Convex functionIn mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain.
Graph of a functionIn mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane. In the case of functions of two variables, that is functions whose domain consists of pairs the graph usually refers to the set of ordered triples where instead of the pairs as in the definition above. This set is a subset of three-dimensional space; for a continuous real-valued function of two real variables, it is a surface.
Version of recordThe version of record of an article is the fully copyedited, typeset and formatted copy of a manuscript as published. The terminology is used in a wide variety of written media (e.g. books, journals, monographs). For print documents, the version of record will be the version as printed and distributed. For electronic documents it is typically the HTML and PDF version. For items published in both a print and electronic version, the electronic copy is often the version of record.
PreprintIn academic publishing, a preprint is a version of a scholarly or scientific paper that precedes formal peer review and publication in a peer-reviewed scholarly or scientific journal. The preprint may be available, often as a non-typeset version available free, before or after a paper is published in a journal. Since 1991, preprints have increasingly been distributed electronically on the Internet, rather than as paper copies. This has given rise to massive preprint databases such as arXiv and HAL (open archive) etc.
ArXivarXiv (pronounced as "archive"—the X represents the Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not peer review. It consists of scientific papers in the fields of mathematics, physics, astronomy, electrical engineering, computer science, quantitative biology, statistics, mathematical finance and economics, which can be accessed online.
