc S=2, (but μ_S=i); disc S _n ^* =n (butμ=1), where S_n=S⊕. ⊕S; disc S=2, (but μ_S=1), where S is the bilateral shift. It is proved that for a normal operator N with simple spectrum, disc N=μ_N=1 ? (the operator N is reductive). There are other results also, and also a list of unsolved problems.     

Incidence structures of affine and protective types

A combinatorial characterization of the incidence structures whose points and blocks are the h– and (h+1)-dimensional subspaces of an affine or protective space is given.Work partially supported by G.N.S.A.G.A. of C.N.R., Italy.     

The infinitesimal and generalized Hodge Conjecture for some families of sextic threefolds

This paper deals with some families of projective hypersurfaces of degree 6 and dimension 3, left invariant under certain actions of the group of the cubic roots of unity. The general Grothendieck-Hodge conjecture, for the families above and for their intersections, is verified. In particular certain families of elliptic curves on the general element of these families are closely investigated and their degeneration at the Fermat point is studied. These results are used to verify the general Infinitesimal Hodge Conjecture extending to the general type case a similar conjecture due to A. Albano and S. Katz. Research partially supported by italian M.U.R.S.T., by the Science Project “Geom. of Alg. Var.” and by G.N.S.A.G.A. (C.N.R.)     

On the maximum genus of some graphs with upper imbeddable subgraphs

In this paper we will consider some properties of the maximum genus of those graphs which decompose into upper imbeddable subgraphs, any two of which have at most one vertex in common.With 1 FigureLavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R.