Residue theoremIn complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula. The residue theorem should not be confused with special cases of the generalized Stokes' theorem; however, the latter can be used as an ingredient of its proof.
Product (business)In marketing, a product is an object, or system, or service made available for consumer use as of the consumer demand; it is anything that can be offered to a market to satisfy the desire or need of a customer. In retailing, products are often referred to as merchandise, and in manufacturing, products are bought as raw materials and then sold as finished goods. A service is also regarded as a type of product. In project management, products are the formal definition of the project deliverables that make up or contribute to delivering the objectives of the project.
Irreducible fractionAn irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). In other words, a fraction a/b is irreducible if and only if a and b are coprime, that is, if a and b have a greatest common divisor of 1. In higher mathematics, "irreducible fraction" may also refer to rational fractions such that the numerator and the denominator are coprime polynomials.
EvolutionIn biology, evolution is the change in heritable characteristics of biological populations over successive generations. Evolution occurs when evolutionary processes such as natural selection (including sexual selection) and genetic drift act on genetic variation, resulting in certain characteristics becoming more or less common within a population over successive generations. The process of evolution has given rise to biodiversity at every level of biological organisation.
Metal carbonylMetal carbonyls are coordination complexes of transition metals with carbon monoxide ligands. Metal carbonyls are useful in organic synthesis and as catalysts or catalyst precursors in homogeneous catalysis, such as hydroformylation and Reppe chemistry. In the Mond process, nickel tetracarbonyl is used to produce pure nickel. In organometallic chemistry, metal carbonyls serve as precursors for the preparation of other organometallic complexes.
HemofiltrationHemofiltration, also haemofiltration, is a renal replacement therapy which is used in the intensive care setting. It is usually used to treat acute kidney injury (AKI), but may be of benefit in multiple organ dysfunction syndrome or sepsis. During hemofiltration, a patient's blood is passed through a set of tubing (a filtration circuit) via a machine to a semipermeable membrane (the filter) where waste products and water (collectively called ultrafiltrate) are removed by convection.
Coordinate covalent bondIn coordination chemistry, a coordinate covalent bond, also known as a dative bond, dipolar bond, or coordinate bond is a kind of two-center, two-electron covalent bond in which the two electrons derive from the same atom. The bonding of metal ions to ligands involves this kind of interaction. This type of interaction is central to Lewis acid–base theory. Coordinate bonds are commonly found in coordination compounds. Coordinate covalent bonding is ubiquitous.
Continued fractionIn mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression.
AnilineAniline (, and -ine indicating a derived substance) is an organic compound with the formula . Consisting of a phenyl group () attached to an amino group (), aniline is the simplest aromatic amine. It is an industrially significant commodity chemical, as well as a versatile starting material for fine chemical synthesis. Its main use is in the manufacture of precursors to polyurethane, dyes, and other industrial chemicals. Like most volatile amines, it has the odor of rotten fish.
Evolution and the Catholic ChurchThe Catholic Church holds no official position on the theory of creation or evolution, leaving the specifics of either theistic evolution or literal creationism to the individual within certain parameters established by the Church. According to the Catechism of the Catholic Church, any believer may accept either literal or special creation within the period of an actual six-day, twenty-four-hour period, or they may accept the belief that the earth evolved over time under the guidance of God.
