Sentence examples for for φ of from inspiring English sources

for φ of 'any' type.

(c) For Φ of 40°, fitting the 2D peak of graphene by a triple-Lorentzian function whose three peaks correspond to the sub-modes of 2D+, 2D−, and 2D0.

Fitting of the 2D peaks is done using a double-Lorentzian function for Φ of (a) 0° and (b) 90°. Figure 2 Polarized Raman spectra of 2D modes under incident lights with different polarization angle.

However, there will be no guarantee of the existence of a unique extension-set for φ, as, of course, there is under the CP, namely a = {x : φ(x)}.

Theorems 3.1 and 3.2 give sufficient conditions for the existence of Φ of Theorem 4.1.

For Φ, each of its atoms (columns) is a unit vector in the l2 norm.

We note here that the conclusion is valid for Φ is of C 2. A natural problem arises here whether or not that is valid for a C 1 functional.

This leads to the confusing hypothesis of a long-range action for φ (about 100 cells of amplitude) which is not in accordance with the reported diffusion lengths of signaling molecules.

Overall, ¯¯¯¯¯Nu is higher for case 2 at φ ⩽ 45° whereas case 1 shows larger ¯¯¯¯¯Nu for φ ⩾ 45° irrespective of Pr at Da = 10−3.

That is, for any formula φ of L, φ is valid if and only φ is a theorem of SQML.

The formulation of the axiom of separation was made explicit: "for each formula φ of the first-order language with equality and membership, {x ∈ A | φ} exists".