Sentence examples for a sequence of arbitrarily from inspiring English sources

This is a sequence of arbitrarily repeated trials which produces a random sequence; yet none of these outcomes happens by chance.[18] To put the point slightly differently: while the sequence of outcomes is random, there is a perfectly adequate theory of the system in question in which probability plays no role.

For a sequence of arbitrarily dependent random variables (X n )n∈Nand Borel sets (B n )n∈N, on real line the strong limit theorems, represented by inequalities, i.e. the strong deviation theorems of the delayed average S n. k n ω are investigated by using the notion of asymptotic delayed log-likelihood ratio.

Motivated by the reasons above, the aim of this paper is to show the existence of infinitely many soliton solutions of problem (1.1), and there exists a sequence of infinitely many arbitrarily small soliton solutions converging to zero by using a new version of the symmetric mountain-pass lemma due to Kajikiya [24].

Motivated by reasons above, the aim of this paper is to show that the existence of infinitely many solutions of problem (1.1), and there exists a sequence of infinitely many arbitrarily small solutions converging to zero by using a new version of the symmetric mountain-pass lemma due to Kajikiya [22].

Motivated by the fact above, the aim of this paper is to show the existence of infinitely many solutions for problem (1.1), and that there exists a sequence of infinitely many arbitrarily small solutions, converging to zero, by using a new version of the symmetric mountain-pass lemma due to Kajikiya [1].

Any s-recursively contractible complex can be reduced, by a sequence of retractions, to an arbitrarily chosen subcomplex generated by some simplex.

Collapsable complexes cannot be reduced by a sequence of elementary collapses to an arbitrarily chosen subcomplex.

The results in [9] showed that most of the monotone equilibrium problems (in the sense of Baire category) have a unique equilibrium point and that each monotone equilibrium problem can be arbitrarily approached by a sequence of such equilibrium problems that each of them has a unique equilibrium point.

One straightforward choice is the nested intervals theorem, which guarantees that given a sequence of nested, closed intervals whose lengths become arbitrarily small, the intervals contain exactly one real number in their intersection.

Choose arbitrarily a point (uin H) and a sequence of positive numbers ({gamma_{n}}) with (gamma_{n}to0) as (ntoinfty).

In a previous paper, we studied the homogenization of a sequence of parabolic linear Dirichlet problems, when the coefficients and the domains vary arbitrarily.