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Context-free grammars are a special form of Semi-Thue systems that in their general form date back to the work of Axel Thue. The formalism of context-free grammars was developed in the mid-1950s by Noam Chomsky, [3] and also their classification as a special type of formal grammar (which he called phrase-structure grammars). [4]
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure.
The Positive predictive value (PPV) of a test is the proportion of persons who are actually positive out of all those testing positive, and can be calculated from a sample as: PPV = True positive / Tested positive. If sensitivity, specificity, and prevalence are known, PPV can be calculated using Bayes theorem.
A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2.
It also features expanded tables and cases, improved notations and figures within the tables, consistent table and equation numbering, and verification of correction factors. The formulas are organized into tables in a hierarchical format: chapter, table, case, subcase, and each case and subcase is accompanied by diagrams.
Bass diffusion model; Black–Scholes equation; Economic growth. Solow–Swan model ′ = [()] Ramsey–Cass–Koopmans model; Dynamic stochastic general equilibrium [8]; Feynman–Kac formula
A frequently cited example of uniform acceleration is that of an object in free fall in a uniform gravitational field. The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g (also called acceleration due to gravity ).
The free group G = π 1 (X) has n = 2 generators corresponding to loops a,b from the base point P in X.The subgroup H of even-length words, with index e = [G : H] = 2, corresponds to the covering graph Y with two vertices corresponding to the cosets H and H' = aH = bH = a −1 H = b − 1 H, and two lifted edges for each of the original loop-edges a,b.