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Since it is undecidable, by Chagrova's theorem, whether an arbitrary modal formula has a first-order correspondent, there are formulas with first-order frame conditions that are not Sahlqvist [Chagrova 1991] (see the examples below). Hence Sahlqvist formulas define only a (decidable) subset of modal formulas with first-order correspondents.
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]
The frame problem is that specifying only which conditions are changed by the actions does not entail that all other conditions are not changed. This problem can be solved by adding the so-called “frame axioms”, which explicitly specify that all conditions not affected by actions are not changed while executing that action.
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
MATLAB: A free MATLAB toolbox with implementation of kernel regression, kernel density estimation, kernel estimation of hazard function and many others is available on these pages (this toolbox is a part of the book [6]).
In mathematics, the convergence condition by Courant–Friedrichs–Lewy (CFL) is a necessary condition for convergence while solving certain partial differential equations (usually hyperbolic PDEs) numerically. It arises in the numerical analysis of explicit time integration schemes, when these are used for the numerical solution.
MATLAB xUnit Test Framework: Yes [383] MATLAB R2008a and later (uses OOP features introduced in this release). Renamed from mtest. Accepts both xUnit-style subclass or simple MATLAB function test cases. Doctest: No: Bitbucket repository - source and documentation [384] Allows automated test cases to be put in the documentation, so use examples ...
Periodic boundary conditions in 2D Unit cell with water molecules, used to simulate flowing water. Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a unit cell. PBCs are often used in computer simulations and mathematical models.