Search results
Results from the WOW.Com Content Network
In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectra), which has particularly broad scope. [1] [2] Thus for instance if T is an operator, applying the squaring function s → s 2 to T yields the ...
Keep a set data structure of all states which the NFA might currently be in. On the consumption of an input symbol, unite the results of the transition function applied to all current states to get the set of next states; if ε-moves are allowed, include all states reachable by such a move (ε-closure).
The structure function, like the fragmentation function, is a probability density function in physics. It is somewhat analogous to the structure factor in solid-state physics , and the form factor (quantum field theory) .
The Digital Library of Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology (NIST) to develop a database of mathematical reference data for special functions and their applications. It is intended as an update of Abramowitz's and Stegun's Handbook of Mathematical Functions (A&S). [1]
The Kolmogorov structure function precisely quantifies the goodness-of-fit of an individual model with respect to individual data. The Kolmogorov structure function is used in the algorithmic information theory, also known as the theory of Kolmogorov complexity, for describing the structure of a string by use of models of increasing complexity.
The standard Gibbs free energy of formation (G f °) of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states (the most stable form of the element at 1 bar of pressure and the specified temperature, usually 298.15 K or 25 °C).
Compositions of two real functions, the absolute value and a cubic function, in different orders, show a non-commutativity of composition. The functions g and f are said to commute with each other if g ∘ f = f ∘ g. Commutativity is a special property, attained only by particular functions, and often in special circumstances.
M/tM is a finitely generated torsion free module, and such a module over a commutative PID is a free module of finite rank, so it is isomorphic to: for a positive integer n. Since every free module is projective module, then exists right inverse of the projection map (it suffices to lift each of the generators of M/tM into M).