Topics in Analysis.
Abstract
The research performed under this grant deals with some classical problems in the area of algebra. Considerable progress has been made from a theoretical point of view. There were two main topics: (1) Newton-Sylvester theorems on the number of zeros of a function in an open interval, (2) reversible transformations in algebraic geometry. The specific results are: A simplified proof of a sharpening of Sylvester's theorems, obtained by replacing the values of the functions considered at a and b with their values at a + 0 and b-0. In this way the result of Marchand can be improved. Further improvements are pointed out for Sylvester's theorems and Newton's Rule. The reversible transformation of space elements can be characterized, starting from ordinary one-to-one transformations between two convenient spaces and the complete sets of integrals of certain partial differential equations, which can be expressed by convenient determinants. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1979
- Accession Number
- ADA080463
Entities
People
- Alexander M. Ostrowski
Organizations
- University of Basel