Sentence examples for by using the convolution from inspiring English sources

Typically, TTDs are estimated by using the convolution integral to model a weekly tracer signal measured in streamflow.

To analyze the experimental results and gain physical insights into the hydraulic bushing system, lumped system models of bushings with different design features are developed, and analytical expressions of transmitted force and internal pressure responses are derived by using the convolution method.

In Section 3, we obtain the algebraic curves by using the convolution sums in Section 2.

We rewrite the operator G μ sh in a convenient form by using the convolution in the hyperbolic disk.

The smoothed pseudo splines were introduced in [12] in order to smoothen the pseudo splines by using the convolution method.

In fact, in their paper[5], the same authors proposed a systematic way to generate PDEs with variable coefficients by using the convolution product.

Now, let us extend the above results from a single convolution to a double convolution as follows:If we multiply Equation 4 by a polynomial by using the double convolution as p(x y)∗∗ where p ( x, y ) = ∑ i = 1 m p ij x i y j Open image in new window, then Equation 4 becomes A ( x, y ) u xx + B ( x, y ) u xy + C ( x, y ) u yy + F ( x, y, u, u x, u y ) = 0 Open image in new window (22).

The calculated result on damaged exploratory petrological entities using the deconvolution simulation can be quite challenging compared to the convolution simulation, but on the other hand, the boundary identification can also be quite misleading by using the regular (convolution) simulation, which should appropriately be performed through the deconvolution method.

A variational theorem is then derived by using the Stieltjes convolution notation which enables the equations governing the geometrically-non-linear dynamic response of linkages fabricated in linear viscoelastic composite materials to be systematically established.

Now, by using the Kronecker convolution product, see [7], the fractional integral becomes ( I α f ) ( x ) = 1 Γ x α − 1 ∗ f ( x ) ≃ ξ T 1 Γ { x α − 1 ∗ ϕ m ( x ) }. (2.2).

by using the single convolution definition and integration by parts; thus we obtain the first coefficient of Equation 5 in the form of A 1 ( x, y = ∑ β = 1 n ∑ i = 1 m ∑ α = 1 m p i a α β i ! x α + i + 1 y β ( α + 1 ) ( ( α + 2 ) … ( α + i + 1 ).