Sentence examples for support points of a from inspiring English sources

We show that points can be removed from the design space during the search for a D-optimum design, using a simple inequality satisfied by support points of a D-optimum design measure.

In 1963, Bishop and Phelps [4] proved a fundamental theorem concerning the density of the set of support points of a closed convex subset of a Banach space by using a maximal element principle in certain partially ordered complete subsets of a normed linear space.

It is shown that for suitable cost functions, by increasing the value of the coefficient one can force the support points of an optimal design measure to concentrate around points of minimum cost.

By Theorem 2.5 each point (x_{0}) in (S(E)) is a support point of (U E)) and therefore gives rise to at least one support hyperplane for (U E)) that supports (U E)) at (x_{0}).

Let H(D) be the topological vector space of all functions F holomorphic in the unit disc D. We consider the compact convex subset B̃1 = {F ∈ H(D) : F 0) = 0 ∧ |F′ z)| (1 − |z|2) ≤ 1 for z ∈ D} of H(D) and show that G ∈ B̃1 is a support point of B̃1 if and only if Λ G) = {z ∈ D : |G′ z) (1 − |z|2) = 1} ≠ ∅.

(2014) propose a more fine-grained, continuous interpolation between the supporting points of the PR curve.

Identify the main idea and the main supporting points of the speech.

Using the explicit representation (7), the strain energy becomes (8) U = ∫ V U d (F AN, t ) dV = ∑ A W A U A d (F A, t ) with strain energy density function U d. W A is an integration weight denoting the fictive volume around integration point A, i.e. (9) W A = ∫ V M A dV Therein, the numerical integration points are chosen to be identical to the support points A of the gradient interpolation.

We show that, for any given design measure ξ, any support point x∗ of a ϕp-optimal design is such that the directional derivative of ϕp at ξ in the direction of the delta measure at x∗ is larger than some bound hp which is easily computed.

We prove that any support point x∗ of a D-optimum design on X must satisfy the inequality d ξ,x∗)⩾m(1+ε/2−√ε(4+ε−4/m)/2).

However, we have included it here because it is a very simple rule that has shown a good performance in practice and can be useful to limit the number of support points by using a fixed value of ε.