{"id":119,"date":"2018-11-09T12:08:09","date_gmt":"2018-11-09T14:08:09","guid":{"rendered":"http:\/\/www.professores.uff.br\/vitorbalestro\/?page_id=119"},"modified":"2018-11-09T12:08:09","modified_gmt":"2018-11-09T14:08:09","slug":"on-a-cosine-function-defined-for-smooth-normed-planes","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/vitorbalestro\/publications\/on-a-cosine-function-defined-for-smooth-normed-planes\/","title":{"rendered":"On a cosine function defined for smooth normed planes"},"content":{"rendered":"<p id=\"h.p_RXwnJkm3JhiJ\" class=\"zfr3Q\">V. Balestro and E. Shonoda, <strong>On a cosine function defined for smooth normed planes<\/strong>, Journal of Convex Analysis 25(1), pp. 21-39, 2018. (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F1607.01515&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNHp4PQT1z-nIeUkqUHPVBhYo8U7sg\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv link<\/a>) (<a class=\"dhtgD\" href=\"http:\/\/www.google.com\/url?q=http%3A%2F%2Fwww.heldermann.de%2FJCA%2FJCA25%2FJCA251%2Fjca25002.htm&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNF07Z7QM1EIiGgUE8i5uRAnNKBH_A\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a>)<\/p>\n<p id=\"h.p_1CNqYz7HJiyj\" class=\"zfr3Q\">Comments: We study a cosine function that can be defined for smooth normed spaces (in the sense that each point of the unit sphere has a unique supporting hyperplane). We derive a geometric flavored definition for it, and relate it to the Minkowski sine function. As applications, we give an expression to the Gateaux derivative of the norm, derive a local characterization of Radon planes (which was still missing, as far as I know), and obtain a formula to measure the distortion between the lengths of external tangents drawn from a point to the unit circle of a Radon plane. A new geometric characterization of Radon curves is also derived.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>V. Balestro and E. Shonoda, On a cosine function defined for smooth normed planes, Journal of Convex Analysis 25(1), pp. 21-39, 2018. (arXiv link) (journal link) Comments: We study a cosine function that can be defined for smooth normed spaces (in the sense that each point of the unit sphere has a unique supporting hyperplane). [&hellip;]<\/p>\n","protected":false},"author":205,"featured_media":0,"parent":12,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-119","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/119","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/users\/205"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/comments?post=119"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/119\/revisions"}],"predecessor-version":[{"id":120,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/119\/revisions\/120"}],"up":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/12"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/media?parent=119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/categories?post=119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/tags?post=119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}