Sentence examples for modular on a from inspiring English sources

Let ω be modular on a set X. A mapping T : X ω → X ω is said to be contraction [[2], Definition 3.1] if there exists k ∈ [ 0, 1 ) such that ω λ ( T x, T y ) ≤ k ω λ ( x, y ) (1). for all λ > 0 and x, y ∈ X ω. Recently, Mongkolkeha et al. [2] proved the following theorems.

Let ω be (pseudo) modular on a set X. Given a sequence { x n } ⊂ X ω and x ∈ X ω, we have d ω ∘ ( x n, x ) → 0 as n → ∞ if and only if ω λ ( x n, x ) → 0 as n → ∞ for all λ > 0. A similar assertion holds for Cauchy sequences.

Figure  5C suggests that the substrate binding sites are modular on a scale of tens of amino acids.

Last month, London producer Miss Modular took on a new alias, MM, to release an eponymous EP on Her Records, which the artist himself co-founded.

The notions of a metric modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by Chistyakov [10].

In 2008, Chistyakov [27] introduced the notion of modular metric spaces generated by F-modular and develop the theory of this spaces, on the same idea he was defined the notion of a modular on an arbitrary set and develop the theory of metric spaces generated by modular such that called the modular metric spaces in 2010 [28].

The band also began experimenting with the Moog modular synthesizer on a number of tracks, making The Notorious Byrd Brothers one of the very first rock albums to feature the instrument.

Let w be a metric modular on X, X w be a complete modular metric space induced by w and T : X w → X w.

Figure 3 shows the effect of modular design on a complex system.

We show how cryptographic protocols using Diffie–Hellman primitives, i.e., modular exponentiation on a fixed generator, can be encoded in Horn clauses modulo associativity and commutativity.

The main property of a (pseudo) modular w on a set X is a following: given x, y ∈ X, the function 0 < λ ↦ w λ (x, y) ∈ [0, ∞] is a nonincreasing on (0, ∞).