Data integrationData integration involves combining data residing in different sources and providing users with a unified view of them. This process becomes significant in a variety of situations, which include both commercial (such as when two similar companies need to merge their databases) and scientific (combining research results from different bioinformatics repositories, for example) domains. Data integration appears with increasing frequency as the volume (that is, big data) and the need to share existing data explodes.
Skew-symmetric matrixIn mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition In terms of the entries of the matrix, if denotes the entry in the -th row and -th column, then the skew-symmetric condition is equivalent to The matrix is skew-symmetric because Throughout, we assume that all matrix entries belong to a field whose characteristic is not equal to 2.
Frobenius theorem (differential topology)In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields.
Old FrenchOld French (franceis, françois, romanz; Modern French: ancien français) was the language spoken in most of the northern half of France approximately between the 8th and the 14th century. Rather than a unified language, Old French was a linkage of Romance dialects, mutually intelligible yet diverse. These dialects came to be collectively known as the langue d'oïl, contrasting with the langue d'oc in the south of France. The mid-14th century witnessed the emergence of Middle French, the language of the French Renaissance in the Île de France region; this dialect was a predecessor to Modern French.
DiphthongA diphthong (ˈdɪfθɒŋ,_ˈdɪp- ; , ), also known as a gliding vowel, is a combination of two adjacent vowel sounds within the same syllable. Technically, a diphthong is a vowel with two different targets: that is, the tongue (and/or other parts of the speech apparatus) moves during the pronunciation of the vowel. In most varieties of English, the phrase "no highway cowboy" (noʊ_ˈhaɪweɪ_ˈkaʊbɔɪ) has five distinct diphthongs, one in every syllable.
BlackBlack is a color that results from the absence or complete absorption of visible light. It is an achromatic color, without hue, like white and grey. It is often used symbolically or figuratively to represent darkness. Black and white have often been used to describe opposites such as good and evil, the Dark Ages versus Age of Enlightenment, and night versus day. Since the Middle Ages, black has been the symbolic color of solemnity and authority, and for this reason it is still commonly worn by judges and magistrates.
Black braneIn general relativity, a black brane is a solution of the equations that generalizes a black hole solution but it is also extended—and translationally symmetric—in p additional spatial dimensions. That type of solution would be called a black p-brane. In string theory, the term black brane describes a group of D1-branes that are surrounded by a horizon. With the notion of a horizon in mind as well as identifying points as zero-branes, a generalization of a black hole is a black p-brane.
Black holeA black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of no escape is called the event horizon. Although it has a great effect on the fate and circumstances of an object crossing it, it has no locally detectable features according to general relativity.
Black catA black cat is a domestic cat with black fur that may be a mixed or specific breed, or a common domestic cat of no particular breed. The Cat Fanciers' Association (CFA) recognizes 22 cat breeds that can come with solid black coats. The Bombay breed is exclusively black. All-black fur pigmentation is slightly more prevalent in male cats than female cats. Most black cats have golden irises due to their high melanin pigment content. In popular myths, witches are believed to be associated with black cats.
Adrien-Marie LegendreAdrien-Marie Legendre (ləˈʒɑːndər,_-ˈʒɑːnd; adʁiɛ̃ maʁi ləʒɑ̃dʁ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. Adrien-Marie Legendre was born in Paris on 18 September 1752 to a wealthy family. He received his education at the Collège Mazarin in Paris, and defended his thesis in physics and mathematics in 1770.
Carbon blackCarbon black (subtypes are acetylene black, channel black, furnace black, lamp black and thermal black) is a material produced by the incomplete combustion of coal and coal tar, vegetable matter, or petroleum products, including fuel oil, fluid catalytic cracking tar, and ethylene cracking in a limited supply of air. Carbon black is a form of paracrystalline carbon that has a high surface-area-to-volume ratio, albeit lower than that of activated carbon.
QR decompositionIn linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Any real square matrix A may be decomposed as where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning ) and R is an upper triangular matrix (also called right triangular matrix).
