{"paper":{"title":"On the sum of squared logarithms inequality and related inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Christian Thiel, Fozi M. Dannan, Patrizio Neff","submitted_at":"2014-11-05T15:02:14Z","abstract_excerpt":"We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors $a,b\\in\\mathbb{R}_+^n$ so that $\\sum_{i=1}^n(\\log a_i)^2\\ \\leq\\ \\sum_{i=1}^n(\\log b_i)^2\\,.\\notag $ Generalizations of some inequalities from information theory are obtained, including a generalized information inequality and a generalized log sum inequality, which states for $a,b\\in\\mathbb{R}_+^n$ and $k_1,...,k_n\\in [0,\\infty)$: $ \\sum_{i=1}^na_i\\,\\log\\prod_{s=1}^m(\\frac{a_i}{b_i} + k_s)\\ \\geq\\ \\log"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1290","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}