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For arbitrary stencil points and any derivative of order < up to one less than the number of stencil points, the finite difference coefficients can be obtained by solving the linear equations [6] ( s 1 0 ⋯ s N 0 ⋮ ⋱ ⋮ s 1 N − 1 ⋯ s N N − 1 ) ( a 1 ⋮ a N ) = d !
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]
Let = be a partition of = + +.It is customary to interpret graphically as a Young diagram, namely a left-justified array of square cells with rows of lengths , …,.A (standard) Young tableau of shape is a filling of the cells of the Young diagram with all the integers {, …,}, with no repetition, such that each row and each column form increasing sequences.
In an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + h / 2 ) and f ′(x − h / 2 ) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f:
A Littlewood–Richardson tableau. A Littlewood–Richardson tableau is a skew semistandard tableau with the additional property that the sequence obtained by concatenating its reversed rows is a lattice word (or lattice permutation), which means that in every initial part of the sequence any number occurs at least as often as the number +.
In mathematics, a Young tableau (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties.
The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo. The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements [38]
The London Science Museum's difference engine, the first one actually built from Babbage's design. The design has the same precision on all columns, but in calculating polynomials, the precision on the higher-order columns could be lower. A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions.