Sentence examples for a arbitrarily from inspiring English sources

M. Ravi, a human-rights lawyer representing the challengers, had argued that Section 377(a) arbitrarily distinguished between gay men and women, leaving the former open to incarceration and the latter untouched, but his argument also held no weight for the court.

Indeed, take x ∗ ∈ Fix ( S ) ∩ Ξ ∩ VI ( C, A ) arbitrarily.

From t → 0, we may assume, without loss of generality, that, where is a arbitrarily small positive number.

Let {λ n } be a sequence in [0, ∞) and {α n } be a sequence in [0,1], ε be a arbitrarily small positive number.

Then the sequences { x n } and { y n } converge weakly to an element of Fix ( S ) ∩ Ξ ∩ VI ( C, A ). Proof First of all, take x ∗ ∈ Fix ( S ) ∩ Ξ ∩ VI ( C, A ) arbitrarily.

We define the force,, applied to every photon i at each iteration as: (8) where x is the position of i in world space, ε is a arbitrarily small constant and K f is the set of nearest neighbours to i which we set to a value to 16. is summarily projected into basis b to enforce migration constraint: (9) where û and are the normalised basis vectors.

Then, for an arbitrarily fixed, a function has a unique minimizer.

A broken line shows a gap at an arbitrarily D 2.76/D 2.90 value of 0.8.

This paper is concerned with a method for solving problems of a composite membrane with an arbitrarily shaped outer boundary and an arbitrarily shaped inner boundary.

Current techniques for calculating PAC provide a numerical index that represents an average value across an arbitrarily long time period.

a HPT number is an arbitrarily assigned unique ID.