Maxima and minima

In mathematical analysis, the maxima and minima (the plural of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.

As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum.

Definition

A real-valued function f defined on a domain X has a global (or absolute) maximum point at x^∗ if f(x^∗) ≥ f(x) for all x in X. Similarly, the function has a global (or absolute) minimum point at x^∗ if f(x^∗) ≤ f(x) for all x in X. The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function.

Minimum (disambiguation)

Minimum, a Latin word meaning the least or the smallest, may refer to:

Akhenaten

Akhenaten (/ˌækəˈnɑːtən/; also spelled Echnaton,Akhenaton,Ikhnaton, and Khuenaten; meaning "Effective for Aten") known before the fifth year of his reign as Amenhotep IV (sometimes given its Greek form, Amenophis IV, and meaning Amun is Satisfied), was a pharaoh of the Eighteenth dynasty of Egypt who ruled for 17 years and died perhaps in 1336 BC or 1334 BC. He is especially noted for abandoning traditional Egyptian polytheism and introducing worship centered on the Aten, which is sometimes described as monotheistic or henotheistic. An early inscription likens the Aten to the sun as compared to stars, and later official language avoids calling the Aten a god, giving the solar deity a status above mere gods.

Akhenaten tried to bring about a departure from traditional religion, yet in the end it would not be accepted. After his death, traditional religious practice was gradually restored, and when some dozen years later rulers without clear rights of succession from the Eighteenth Dynasty founded a new dynasty, they discredited Akhenaten and his immediate successors, referring to Akhenaten himself as "the enemy" or "that criminal" in archival records.

Akhenaton (rapper)

Philippe Fragione, better known by his stage name Akhenaton (born 17 September 1968, Marseille), is a French rapper and producer of French hip hop. He has also worked under the aliases Chill, AKH, Sentenza, and Spectre. He became famous as a member of the group IAM, and has since made a number of records, both with IAM and as a solo artist.

Akhenaton has worked as a producer, producing songs for several French rappers and groups such as Passi, Stomy Bugsy, Fonky Family, Freeman (a fellow member of IAM who has since made his break as a solo artist), La Brigade, Le 3ème Œil, etc. He is the creator of the record label Côté Obscur, the publishing house La Cosca, and the vinyl record label 361.

Biography

Akhenaton was born Philippe Fragione in Marseille in 1968, and spent his youth in Plan-de-Cuques, a small village on the outskirts of the city. His family is of Italian origins. His paternal grandmother, Immacolata Scotti, was of Campanian descent, his great-grandfather Francesco Fragione, emigrated from Sperlonga and on his maternal side a great-great-grandfather, Pierre Malano, emigrated from Porte, a great-great-great-grandfather Barthelemy Gionotti, emigrated from Camporgiano and another great-grandmother Maria Lanzarotti, emigrated from Bedonia. In 1981, he discovered hip hop music and started traveling frequently to New York City where he received the nickname "Chill Phil." At about the same time, back in Marseille, he met Éric Mazel, a DJ who would later be known as "Khéops". Mazel and Fragione started working together to advance the cause of French hip hop.

Akhenaten (disambiguation)

Akhenaton, Akhnaton, Akhnaten or Akhenaten may refer to: