Sentence examples for reflection formula from inspiring English sources

For a flat surface having an AR overlayer, using Fresnel's reflection formula, we measured the reflectance at different wavelengths.

Thus, the dual form of (1) includes the constant which reduces to L ∗ ⋅ Γ Γ ( − β + m ) = π sin s π p ⋅ Γ ( s q ) Γ ( s ) Γ ( m + 1 − s p ), after applying the Euler reflection formula Γ ( x ) Γ ( 1 − x ) = π sin x π.

We complete this section with another Hardy-Hilbert-type inequality, making use of the well-known reflection formula for the Digamma function ψ, ∫ 0 ∞ log t t − 1 t − α d t = ψ ′ ( 1 − α ) + ψ ′ = π 2 sin 2 π α, α ∈ ( 0, 1 ), and of the fact that Z ( a, b ) = ∫ 0 ∞ t b e − a t ( 1 − e − t ) b d t < ∞, a ∈ R +, b ≥ 1.

When F = 1, however, we may use the reflection formula Γ(1 − η s) − Γ(η s) = π cot(πη s) to solve for η s analytically.

Using the simple Fresnel reflection formulae, the optimal material composition was determined.

On the other hand from (4.1) we easily obtain Gamma (s bigl{ F theta,s+1)+F 1-theta,s+1)bigr} =-F 1-theta)^{s+1}}{2s sinfrac{pi s}{2}}bigl{ zeta(-s,s+1 bigrzeta(-s,1-theta)bigr}, (4.2) where we are able to simplify (4.2) by the well-known reflection formulas frac{pi}{sinpi s}=Gamma(s)Gamma(1-s),qquad frac{sinpi s}{pi}= frac{2pipi}sinfrac{pi s}{2}}bigl{rac{pi(1- s)}{2}.

Given the fact that, for each φ∈Form, φ and its subformulas, subsubformulas, etc., are all of length < κ,[6] a moment's reflection reveals that formulas of L "correspond" to sets x hereditarily of cardinality < κ in the sense that x, its members, its members of members, etc., are all of cardinality < κ.

Using these reflections, the Scherrer formula, and a Gaussian distribution for the diffracted radiation intensity, it was possible to estimate the size D Ag of the silver NPs in the different crystalline directions: D 111 = (16.2 ± 0.2) nm, D 200 = (13.0 ± 0.2) nm, and D 220 = (17.4 ± 0.3) nm.

The mean crystalline sizes are 2.75 (for core NCs) and 2.78 nm (for core/shell NCs), respectively, calculated from (111) reflection by the Scherrer formula.

The size of the Fe3O4 nanoparticle was deduced to be 13 nm from the peak width at half maximum (from 311 reflection) and Sherrer's formula.

The grain sizes of the Fe3O4 particles calculated from the breadth of the (311) reflection using Debye-Scherrer's formula [23, 24] decrease dramatically from 14.8 to 7.6 nm when the initial EDTA concentration increases from 0 to 80 mmol L−1.