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.)     

Sulla regolarità delle soluzioni deboli al sistema di Navier-Stokes in domini arbitrari

Lavoro eseguito sotto gli auspici del G.N.F.M. (C.N.R.) e di un contratto MPI 40% dell'Università di Ferrara.     

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%)     

General binomial-type coefficients in the sequence of Bernstein operators

In this paper we study the sequence of Bernstein operators in the case when the binomial coefficients are substituted by general ones satisfying a similar recursive rule. Besides the characterization of the convergence and the approximation properties of the sequence of operators obtained in this manner, the main application regards the approximation of the solutions of suitable second-order parabolic problems. Work performed under the auspices of G. N. A. F. A. (C. N. R.) and M. U. R. S. T.     

Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive

We consider a general model of discrete-time random walk X_t on the lattice , = 1,..., in a random environment ={(t,x):(t,x)⁺¹} with i.i.d. components (t,x). Previous results on the a.s. validity of the Central Limit Theorem for the quenched model required a small stochasticity condition. In this paper we show that the result holds provided only that an obvious non-degeneracy condition is met. The proof is based on the analysis of a suitable generating function, which allows to estimate L₂ norms by contour integrals.Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds.Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds, by R.F.F.I. grants n. 99-01-00284, 97-01-00714, and CRDF research funds N RM1-2085.Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds.Mathematics Subject Classification (2000): 60J15, 60F05, 60G60, 82B41     

A diffusion model for patch formation on cellular surfaces

A number of phenomena of interest in the biology of the cellular membrane can be modeled by a diffusion process which is undergone by certain objects on the cellular surface.We consider one such model and are led to the task of estimating the principal eigenvalue of an elliptic operator with homogeneous Dirichlet boundary conditions.The requested estimate is carried out by two different methods: one makes use of a Lyapunov-type technique and the other applies the Cameron—Martin—Girsanov formula. These methods apply to much more general situations than the specific one considered here.This work was carried out within the frame of a research program partially supported by C.N.R.-GNAFA (G.D.G.) and C.N.R.-GNFM (A.G., F.M.).     

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.     

Nonlinear equations with expansive nonlinearities

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

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

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

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Supported by C.N.R., G.N.A.F.A.     

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.

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Entrata in Redazione il 12 novembre 1971.

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

Maximal arcs in Desarguesian planes of odd order do not exist

Forq an odd prime power, and 1<n<q, the Desarguesian planePG(2,q) does not contain an(nq–q+n,n)-arc.Supported by Italian M.U.R.S.T. (Research Group onStrutture geometriche, combinatoria, loro applicazioni) and G.N.S.A.G.A. of C.N.R.     

A uniqueness result for a nonlinear hyperbolic equation

Summary We prove the uniqueness of the solution of a Cauchy problem for a nonlinear and non-local hyperbolic equation, which arises in a model of the dynamic of cardiac muscle.The authors were supported by G.N.A.F.A., G.N.I.M. and I.A.N. of C.N.R. and by M.P.I.     

Insiemi irriducibili di seminorme e spazi localmente convessi

Sunto. La nozione di insieme irriducibile di seminorme secondo F. Treves, viene ripresa ed utilizzata per studiare in una nuova prospettiva la struttura degli spazi localmente convessi. Entrata in Redazione il 17 luglio 1971. Lavoro eseguito nell'ambito delle attività del Gruppo Nazionale per l'Analisi Funzionale e sue Applicazioni (G.N.A.F.A.) del C.N.R.     

Restrizioni termodinamiche in elettromagnetismo ereditario

Summary This paper is concerned with the linear theory of ereditary electromagnetism. The second law is stated through the Clausius property for approximately-cyclic processes and by considering sinusoidal electromagnetic fields, the necessary and sufficient conditions for its validity have been obtained.

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Lavoro eseguito nell'ambito delle attività di ricerca del G.N.F.M. del C.N.R. e dei progetti 40% e 60% del M.P.I.     

Seminorme semicontinue inferiormente e spazi localmente convessi

Sunto Si studiano gli spazi localmente convessi in cui ogni seminorma minore di una seminorma semicontinua inferiormente risulta semicontinua inferiormente. Entrata in Redazione il 3 aprile 1973. Lavoro eseguito nell'ambito delle attività del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni (G.N.A.F.A.) del C.N.R.     

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.     

Polynomial root computation by means of the LR algorithm

By representing the LR algorithm of Rutishauser and its variants in a polynomial setting, we derive numerical methods for approximating either all of the roots or a numberk of the roots of minimum modulus of a given polynomialp(t) of degreen. These methods share the convergence properties of the LR matrix iteration but, unlike it, they can be arranged to produce parallel and sequential algorithms which are highly efficient especially in the case wherek≪n. Supported by 40% and 60% funds of the Progetto Analisi numerica e matematica computazionale of MURST and by G.N.I.M. of C.N.R.     

Regular orbits for projective orthogonal groups over finite fields of odd characteristic

In this paper we prove that the projective orthogonal groups over finite fields of odd characteristic acting on the set of points of the corresponding quadrics, have regular orbits apart from a finite number of explicitly listed exceptions occurring in dimension 2 and 3.Lavoro eseguito nell'ambito dei gruppi nazionali del C.N.R. (G.N.S.A.G.A.) e del finanziamento del M.P.I.     

Classes of plus matrices in finite dimensional indefinite scalar product spaces

We describe in terms of canonical forms various classes of plus matrices in real and complex finite dimensional spaces with indefinite scalar product and study their topological structures (such as closure and interior).Dedicated to M.G. Kreîn, one of the founding fathers of the theory of plus-operators.The work of this author was performed under the auspices of C.N.R.-G.N.F.M. and partially supported by the research project, Nonlinear problems in analysis and its physical, chemical and biological applications: Analytical, modelling and computational aspects, of the Italian Ministry of Higher Education and Research (M.U.R.S.T.)The work of this author partially supported by the NSF grant DMS 9500924.The work of all authors is partially supported by the NATO grant CGR 960700.     

On the well-posedness of the Hammer X-ray problem

Summary In un precedente articolo [10] il secondo autore ha dimostrato che ogni corpo convesso piano è univocamente determinato dalle lunghezze dette corde tagliate da tre fasci propri, i cui sostegni non sono allineati. Si dimostra in questo articolo che il corrispondente problema ricostruttivo è ben posto, se si assume che il corpo convesso da ricostruire è contenuto in un preassegnato insieme limitato.

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Supported in part by a grant from the National Research Council (C.N.R.) of Italy.

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Contribution to the research projectReconstruction, Ko 506/8-1 of the German Research Council (D.F.G.), directed by Professor D.Kölzow, Erlangen.     

Peripheral acyclicity and homology manifolds

In this paper we study various concepts of peripheral acyclicity and local homotopical properties, generalizing and extending earlier work due to R. C. Lacher, D. R. McMillan jr. and the authors. Then we obtain some applications for cell-like decompositions of manifolds and construct exotic factors (i.e. homology manifolds) of certain Euclidean spaces.Work performed under the auspices of the G.N.S.A.G.A of Italian C.N.R. and during the permanence of the second author at the Dept. of Math. (Univ. of Modena) as a visiting professor.Supported in part by the Ministero della Università e della Ricerca Scientifica e Tecnologica within the project «Geometria Reale e Complessa».Supported in part by the Commission of the European Communities Go West Fellowship No. 792 and by the Ministry for Science and Technology of the Republic of Slovenia Research Grant No. P1-0214-101-94.