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CALPHAD stands for Computer Coupling of Phase Diagrams and Thermochemistry, a methodology introduced in 1970 by Larry Kaufman, originally known as CALculation of PHAse Diagrams. [1] [2] [3] An equilibrium phase diagram is usually a diagram with axes for temperature and composition of a chemical system. It shows the regions where substances or ...
Then a coupling of and is a new probability space (,,) over which there are two random variables and such that has the same distribution as while has the same distribution as . An interesting case is when Y 1 {\displaystyle Y_{1}} and Y 2 {\displaystyle Y_{2}} are not independent.
[3] Coupling and cohesion. Coupling is usually contrasted with cohesion. Low coupling often correlates with high cohesion, and vice versa. Low coupling is often thought to be a sign of a well-structured computer system and a good design, and when combined with high cohesion, supports the general goals of high readability and maintainability.
A 2-satisfiability problem may be described using a Boolean expression with a special restricted form. It is a conjunction (a Boolean and operation) of clauses, where each clause is a disjunction (a Boolean or operation) of two variables or negated variables. The variables or their negations appearing in this formula are known as literals. [1]
where is the Kullback–Leibler divergence, and is the outer product distribution which assigns probability () to each (,).. Notice, as per property of the Kullback–Leibler divergence, that (;) is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when and are independent (and hence observing tells you nothing about ).
In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations; a coordinate plane with axes being the values of the two state variables, say (x, y), or (q, p) etc. (any pair of variables).
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In combinatorial mathematics, the hook length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram.It has applications in diverse areas such as representation theory, probability, and algorithm analysis; for example, the problem of longest increasing subsequences.
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