Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Hadamard’s inequality for convex functions | Statement: [Hadamard inequality, hasVariant, Hadamard’s inequality for convex functions]

Target entity: Hadamard’s inequality for convex functions
Context triple: [Hadamard inequality, hasVariant, Hadamard’s inequality for convex functions]

• A. Hadamard inequality chosen
  The Hadamard inequality is a fundamental result in linear algebra and analysis that bounds the absolute value of a determinant by the product of the Euclidean norms of its row or column vectors.
• B. Maclaurin’s inequality in symmetric means
  Maclaurin’s inequality in symmetric means is a classical result in mathematical analysis that relates and bounds the sequence of elementary symmetric means of a set of nonnegative real numbers, showing they form a decreasing sequence.
• C. Karamata's inequality
  Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
• D. Inequalities for analytic functions
  "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
• E. Chebyshev’s sum inequality
  Chebyshev’s sum inequality is a mathematical inequality that provides bounds on the sum of products of similarly ordered sequences, widely used in analysis and probability theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.