Sentence examples for be an increasing chain from inspiring English sources

Clearly, Q is nonempty since x 0 ⪯ T x 0. Let { x α } α ∈ Γ ⊂ Q be an increasing chain, where Γ is a directed set.

(mathbb{R}subsetmathbb{C}subsetmathbb{H}subset Cell_{n}^{3}subset cdots) is an increasing chain.

Thus, Clifford algebra C ℓ n = ⨁ k C ℓ n k is a graded algebra, especially C ℓ n 0 = R and C ℓ n 1 = R n. R ⊂ C ⊂ H ⊂ C ℓ n 3 ⊂ ⋯ is an increasing chain, where ℍ is the Hamilton's algebra of quaternions.

Assume that { ( E α, F α ) } α is a increasing chain in Σ. Set E : = ⋂ E α and F : = ⋂ F α. Since X has the property (C), we conclude that ( E, F ) is a nonempty pair.

Moreover, if we transform a centered subordinator ( X ( t ), t ≥ 0 ) into a wear process X ∗ ( t ) : = X ( a 2 ( t ) ), in which a 2 ( t ) is an increasing and differentiable function, the chain rule allows us to write d d t E F Y ( X ∗ ( t ) ) = a 2 ′ ( t ) E f Y ( X ( a 2 ( t ) ) + U T ), t > 0. (18).

A clear reduction of conductivity was found with increasing chain length and decreasing grafting density, while lower conductivity was observed for Van der Waals interdigitated chains compared to covalently bound ones.

The hydrophobic character of perfluoroalkyl acids is stronger with increasing chain length [43].

The brittle-to-ductile transition temperature was lowered with increasing chain length.

This was attributed to increasing chain entanglements with the proportion of branching comonomer of the BPETs.

Plots are arranged by increasing chain length (bottom to top) and increasing degrees of unsaturation.

T2 distributions are arranged by increasing chain length and degree of unsaturation.