Sentence examples for using the solutions to from inspiring English sources

Let us consider the (forward) Cauchy problem (9); we construct a positive lower solution by using the solutions to begin{cases} y'= betafrac{sqrt{y 2-y)}}{1-y}, y(0) = 0, end{cases} (13) in dependence of (betafrac{sqrt{y 2-y

The outage performance of the single cluster limited-feedback problem is obtained using the solutions to the KKT conditions for Problem (4) for 1 bit feedback and the EPPR approximation for 2, 4 or 6 bits of feedback.

The BLUP of g obtained as equation (24), using the solutions to equation (23), are identical to those obtained from equation (26), and are in Table 1.> -wrap-foot>>> -wrap-foot>>> -wrap-foot>> -wrap-foot> Genotypes are available for individuals 1, 2 and 4. Phenotypes are available for all individuals except individual 1, the sire.

This effect has been modelled using the solution to differential equations describing pump-induced electron temperature and density perturbations.

The algorithm solves a number of sub problems for decreasing values of λ, using the solution to the previous sub problem as a prior for the next.

The optical properties (i.e., μ a and μ s′) of the homogeneous phantom were determined using the solution to the diffusion equation for a homogeneous semi-infinite medium [ 27].

They solved the convective transport part analytically and used the solution to approach the diffusion part.

We compute the l 1-multivariate median of as: arg min x ∑ y ∈ U d ( x, y ) (1). and use the solution to eq. 1 for event location.

Use the solution to clean the glass.

Use the solution to flush out your nasal passageways.

Combine soap and hot water in a large bucket and use the solution to scrub down all sides of the boat.