Sentence examples for as a modulus of from inspiring English sources

A mapping (eta :(0, infty ) times (0, 2] rightarrow (0,1],) which providing such a (delta = eta (r, varepsilon )) for given (r>0) and (varepsilon in (0, 2],) is called as a modulus of uniform convexity.

A mapping η : ( 0, ∞ ) × ( 0, 2 ] → ( 0, 1 ] such that η ( r, ε ) = δ for a given r > 0 and ε ∈ ( 0, 2 ] (as in the definition of UC) is known as a modulus of uniform convexity.

A map (eta:(0,infty)times(0,2]rightarrowhich]), which provides such (delta=eta r,epsilon)) for given (r>0) and (epsilonin (0,2]), is known as a modulus of uniform convexity of X. η is said to be monotone if it decreases with r (for fixed ϵ), i.e., for any given (epsilon>0) and for any (r_{2}geq r_{1}>0), we have (eta(r_{2},epsilon)leqeta(r_{1},epsilon)).

An Example of Magnitude Estimation of Acceptability Presentation in the laboratory The experiment began with a practice phase during which participants estimated the lengths of seven lines using another line as a standard set to a modulus of 100.

They possess suitable mechanical properties for soft tissue replacement, such as a shear modulus of 1 20 kPa, as determined by rheology.

The simplest and most commonly used time-frequency distribution is the spectrogram [3], defined as a square modulus of the short-time Fourier transform (STFT): (1).

It is commonly used as a screening modulus of the fetus to detect in advance possible fetal problems that could result in irreversible neurological damage or even fetal death during labor.

Individual perfect multi-wall carbon nanotubes (MWCNT) can exhibit exceptional properties, such as an elastic modulus of ∼1 TPa.

Since ω p [ g, A ] ( t ) is a decreasing function and lim t → 0 ω p [ g, A ] ( t ) = 0, we can refer to ω p [ g, A ] as the modulus of continuity of g in L p ( A ). Let Ω be an open subset of R n, n ≥ 2. We denote by A the class of measurable weight functions ρ : Ω → R + such that γ − 1 ρ ( y ) ≤ ρ ( x ) ≤ γ ρ ( y ), ∀ y ∈ Ω, ∀ x ∈ Ω ∩ B ( y, ρ ( y ) ), (2.1).

(iii), where is, as usual, a monotone modulus of convexity of the space.

At the micro-scale, sampling a volume of material (2 × 2 × 10 μm) excludes micro- and macro-size pores, the strength was measured to be as high as 1000 MPa (an elastic modulus of about 67 GPa).