Sentence examples for with distinct elements from inspiring English sources

Let ( X, d ) be a generalized metric space, and let { x n } be a sequence in X with distinct elements ( x n ≠ x m for n ≠ m ).

In the case (3) when the function f is continuous, it immediately follows that f x ∗ = x ∗, since a Cauchy sequence with distinct elements in ( X, d ) cannot have two limits, by Lemma 1.

Let ( X, d ) be a g.m.s. and let { y n } be a sequence in X with distinct elements ( y n ≠ y m for n ≠ m ).Suppose that d ( y n, y n + 1 ) and d ( y n, y n + 2 ) tend to 0 as n → ∞ and that { y n } is not a Cauchy sequence.

In this paper a parametric study is performed with distinct element program UDEC for different joint characteristics and in situ stresses to evaluate the ground behavior in blocky rock masses.

To define the expression pattern of these genes in the various sugarcane tissues cDNA microarrays with 1,280 distinct elements were constructed.

The final study in this review, conducted in Spain [ 18], used integrative psychological therapy (IPT) as their main care approach, which is a structured group intervention with five distinct elements: cognitive differentiation, social perception, verbal communication, social skills training, and interpersonal problem solving.

However in our scheme, different blocks within frames are encrypted with different and distinct elements of the random sequence of permutations.

If S is a set with finitely many distinct elements then # S is the number of distinct elements in S ; if S has infinitely many distinct elements then # S = ∞.

That is, if we introduce the type 2 with the two distinct elements 0 and 1, a proof of \ \bA \vee \bB\) may be identified as a pair \((c, n)\) in which either \(c\) is a proof of \ \bA\) and \(n\) is 0, or \(c\) is a proof of \ \bB\) and \(n\) is 1.

A sense of hopelessness in active service follows that leads one to the question "What act of service can you really throw yourself into that won't just be washed away by the tides of unexpected events?" To answer this question we must first recognize that service carries with it two distinct elements - the form of service that you perform - and the spirit of service that you give.

As with any agglomerative hierarchical clustering algorithm, the exact linkage algorithm begins with n terminal nodes, each of which is labelled with a distinct element of the label set S of the sample.