Partial fraction decompositionIn algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. The importance of the partial fraction decomposition lies in the fact that it provides algorithms for various computations with rational functions, including the explicit computation of antiderivatives, Taylor series expansions, inverse Z-transforms, and inverse Laplace transforms.
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.
Well-defined expressionIn mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if takes real numbers as input, and if does not equal then is not well defined (and thus not a function).
Acetic acidAcetic acid əˈsiːtᵻk, systematically named ethanoic acid ˌɛθəˈnoʊᵻk, is an acidic, colourless liquid and organic compound with the chemical formula (also written as , , or ). Vinegar is at least 4% acetic acid by volume, making acetic acid the main component of vinegar apart from water and other trace elements. Acetic acid is the second simplest carboxylic acid (after formic acid). It is an important chemical reagent and industrial chemical, used primarily in the production of cellulose acetate for photographic film, polyvinyl acetate for wood glue, and synthetic fibres and fabrics.
Dichloroacetic acidDichloroacetic acid (DCA), sometimes called bichloroacetic acid (BCA), is the chemical compound with formula C H Cl2COOH. It is an acid, an analogue of acetic acid, in which 2 of the 3 hydrogen atoms of the methyl group have been replaced by chlorine atoms. Like the other chloroacetic acids, it has various practical applications. The salts and esters of dichloroacetic acid are called dichloroacetates. Salts of DCA have been studied as potential drugs because they inhibit the enzyme pyruvate dehydrogenase kinase.
Greedy algorithm for Egyptian fractionsIn mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as 5/6 = 1/2 + 1/3. As the name indicates, these representations have been used as long ago as ancient Egypt, but the first published systematic method for constructing such expansions was described in 1202 in the Liber Abaci of Leonardo of Pisa (Fibonacci).
Generalized continued fractionIn complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary complex values. A generalized continued fraction is an expression of the form where the an (n > 0) are the partial numerators, the bn are the partial denominators, and the leading term b0 is called the integer part of the continued fraction.
Consumption (economics)Consumption is the act of using resources to satisfy current needs and wants. It is seen in contrast to investing, which is spending for acquisition of future income. Consumption is a major concept in economics and is also studied in many other social sciences. Different schools of economists define consumption differently. According to mainstream economists, only the final purchase of newly produced goods and services by individuals for immediate use constitutes consumption, while other types of expenditure — in particular, fixed investment, intermediate consumption, and government spending — are placed in separate categories (see consumer choice).
Consumption functionIn economics, the consumption function describes a relationship between consumption and disposable income. The concept is believed to have been introduced into macroeconomics by John Maynard Keynes in 1936, who used it to develop the notion of a government spending multiplier. Its simplest form is the linear consumption function used frequently in simple Keynesian models: where is the autonomous consumption that is independent of disposable income; in other words, consumption when disposable income is zero.
Liquid fluoride thorium reactorThe liquid fluoride thorium reactor (LFTR; often pronounced lifter) is a type of molten salt reactor. LFTRs use the thorium fuel cycle with a fluoride-based molten (liquid) salt for fuel. In a typical design, the liquid is pumped between a critical core and an external heat exchanger where the heat is transferred to a nonradioactive secondary salt. The secondary salt then transfers its heat to a steam turbine or closed-cycle gas turbine. Molten-salt-fueled reactors (MSRs) supply the nuclear fuel mixed into a molten salt.
