SEMINARIO MATEMATICO Università' e Politecnico Torino

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1 ii^ffi^^iì^^ * *» *» ' i' SEMINARIO MATEMATICO Università' e Politecnico Torino -,,»*-!?' '-[ "fa> ( '-< j te: ty-^^'i,, ". < ' '» *. ', "i.

2 Aims The Seminario Matematico is a society of members of various Mathematics-related departments in the University and Polytechnic of Turin. Its scope is to promote study and research in ali fields of Mathematics and its application, and to contribute to the diffusion of mathematical culture. The Scientìfic Committee of the Seminario Matematico is elected amongst the full professors of Mathematics. The Rendiconti is the officiai journal of the Seminario Matematico. It publishes papers, surveys and invited lectures. Papers should provide originai research contributions. Surveys and invited lectures should have a tutorial or overview character. Other information and the contents ofrecent issues are available at: http ://calvino.polito.it/rendi/rendico.html Instructions to Authors Inlerested authors should submit three copies of their papers to the following address: Seminario Matematico dell'università e del Politecnico di Torino Via Carlo Alberto Torino (Italy) The final decision on acceptance of a paper is taken by the Scientific Committee, based upon the evaluations of an external referee. English is the preferred language, but papers in Italian or French may also be submitted. The Rendiconti welcomes papers prepared in some version of TjnX, but the corresponding file should only be supplied if and when the paper is accepted. After acceptance the authors can contact the editorial staff at rendicodm.unito.it The first page should contain the title, the name and affiliation of each author, a brief abstract and the complete mailing address. An address, if available, should be provided. 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 issues may be devoted to special topics. Subscription rates for 1997: Italy, L. 175,000 - Europe, L. 215,000 - Other Countries, L. 305,000. Prices are quoted in Italian lira and surface mail is included. Back years are offered at the current subscription price. Advance payment required. Available on standing order. Payment may be made by: - postai giro or international money order - bank transfer (please, add. L. 15,000): BIPOP, Agenzia 4, C/C 29 - sending invoice (institutions only) Ali Communications concerning subscriptions should be addressed to: Libreria Lev rotto e Bella Corso Vittorio Emanuele If, 26/F Torino (Italy) Phone: Fax:

3 RENDICONTI DEL SEMINARIO MATEMATICO CONTENTS A. Miernowski, W. Mozgawa, On some geometrie conditionfor convexity of isoptics 93 M. Ashraf, Some commutativity theorems far associative rings 99 C. Bu e, Asymptotic stability of evolutors and normed function spaces 109 M. Cicognani, L. Zanghirati, Quasilinear weakly hyperbolic equations with Levi's conditions 123 E. Baltico, L. Gatto, Weierstrass points on singular curves 145 Volume 55, N

4 DIRETTORE ANDREA BACCIOTTI COMMISSIONE SCIENTIFICA ( ) A. Bacciotti (Direttore), S. Benenti (Vicedirettore), G. AUasia, P. Colli, C. Massaza G. Monegato, L. Pandolfi, G. Pirola, G. Pistone, E Previale COMITATO DIRETTIVO ( ) S. Console, C. Cumino, S. Garbiero, A. Marcone, G. Rossi Proprietà letteraria riservata Autorizzazione del Tribunale di Torino N del 6.VL1980 Direttore Responsabile: ANDREA BACCIOTTI QUESTA RIVISTA E' STAMPATA CON IL CONTRIBUTO DI: UNIVERSITÀ DEGLI STUDI DI TORINO DIPARTIMENTO DI MATEMATICA DEL POLITECNICO DI TORINO CONSIGLIO NAZIONALE DELLE RICERCHE

5 Finito di stampare nel mese di dicembre 1998 presso la M.S. Litografia S.r.l. - Torino per conto della Editrice Universitaria Levrotto & Bella - Torino

6 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, I-II (1990) Commutative Algebra and Algebraic Geometry, I-TEI ( ) Numerical Methods in Applied Science and Industry (1991) Singularities in Curved Space-Times (1992) Differential Geometry (1992) Numerical Methods in Astrophysics and Cosmology (1993) Partial Differential Equations, I-II ( ) Problems in Algebraic Learning, I-II (1994) Number Theory, I-II (1995) Geometrica! Structures for Physical Theories, I-II (1996)

7 Rendiconti del Seminario Matematico dell'università e del Politecnico di Torino Volume 55 No. 2 (1997) À. Mierriowski, W. Mozgawa, On some geometrie conditionfor convexity of isoptics 93 CONTENTS M. Ashraf, Some commutativity theorems for associative rings 99 C. Bu e, Asymptotic stability of evo luto rs and normed function spaces 109 M. Cicognani, L. Zanghirati, Quasilinear weakly hyperbouc equatiohs with Levi's conditions 123 E. Ballico, L. Gatto, Weierstrass points on singular curves 145 ISSN EDITRICE UNIVERSITARIA LEVROTTO & BELLA - TORINO