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The frame condition was first described by Richard Duffin and Albert Charles Schaeffer in a 1952 article on nonharmonic Fourier series as a way of computing the coefficients in a linear combination of the vectors of a linearly dependent spanning set (in their terminology, a "Hilbert space frame"). [4]
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The 5% Value at Risk of a hypothetical profit-and-loss probability density function. Value at risk (VaR) is a measure of the risk of loss of investment/capital.It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day.
A ratio's values may be distorted as account balances change from the beginning to the end of an accounting period. Use average values for such accounts whenever possible. Financial ratios are no more objective than the accounting methods employed. Changes in accounting policies or choices can yield drastically different ratio values. [6]
We know a nice sufficient condition: Henrik Sahlqvist identified a broad class of formulas (now called Sahlqvist formulas) such that a Sahlqvist formula is canonical, the class of frames corresponding to a Sahlqvist formula is first-order definable, there is an algorithm that computes the corresponding frame condition to a given Sahlqvist formula.
The following table lists several common normal modal systems. The notation refers to the table at Kripke semantics § Common modal axiom schemata.Frame conditions for some of the systems were simplified: the logics are sound and complete with respect to the frame classes given in the table, but they may correspond to a larger class of frames.
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The different systems of modal logic are defined using frame conditions. A frame is called: reflexive if w R w, for every w in G; symmetric if w R u implies u R w, for all w and u in G; transitive if w R u and u R q together imply w R q, for all w, u, q in G. serial if, for every w in G there is some u in G such that w R u.