Sentence examples for For the reflected from inspiring English sources

For the reflected diffusion generated by L="Δ−∇V⋅∇ on a connected and complete Riemannian manifold M with empty or convex boundary, we establish some sharp estimates of supx∈M|∇G|(x) of the Poisson equation −LG= g in terms of the dimension, the diameter and the lower bound of curvature.

For the reflected prefibration (widetilde{F}^flat ), the formulas are essentially the same, but we have to count from the other end of a diagram.

Applying d'Alembert's method combined with the reflection properties, expressions for the reflected waves at the two boundaries are obtained.

Curves show the reflection and transmission coefficients for the reflected and transmitted waves as functions of the frequency.

These expansions relate to the pressure and velocity fluctuations in the jet flow and in the far field, and to the reflection coefficient, end-impedance and end-correction for the reflected wave in the pipe.

The equation for the reflected ray errors is generally fit for all reflection surfaces without refraction, and can also be applied to control the errors in designing an abaxial optical system.

For calculation purposes, the reflected coefficient for the RHCP field component is represented as the difference between the reflected coefficients for the horizontally and vertically polarized fields [19].

The numbers for the final reflected the increases experienced through the tournament.

Part of the explanation for the discrepancy reflects the ages selected for comparison.

The reason for the case reflects the attributes of its civil legal relationship.

The Dwarven calendar invented for The Hobbit reflects the Jewish calendar in beginning in late autumn.