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SEMINARIO MATEMATICO Universita' e Politecnico Torino

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Aims

The Seminario Matematico is a society of members of various departments concerned with Mathematics in the University and Polytechnic of Turin. Its scope is to promote studies and research in all fields of Mathematics and its applications, and to contribute to the difFusion of mathematical culture. The Scientific Committee of the Seminario Matematico is elected from full professors of Mathematics.

The Rendicontiis the journal of the Seminario Matematico. It publishes papers and invited lectures. Papers should provide original research contributions. Invited lectures should have a tutorial or overview character.

Instructions to Authors

Interested authors should submit three copies of their papers to the following address:

Seminario Matematico dell'Universita e del Politecnico di Torino Via Carlo Alberto 10 10123 Torino (Italy)

The final decision on acceptance of a paper is made by the Scientific Committee, based upon the evaluations of an external referee. Papers must be typewritten, double-spaced using A4 format paper on one side only. Preferred language is English, but Italian and French may also be submitted. We should prefer authors to prepare their manuscripts using any version of T^X. Corresponding files should only be supplied in the case of acceptance. The first page should contain name of author(s) and affiliation(s), title of the paper, a brief abstract and complete mailing address. Authors will receive 50 free reprints of their papers. Orders for larger numbers should be sent together with corrected proofs.

Subscriptions

The Rendiconti is published in volumes of 4 issues per year. One or more issue(s) may be devoted to special topics.

Subscription rates for 1992: Italy, L. 143,000 - Europe, L. 180,000 - Other Countries, L. 270,000.

Prices are quoted in Italian liras, surface mail postage included. The back years are offered at the current subscription price. Advance payment required. Available on standing order.

Payment: - by postal giro 11571106 or international money order - bank transfer (please, add. 5,000) - sending invoice (institutions only) - charge on credit card (Mastercard, Visa)

All communications concerning subscriptions should be addressed to:

Rosenberg &; Sellier, Editori in Torino Via Andrea Doria 14 10123 Torino (Italy)

COMMISSIONE SCIENTIFICA Triennio 1987-1990

F. Ricci (Direttore), A. Negro (Vice Direttore), A. Bacciotti, S. Benenti, A. Collino, F. Fava, S. Greco,

G. Monegato, F. Previale, L. Rodino

COMITATO DI REDAZIONE Triennio 1987-1990

E. Abbena, P. Baratella, L. Giacardi, F. Pastrone, G. Rossi

* * *

COMMISSIONE SCIENTIFICA Triennio 1990-1993

S. Benenti (Direttore), A. Bacciotti (Vice Direttore), R. Betti, C. Canuto, F. De Felice, B. Gabutti, C. Massaza,

A. Negro, L. Picco Botta, A. Sanini

COMITATO DI REDAZIONE Triennio 1990-1993

E. Abbena, F. Arzarello, P. Baratella, C.S. Roero, G. Rossi

VOLUME 48, N. 4 1990

RENDICONTI DEL

SEMINARIO MATEMATICO

ALGEBRA COMMUTATIVA E GEOMETRIA ALGEBRICA, I

UNIVERSITA' E POLITECNICO TORINO

Proprieta leUeraria riservata

La presente Ri vista e parzialmente finaiiziata dal Consiglio Nazionale delle Ricerche

Direttore responsabile: Fulvio RICCI (1987-1990) Sergio BENENTI (1990-1993)

Autorizzazione del Tribunale di Torino N. 2962 del 6/VI/1980

C O N T E N T S

P. Salmon, Le origini delValgebra commutativa in Italia 431

M. Boratinski, On the curves of contact on surfaces in a projective

space II 449

G. Beccari, E. Davis, C. Massaza, Extremality with respect to the

estimates of Dubreil-Campanella: the Hilbert matrix ........... 457

A.J. Parameswaran, V. Srinivas, A variant of Noether normalisation 483

P. Maroscia, U. Nagel, W. Vogel, On degree bounds for the syzygies of a finite set of points in IP" 491

R. Strano, Plane sections of curves of W and a conjecture of

Hartshorne and Hirschowitz 511

E. Mezzetti, I. Raspanti, A Laudal-type theorem for surfaces in F4 . 529

R. Achilles, M. Manaresi, Multiplicities for improper intersections of

analytic subsets 539

Y. Beorchia, Ph. Ellia, Normal bundle and complete intersections .. 553

Prefazione

Questo volume contiene una parte delle conferenze tenute presso il Dipartimento di Matematica del Politecnico di Torino in occasione del convegno di Algebra Commutativa e Geometria Algebrica in onore di Paolo Salmon del settembre 1990. Alle conferenze si sono aggiunti anche numerosi lavori di invitati al convegno e di specialisti italiani e stranieri del settore, che ci hanno costretto a prevedere altri due volumi (di prossima pubblicazione)

Dopo un breve articolo storico, dovuto al festeggiato, che illustra le origini e lo sviluppo dell'Algebra Commutativa in Italia a partire dagli anni Cinquanta, presentiamo lavori con risultati recenti in vari settori dell'Algebra Commutativa e Omologica e della Geometria Algebrica.

Gli autori sono in parte allievi di Paolo Salmon; a questi si sono aggiunti altri studiosi che, presentando le proprie ricerche, hanno ritenuto di onorare il festeggiato per il suo fondamentale contributo a introdurre in Italia tematiche di Algebra Commutativa all'inizio degli anni sessanta e a formare una scuola con numerosissimi allievi, oggi sparsi per le Universita italiane.

H Comitato Organizzatore

Torino, 30 settembre 1991

A U T H O R S ' I N D E X

Achilles, R. 539 Andres, J. 171 Anichini, G 149 Beccari, G. 457 Beorchia, V 553 Bianchini, R.M. . . . . . . 401 Boratinski, M. 439 Borelli Forti, C. 45 Capodanno, P. 81 Cecchi, M. 195 Cellina, A 105 Colombo, R.M 105 Conte, G. 225 Conti, G 149 Davis, E 457 De Michele, L 57 Ellia, P 553 Gaudenzi, M 171 Grantcharov, G 61, 171 Halanay, A 251 Lupo, D 125 Manaresi, M. 539 Marini, M. 195 Maroscia, P. 491 Massaza, C. 457 Mazzi, L. ....' 211 Mezzetti, E. 529 Muskarov, O . . . . . 61 Musso, E. 21 Nagel, U. 491 Oleinik, O.A. 1 Pandolfi, L 351 Parameswaran, A.J 483 Perdon, A.M.. 225 Ramos, M 125

Rampazzo, F 367 Raspanti, 1 529 Roux, D 57 Sabatini, M 97 Sain, K 225 Salmon, P 431 Sartori, C 383 Serra, E. . . . . . . . . . . . . . . . . 161 Srinivas, V. 483 Staicu, V 137 Stefani, G 401 Strano, R. 511 Tchon, K. 187 Vogel, W. 491 Wyman, F 225 Zanolin, F 171

C O N T E N T S O F V O L U M E 48 (1990)

Vol. 48, No. 1

O.A. Oleinik, On Boussinesq and Cerruti problems in elasticity 1

E. Musso, Le condizioni d'integrabilitd del le forme fondamentali di Fubini ... 21

C. Borelli Forti, Soluzioni di una equazione funzione alternativa sui gruppi

abeliani 45

L. De Michele, D. Roux, Non monotonicity of Fejer means in Lp spaces 57

G. Grantcharov, O. Muskarov, On a class of Riemannian k-symmetric spaces 61

P. Capodanno, Quelques remarques sur un probleme de G. Fubini 81

Vol. 48 , No. 2

"Mathematical Theory of Dynamical Systems and O.D.E.", I

M. Sabatini, Global asymptotic stability of critical points in the

plane 97

A. Cellina, R.M. Colombo, Some qualitative and quantitative results on a dif­

ferential inclusion 105

D. Lupo, M. Ramos, Some multiplicity results for two-point boundary-value

problems near resonance 125

V. Staicu, On the existence of solutions to a class of differential equations . . . 137

G. Anichini, G. Confci, Existence of solutions of a boundary value problem

through the solution map of a linearized type problem 149

E. Serra, Some remarks on a delay-differential equation 161

J. Andres, M. Gaudenzi, F. Zanolin, A transformation theorem for periodic

solutions of nondissipative systems 171

K. Tchon, Non genericity of a realization problem for observed dynamics .... 187

M. Cecchi, M. Marini, On the continuability and boundedness of solutions of functional differential equations 195

L. Mazzi, Invariant measures for plane systems with finitely many singularities 211

Vol. 48 , N o . 3

"Mathematical Theory of Dynamical Systems and O.D.E.", II

F. Wyman, K. Sain, G. Conte, A.M. Perdon, Algebraic and system theoretic

notions of poles and zeros for matrices of rational functions 225

A. Halanay, Advances in linear control theory and Riccati equations 251

L. Pandolfi, Dichotomy properties and inertia of perturbed matrices 351

F. Rampazzo, Some remarks on the use of constraints as controls in rational

mechanics . . . . . ' 367

C. Sartori, On the continuity with respect to a parameter of the value function

in some optimal control problems 383

R.M. Bi an chini, G. Stefani, Time optimal problem and time-optimal map . . . . 401

Vol. 48, No . 4

"Algebra Commutativa e Geometria Algebrica", I

P. Salmon, Le origini delValgebra commutativa in Italia 431

M. Boratinski, On the curves of contact on surfaces in a projective space II . 439

G. Beccari, E. Davis, C. Massaza, Extremality with respect to the estimates of

DubreiUCampanella: the Hilbert matrix 457

A.J. Parameswaran, V. Srinivas, A variant of Noether normalisation 483

P. Maroscia, U. Nagel, W. Vogel, On degree bounds for the syzygies of a finite

set of points in Wn 491

R. Strano, Plane sections of curves of Or and a conjecture of Hartshome and

Hirschowitz 511

E. Mezzetti, I. Raspanti, A Laudal-type theorem for surfaces in P4 529

R. Achilles, M. Manaresi, Multiplicities for improper intersections of analytic

subsets 539

V. Beorchia, Ph. Ellia, Normal bundle and complete intersections 553

Finito di stampare nel mese di febbraio 1993 presso la M. S./Litografia s.r.l. - Torino

per conto del Seminario Matematico dell'Universita e del Politecnico di Torino Via Carlo Alberto, 10 - 10123 TORINO

Special issues and Conference Proceedings published in Rendiconti

Stochastic Problems in Mechanics (1982) Linear Partial and Pseudo-differential Operators (1983) Differential Geometry on Homogeneous Spaces (1983) Special Functions: Theory and Computation (1985) Algebraic Varieties of Small Dimension (1986) Linear and Nonlinear Mathematical Control Theory (1987) Logic and Computer Sciences: New Trends and Applications (1987) Nonlinear Hyperbolic Equations in Applied Sciences (1988) Partial Differential Equations and Geometry (1989) Some Topics in Nonlinear PDE's (1989) Mathematical Theory of Dynamical Systems and ODE's, I-II (1990) Commutative Algebra and Algebraic Geometry, I-III (1990-1991) Numerical Methods in Applied Science and Industry (1991) Singularities in Curved Space-Times (1992)

R e n d i c o n t i del Seminar io M a t e m a t i c o U n i v e r s i t a e P o l i t e c n i c o - Torino

Volume 48 No. 4 (1990) "Algebra Commutativa e Geometria Algebrica", I

C O N T E N T S

P. Salmon, Le origini dell'algebra commutativa in Italia . . . . 431

M. Boratinski, On the curves of contact on surfaces in a projective space II . 439

G. Beccari, E. Davis, C. Massaza, Extremality with respect to the estimates of

Dubreil-Campanella: the Hilbert matrix , 457

A.J. Parameswaran, V. Srinivas, A variant of Noether normalisation 483

P. Maroscia, U. Nagel, W. Vogel, On degree bounds for the syzygies of a finite

set of points in ¥n 491

R. Strano, Plane sections of curves ofW and a conjecture of Hartshorne and

Hirschowitz 511

E. Mezzetti, I. Raspanti, A Laudal-type theorem for surfaces inW4 529

R. Achilles, M. Manaresi, Multiplicities for improper intersections of analytic

subsets 539

V. Beorchia, Ph. Ellia, Normal bundle and complete intersections 553

ISSN 0373-1243 EDITRICE UNIVERSITARIA LEVROTTO & BELLA - TORINO