Irreducible polynomialIn mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the field to which the coefficients of the polynomial and its possible factors are supposed to belong. For example, the polynomial x2 − 2 is a polynomial with integer coefficients, but, as every integer is also a real number, it is also a polynomial with real coefficients.
PermutationIn mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1).
Weight (representation theory)In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space.
Unitary divisorIn mathematics, a natural number a is a unitary divisor (or Hall divisor) of a number b if a is a divisor of b and if a and are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and have a common factor other than 1, namely 2. 1 is a unitary divisor of every natural number. Equivalently, a divisor a of b is a unitary divisor if and only if every prime factor of a has the same multiplicity in a as it has in b.
Philippe Michel (economist)Philippe Michel (October 6, 1937 – July 22, 2004) was a French mathematical economist. Philippe Michel earned a PhD in Mathematics from the University of Paris VI in 1972, and became a Professor of Mathematics in 1976 at the University of Paris I. In 1993, he joined the Faculty of Economics at the University of Aix-Marseille II at GREQAM. Philippe Michel first scientific contributions were in the field of mathematics, with a focus on optimal control theory.
Philippe Michel (number theorist)Philippe Gabriel Michel (born 23 January 1969) is a French mathematician who holds the chair in analytic number theory at the École Polytechnique Fédérale de Lausanne in Switzerland. Michel was born in Lyon. He studied from 1989 to 1993 at the École normale supérieure de Cachan, and then moved to the University of Paris-Sud, where he earned a doctorate in 1995 under the supervision of Étienne Fouvry and then a habilitation in 1998. He was a professor at the University of Montpellier from 1998 to 2008, when he moved to EPFL.
Philippe of BelgiumPhilippe or Filip (Filip Leopold Lodewijk Maria ˈfilɪp ˈleːjoːpɔlt ˈloːdəʋɛik maːˈrijaː; Philippe Léopold Louis Marie filip leɔpɔld lwi maʁi; born 15 April 1960) is King of the Belgians. He is the eldest child of King Albert II and Queen Paola. He succeeded his father upon the latter's abdication for health reasons on 21 July 2013. He married Mathilde d'Udekem d'Acoz in 1999, with whom he has four children. Their eldest child, Princess Elisabeth, is first in the line of succession.
InfinitesimalIn mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinity-th" item in a sequence. Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another.
History of calculusCalculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. Infinitesimal calculus was developed in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz independently of each other. An argument over priority led to the Leibniz–Newton calculus controversy which continued until the death of Leibniz in 1716.
Louis-Michel van LooLouis-Michel van Loo (2 March 1707, Toulon – 20 March 1771, Paris) was a French painter. He studied under his father, the painter Jean-Baptiste van Loo, at Turin and Rome, and he won a prize at the Académie Royale de Peinture et de Sculpture in Paris in 1725. With his uncle, the painter Charles-André van Loo, he went to Rome in 1727–1732, and in 1736 he became court painter to Philip V of Spain at Madrid, where he was a founder-member of the Royal Academy of Fine Arts of San Fernando in 1752.
Unitary groupIn mathematics, the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation of matrix multiplication. The unitary group is a subgroup of the general linear group GL(n, C). Hyperorthogonal group is an archaic name for the unitary group, especially over finite fields. For the group of unitary matrices with determinant 1, see Special unitary group. In the simple case n = 1, the group U(1) corresponds to the circle group, consisting of all complex numbers with absolute value 1, under multiplication.
Louis Philippe ILouis Philippe I (6 October 1773 – 26 August 1850), nicknamed the Citizen King, was King of the French from 1830 to 1848, and the penultimate monarch of France. As Louis Philippe, Duke of Chartres, he distinguished himself commanding troops during the Revolutionary Wars and was promoted to lieutenant general by the age of nineteen, but he broke with the Republic over its decision to execute King Louis XVI. He fled to Switzerland in 1793 after being connected with a plot to restore France's monarchy.
