Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz Maps
A real univariate polynomial is called hyperbolic or stable if all its roots are real. We search for hyperbolic polynomials of two and three degrees by using the Wronskian map <i>W</i> and a dual map to <i>W</i> called Leibniz, since it involves the classical Leibniz rule for...
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| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/13/2/104 |
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| author | Mircea Crasmareanu |
| author_facet | Mircea Crasmareanu |
| author_sort | Mircea Crasmareanu |
| collection | DOAJ |
| description | A real univariate polynomial is called hyperbolic or stable if all its roots are real. We search for hyperbolic polynomials of two and three degrees by using the Wronskian map <i>W</i> and a dual map to <i>W</i> called Leibniz, since it involves the classical Leibniz rule for the derivative of a product of functions. In addition to hyperbolicity, we use these two methods to search for a class of polynomials introduced by the first author and now called weak Euclidean. |
| first_indexed | 2024-03-07T22:42:36Z |
| format | Article |
| id | doaj.art-5cdbb276a39246ee89b51deb5128daf7 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-07T22:42:36Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5cdbb276a39246ee89b51deb5128daf72024-02-23T15:07:25ZengMDPI AGAxioms2075-16802024-02-0113210410.3390/axioms13020104Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz MapsMircea Crasmareanu0Faculty of Mathematics, University “Al. I. Cuza”, 700506 Iasi, RomaniaA real univariate polynomial is called hyperbolic or stable if all its roots are real. We search for hyperbolic polynomials of two and three degrees by using the Wronskian map <i>W</i> and a dual map to <i>W</i> called Leibniz, since it involves the classical Leibniz rule for the derivative of a product of functions. In addition to hyperbolicity, we use these two methods to search for a class of polynomials introduced by the first author and now called weak Euclidean.https://www.mdpi.com/2075-1680/13/2/104hyperbolic polynomial(weak) Euclidean polynomialWronskianLeibniz map |
| spellingShingle | Mircea Crasmareanu Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz Maps Axioms hyperbolic polynomial (weak) Euclidean polynomial Wronskian Leibniz map |
| title | Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz Maps |
| title_full | Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz Maps |
| title_fullStr | Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz Maps |
| title_full_unstemmed | Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz Maps |
| title_short | Hyperbolic and Weak Euclidean Polynomials from Wronskian and Leibniz Maps |
| title_sort | hyperbolic and weak euclidean polynomials from wronskian and leibniz maps |
| topic | hyperbolic polynomial (weak) Euclidean polynomial Wronskian Leibniz map |
| url | https://www.mdpi.com/2075-1680/13/2/104 |
| work_keys_str_mv | AT mirceacrasmareanu hyperbolicandweakeuclideanpolynomialsfromwronskianandleibnizmaps |