Sentence examples for for any given element from inspiring English sources

Definition 2.2 An ordered vector space ( X, ≽ X ) is said to be generalized Archimedean if and only if for any given element x ≽ X 0 and any decreasing sequence of positive numbers { a n } with limit 0, we have a n x ↓ 0. Let X be a vector space and K a closed convex cone in X. Define a binary relation ≽ K on X as follows: x ≽ K y if and only if x − y ∈ K, for every  x, y  in  X.

It's hard to say for sure that any given element of the American psyche results from our Puritan founders.

A relatively pseudo-complemented lattice (or Brouwerian lattice) is a lattice L in which, for any given elements a, b ∈ L, the set of all x ∈ L such that a ∧ x ≤ b contains a greatest element b : a, the relative pseudo-complement of a in b.

In neurophysiological terms, the retinal elements are said to be connected to cortical cells, each being specific for a given element, so that when a given cortical cell is excited the awareness is of a specific local sign.

For a given element, energy was calibrated using a reference foil spectrum.

For a given element and, consider the following auxiliary problem for GMEP(1.2): find such that (2.8).

The so-called quasi-variational inclusion problem is to find a for a given element such that.

On the other hand, the access time of an array is O(1) for a given element.

Another option is to test fossil teeth for the ratio of stable isotopes present for a given element, such as the ratio of carbon C12 to C13.

Assume that is a strictly contractive operator, that is, there exists a Lipschitz constant with such that for all Then for a given element one of the following assertions is true: for all ; there exists a nonnegative integer such that.

Assume that is a strictly contractive operator with the Lipschitz constant Then for a given element one of the following assertions is true: (A1) for all ; (A2) there exists a nonnegative integer such that.