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Since a linear program is solved at extreme points, the results of Edmonds (stated in the language of polymatroids) and Shapley (stated in the language of convex games) imply that any linear function defined on the core of a convex game (or the dominant face of a polymatroid) must be extremized at a marginal vector.
Alternatively, for a two-dimensional spatial region, we use a piecewise-linear function defined on the Delaunay tessellated region.
The experimental data displayed an almost perfect fit to the linear function defined by Lewis' law.
Then the linear function defined by is a linear -ANOT, where (2).
A very important result in functional analysis about the extension of a linear functional dominated by a sublinear function defined on a real vector space was first presented by Hahn [1] and Banach [2], which is known as the Hahn-Banach extension theorem.
A time variant linear function defines the offset range for each zero offset sample in the stacking operator.
Their results cover the earlier works related to A-continuity where a method of sequential convergence, or briefly a method, is a linear function G defined on a linear subspace of s, denoted by c G, into R.
A dual system in linear analysis consists of a linear space and a collection of linear functionals defined on the linear space.
and let be a function defined on a neighborhood of.
If fn is a function defined on the positive integers, then a relation that expresses fn + k as a linear combination of function values of integer index less than n + k, in which a fixed constant in the linear combination is written ai, is called a recurrence relation The relation together with the initial values f0, f1,…, fk − 1 determines fn for all n.
Let be a real-valued function defined on an interval.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com