Homogeneity on three-dimensional contact metric manifolds

We study ball-homogeneity, curvature homogeneity, natural reductivity, conformal flatness and ϕ-symmetry for three-dimensional contact metric manifolds. Several classification results are given. Member of G.N.S.A.G.A. Supported by funds of the M.U.R.S.T.     

Rami globali e parametrizzazione

Summary In this paper, using the theory of henselian rings and in particular the notion of henselian and strict henselian couples, we study the behaviour of analytic branches of an affine algebraic variety at a point x, when x varies along a singular subvariety; moreover we construct an algebraic and canonical procedure, which parametrises the branches.

---

---

Lavoro eseguito nell'ambito della sez. 3 del G.N.S.A.G.A. del C.N.R. e con il supporto finanziario del Ministero della Pubblica Istruzione.     

On a differential problem coming from cell biology

Summary An initial and boundary value problem for a system of first order linear partial differential equations is studied. This problem arises in cell biology, when the evolution of a homogeneous cell population is modelled. Some existence, uniqueness and regularity results are proven; an estimate for the growth of the cell population is also obtained.This work was in part supported by the Istituto di Analisi Numerica of the C.N.R. in Pavia (Italy), the G.N.A.F.A. of the C.N.R. (Italy) and the Ministero della Pubblica Istruzione (Italy).     

Decidability of the separation problem in dimension 2

The problem of separating two semialgebraic sets in an algebraic R-variety is proved to be decidable in dimension 2 with geometric and topologic means. An interpretation of the equivalence between the known criteria of separation is also given.

---

Sunto Il problema della decidibilità della separazione tra due insiemi semialgebrici di una varietà algebrica reale viene risolto positivamente in dimensione 2, con mezzi geometrici e topologici. Inoltre viene data un'interpretazione dell'equivalenza tra i differenti criteri di separazione, di tipo geometrico e algebrico, noti fino ad ora.

---

---

Member of G.N.S.A.G.A. of C.N.R., partialy supported by Scuola Normale Superiore and by DGICYT, contract #CHRX-CT94-0506.     

On a class of singular nonlinear parabolic variational inequalities

Summary We study a class of singular or degenerate parabolic variational inequalities, containing some nonlinear operators. We prove an existence and uniqueness result for weak solutions, in the framework of suitable Banach weighted spaces.

---

Sunto Si studia una classe di disequazioni variazionali paraboliche singolari o degeneri, contenenti operatori non lineari. Si dimostra un risultato di esistenza e unicità per soluzioni deboli, nell'ambito di opportuni spazi di Banach con peso.

---

---

This work was supported in part by the «Istituto di Analisi Numerica del C.N.R.» (Pavia, Italy), the G.N.A.F.A. of the C.N.R. and the Ministero della Pubblica Istruzione (Italy) (through 60% and 40% grants).     

About a forty years old conjecture by P. Erdős

In connection with a characterization ofc logn within the class of additive arithmetic functions, i.e. such thatf (mn)=f(m)+f(n), which has been conjectured by P. Erdős in 1946 and is still unproved, we outline some subsequent researches involving various tools and standpoints, and we report some expressive results either lying close to that conjecture or revealing a similar spirit. Conferenza tenuta il giorno 30 Novembre 1998 Lavoro eseguito nell’ambito del Gruppo G.N.A.F.A. del C.N.R. e con il contributo del Ministero dell’ Università e della Ricerca Scientifica e Tecnologica (ex 40%).     

Classifying Genus Two 3-Manifolds up to 34 Tetrahedra

In this paper, we present a catalogue of all genus two 3-manifolds admitting a contracted triangulation with at most 34 simplexes. Then we give a complete classification of the above manifolds. Mathematics Subject Classifications (2000) 57M05, 57N10, 57M15.Work performed under the auspicies of the G.N.S.A.G.A. of the C.N.R. (National Research Council of Italy) and financially supported by M.I.U.R. of Italy (project Strutture geometriche delle varietà reali e complesse).     

Parametrized\bar \partial operator on pseudoconvex setsoperator on pseudoconvex sets

Sunto Si dimostra l'esistenza della soluzione per l'operatore di Cauchy-Riemann parametrizzato, nel caso continuo per varietà fortemente pseudoconvesse e nel caso differenziabile per varietà di Stein.

---

---

Entrata in Redazione il 20 maggio 1975.

---

Supported by C.N.R. research groups.     

A note on norm-one projections onto subspaces of finite codimension ofl ∞

Research partially supported by Italian Ministero della Pubblica Istruzione (M.P.I.) and G.N.A.F.A. (C.N.R.)     

Characteristic shocks of crossing velocities in magnetohydrodynamics

We illustrate, in the framework of magnetohydrodynamics, an application of crossing shock formulas to a characteristic shock moving perpendicularly to the magnetic field.Supported by C.N.R. (G.N.F.M.)Supported by C.N.R. (G.N.F.M.) and MURST (Fondi Ricerche 40% and 60%)     

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.     

Nonlinear equations with expansive nonlinearities

Summary We prove existence and multiplicity theorems for nonlinear equations at resonance with expansive nonlinearities.

---

Riassunto Si provano teoremi di esistenza e molteplicità per equazioni nonlineari in risonanza con nonlinearità espansiva.

---

---

These results were obtained while the second author was visiting the University of Ferrara through a grant of C.N.R.

---

Supported by C.N.R., G.N.A.F.A.     

On the existence of optimal integration formulas for analytic functions

Summary In this paper we prove the existence of quadrature formulas that are optimal with respect to a Hilbert space of analytic functions solving a problem unsuccessfully attacked so far. Although we allow the formulas to be of type (2) the optimal formulas will be of the form (1).Supported in part by N.S.F. Grant G.P.-28111.Supported in part by Sonderforschungsbereich 72 at Institute for Applied Mathematics, University of Bonn and N.S.F. Grant G.P.-18609.     

On lattice-like properties of orthoquaternary categories

Summary We point a class of categories for which necessary and sufficient conditions in order they have an orthodox quaternary symmetrization are expressible by means of lattice-like properties of subobjects, these one given by axiomsD1)-5). This implies that canonical isomorphisms between subquotients are composable and that Noether isomorphism theorems hold.

---

Riassunto Si individua una classe di categoric per le quali l’esistenza e l’ortodossia della simmetrizazione quaternaria è exprimibile mediante proprietà di tipo reticolare di sottooggetti, enunciate nella forma di assiomiD1)-5). Ciò garantisce la componibilità degli isomorfismi canonici tra subquozienti e la validità dei teoremi di isomorfismo di Noether.

---

---

Written while the authors were members of C.N.R. sec. G.N.S.A.G.A.     

On the universal convergence sets

Summary In this paper we study various universal convergence sets, in connection with some problem arising from the Korovkin approximation theory. This analysis is made in the context of topological vector lattices, of commutative Banach algebras, of Banach algebras with an involution and of C ^*-algebras. Some applications and examples are given in specific function spaces and function algebras.Work performed out under the auspices of the G.N.A.F.A. (C.N.R.) and of Ministero della Pubblica Istruzione (60%) for the year 1982.     

Abstract Riemann surfaces of integral domains and spectral spaces

Sunto La superficie astratta di Riemann di un dominio R, introdotta da Zariski, è uno spazio topologico X(R) il cui insieme sostegno consiste di tutti i sovranelli di valutazione di R. L'applicazione canonica suriettiva f_R: X(R) Spec(R), V centro di V su R, è un'applicazione chiusa, dunque Spec(R) è uno spazio-quoziente di X(R). Il teorema principale di questo lavoro è il seguente: X(R) è uno spazio spettrale, nel senso di M. Hochster, e f_R è un'applicazione spettrale. Inoltre, facendo uso della cosiddetta topologia costruttibile, viene dimostrato che se R è integralmente chiuso e Spec(R) è uno spazio noetheriano allora f_R è un'applicazione aperta se e soltanto se R è un going-down dominio.

---

---

Supported in part by the University of Tennessee Faculty Development Grant, by Dipartimento di Matematica dell'Università di Roma «La Sapienza» and by a NATO Collaborative research Grant N. 35/85.

---

Supported in part by a grant from the Research Council of the Graduate School of the University of Missouri, Columbia.

---

Work done under the auspices of GNSAGA of the Consiglio Nazionale delle Ricerche, partially supported by a NATO Grant N. 35/85.     

A generalization of a theorem by C. Miranda

Summary In this paper we study the well-posedness of the Dirichlet problem for an elliptic non divergence form second order equation. The coefficients are not assumed to be continuous but their derivatives are supposed to belong to a suitable Morrey space hence generalizing a classical result by C. Miranda.This work was partly financially supported by a national project of the Italian Ministero della Pubblica Istruzione and by G.N.A.F.A.-C.N.R.     

On the inversion of some differentiable mappings with singularities between Banach spaces

Sunto. Il classico metodo di P. Levy e R. Caccioppoli è esteso al caso di applicazioni tra spazi di Banach che presentino singolarità. Viene fatta un'applicazione ad un problema non lineare in cui si ha modo di valutare esattamente il numero delle soluzioni.

---

---

Entrata in Redazione il 12 novembre 1971.

---

Supported by G.N.A.F.A. (Gruppo Nazionale di Analisi Funzionale ed Applicazioni, C.N.R.).     

On self-mapping degrees of <Emphasis Type="Italic">S</Emphasis><Superscript>3</Superscript>-geometry manifolds

In this paper we determined all of the possible self-mapping degrees of the manifolds with S3-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self-mapping degrees of all closed orientable 3-manifold in Thurston＇s picture.     

On symplectic half-flat manifolds

We construct examples of symplectic half-flat manifolds on compact quotients of solvable Lie groups. We prove that the Calabi-Yau structures are not rigid in the class of symplectic half-flat structures. Moreover, we provide an example of a compact 6-dimensional symplectic half-flat manifold whose real part of the complex volume form is d-exact. Finally we discuss the 4-dimensional case. This work was supported by the Projects M.I.U.R. “Geometric Properties of Real and Complex Manifolds”, “Riemannian Metrics and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M.