On the Global Continuity of the Roots of Families of Monic Polynomials (in Russian)
We raise a question on the existence of continuous roots of families of monic polynomials (by the root of a family of polynomials we mean a function of the coefficients of polynomials of a given family that maps each tuple of coefficients to a root of the polynomial with these coefficients). We prov...
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| creator | Bukzhalev, Evgeny E |
| description | We raise a question on the existence of continuous roots of families of monic
polynomials (by the root of a family of polynomials we mean a function of the
coefficients of polynomials of a given family that maps each tuple of
coefficients to a root of the polynomial with these coefficients). We prove
that the family of monic second-degree polynomials with complex coefficients
and the families of monic fourth-degree and fifth-degree polynomials with real
coefficients have no continuous root. We also prove that the family of monic
second-degree polynomials with real coefficients has continuous roots and we
describe the set of all such roots. |
| doi_str_mv | 10.48550/arxiv.1710.00640 |
| format | Article |
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polynomials (by the root of a family of polynomials we mean a function of the
coefficients of polynomials of a given family that maps each tuple of
coefficients to a root of the polynomial with these coefficients). We prove
that the family of monic second-degree polynomials with complex coefficients
and the families of monic fourth-degree and fifth-degree polynomials with real
coefficients have no continuous root. We also prove that the family of monic
second-degree polynomials with real coefficients has continuous roots and we
describe the set of all such roots.</description><identifier>DOI: 10.48550/arxiv.1710.00640</identifier><language>eng</language><subject>Mathematics - Classical Analysis and ODEs</subject><creationdate>2017-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1710.00640$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1710.00640$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bukzhalev, Evgeny E</creatorcontrib><title>On the Global Continuity of the Roots of Families of Monic Polynomials (in Russian)</title><description>We raise a question on the existence of continuous roots of families of monic
polynomials (by the root of a family of polynomials we mean a function of the
coefficients of polynomials of a given family that maps each tuple of
coefficients to a root of the polynomial with these coefficients). We prove
that the family of monic second-degree polynomials with complex coefficients
and the families of monic fourth-degree and fifth-degree polynomials with real
coefficients have no continuous root. We also prove that the family of monic
second-degree polynomials with real coefficients has continuous roots and we
describe the set of all such roots.</description><subject>Mathematics - Classical Analysis and ODEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjz1vwjAQhr0wVLQ_oFM90iH04o_YjCgqFImKirJHTuyIkxy7SkLV_PuGwPLee89JJz2EPKewFFpKeDPtH_4uUzUCgEzAA_k-BNqfHd36WBpP8xh6DBfsBxrr6XCMse-uy8Y06NFN_TMGrOhX9EOIDRrf0QUGerx0HZrw-khm9cjc033OyWnzfso_kv1hu8vX-8RkChJZsdryjAluuVRcMV6DMhJ4NabISuuE04pJWJXKgpIr65gTukqZ1k5aw-fk5fZ2sip-WmxMOxRXu2Ky4_9Q3kj4</recordid><startdate>20170921</startdate><enddate>20170921</enddate><creator>Bukzhalev, Evgeny E</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20170921</creationdate><title>On the Global Continuity of the Roots of Families of Monic Polynomials (in Russian)</title><author>Bukzhalev, Evgeny E</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a670-5c2fd36243d3573723f07a503c7a546bde4e872509b7d0759de2e48c1288e5da3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Classical Analysis and ODEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Bukzhalev, Evgeny E</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bukzhalev, Evgeny E</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Global Continuity of the Roots of Families of Monic Polynomials (in Russian)</atitle><date>2017-09-21</date><risdate>2017</risdate><abstract>We raise a question on the existence of continuous roots of families of monic
polynomials (by the root of a family of polynomials we mean a function of the
coefficients of polynomials of a given family that maps each tuple of
coefficients to a root of the polynomial with these coefficients). We prove
that the family of monic second-degree polynomials with complex coefficients
and the families of monic fourth-degree and fifth-degree polynomials with real
coefficients have no continuous root. We also prove that the family of monic
second-degree polynomials with real coefficients has continuous roots and we
describe the set of all such roots.</abstract><doi>10.48550/arxiv.1710.00640</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Classical Analysis and ODEs |
| title | On the Global Continuity of the Roots of Families of Monic Polynomials (in Russian) |
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