PaperPaper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses, or other vegetable sources in water, draining the water through a fine mesh leaving the fibre evenly distributed on the surface, followed by pressing and drying. Although paper was originally made in single sheets by hand, almost all is now made on large machines—some making reels 10 metres wide, running at 2,000 metres per minute and up to 600,000 tonnes a year.
Primary sourceIn the study of history as an academic discipline, a primary source (also called an original source) is an artifact, document, diary, manuscript, autobiography, recording, or any other source of information that was created at the time under study. It serves as an original source of information about the topic. Similar definitions can be used in library science and other areas of scholarship, although different fields have somewhat different definitions.
Beal conjectureThe Beal conjecture is the following conjecture in number theory: If where A, B, C, x, y, and z are positive integers with x, y, z ≥ 3, then A, B, and C have a common prime factor. Equivalently, The equation has no solutions in positive integers and pairwise coprime integers A, B, C if x, y, z ≥ 3. The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed proof of this conjecture or a counterexample.
Derived functorIn mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. It was noted in various quite different settings that a short exact sequence often gives rise to a "long exact sequence". The concept of derived functors explains and clarifies many of these observations. Suppose we are given a covariant left exact functor F : A → B between two A and B.
Shannon's source coding theoremIn information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the limits to possible data compression, and the operational meaning of the Shannon entropy. Named after Claude Shannon, the source coding theorem shows that (in the limit, as the length of a stream of independent and identically-distributed random variable (i.i.d.) data tends to infinity) it is impossible to compress the data such that the code rate (average number of bits per symbol) is less than the Shannon entropy of the source, without it being virtually certain that information will be lost.
Least-upper-bound propertyIn mathematics, the least-upper-bound property (sometimes called completeness or supremum property or l.u.b. property) is a fundamental property of the real numbers. More generally, a partially ordered set X has the least-upper-bound property if every non-empty subset of X with an upper bound has a least upper bound (supremum) in X. Not every (partially) ordered set has the least upper bound property. For example, the set of all rational numbers with its natural order does not have the least upper bound property.
ProvenceProvence (prəˈvɒ̃s, USalsoprəʊˈ-, UKalsoprɒˈ-, pʁɔvɑ̃s) is a geographical region and historical province of southeastern France, which extends from the left bank of the lower Rhône to the west to the Italian border to the east; it is bordered by the Mediterranean Sea to the south. It largely corresponds with the modern administrative region of Provence-Alpes-Côte d'Azur and includes the departments of Var, Bouches-du-Rhône, Alpes-de-Haute-Provence, as well as parts of Alpes-Maritimes and Vaucluse.
Derived categoryIn mathematics, the derived category D(A) of an A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes. Derived functors can then be defined for chain complexes, refining the concept of hypercohomology.
Coated paperCoated paper (also known as enamel paper, gloss paper, and thin paper) is paper that has been coated by a mixture of materials or a polymer to impart certain qualities to the paper, including weight, surface gloss, smoothness, or reduced ink absorbency. Various materials, including kaolinite, calcium carbonate, bentonite, and talc, can be used to coat paper for high-quality printing used in the packaging industry and in magazines. The chalk or china clay is bound to the paper with synthetic s, such as styrene-butadiene latexes and natural organic binders such as starch.
Pairwise independenceIn probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random variables with finite variance are uncorrelated. A pair of random variables X and Y are independent if and only if the random vector (X, Y) with joint cumulative distribution function (CDF) satisfies or equivalently, their joint density satisfies That is, the joint distribution is equal to the product of the marginal distributions.
Yield (wine)In viticulture, the yield is a measure of the amount of grapes or wine that is produced per unit surface of vineyard, and is therefore a type of crop yield. Two different types of yield measures are commonly used, mass of grapes per vineyard surface, or volume of wine per vineyard surface. The yield is often seen as a quality factor, with lower yields associated with wines with more concentrated flavours, and the maximum allowed yield is therefore regulated for many wine appellations.
Yield (finance)In finance, the yield on a security is a measure of the ex-ante return to a holder of the security. It is one component of return on an investment, the other component being the change in the market price of the security. It is a measure applied to fixed income securities, common stocks, preferred stocks, convertible stocks and bonds, annuities and real estate investments. There are various types of yield, and the method of calculation depends on the particular type of yield and the type of security.
