Sentence examples for realizing the minimum from inspiring English sources

end{aligned} (6.29)Note that a function f realizing the minimum on the right hand side is called an eigenfunction for the Laplacian and satisfies the equation begin{aligned} -Delta f=lambda f quad text { in } quad Omega, quad f=0 quad text { on } quad partial Omega.

Let us show that all vectors ( x 1, …, x n − 1 ) ∈ Δ, realizing the minimum of F λ, have x 5 = ⋯ = x n − 2 = 0. Actually, suppose that there is an index 5 ≤ i ≤ n − 2 such that x i = 1 and x k = 0 for all 5 ≤ k ≤ n − 2, k ≠ i.

4. The final insight came when I realized the minimum road configuration was achieved when each of the four wheel paths had to touch an edge of minimal road just once. 5.

In this paper, an intersecting chord method is first proposed to realize the minimum zone model of roundness deviation with coordinate data.

Hence a steepest descent optimization technique is employed to realize the minimum energy path and the transition states of the transformations over the energy landscape.

It is possible to assimilate the de-noised signal to the estimator of the unknown regression function, therefore, the minimax estimator realizes the minimum of the maximum mean square error for the worst function in a certain set.

In addition, we showed that Gaussian distributions realize the minimum uncertainty condition using the Cramèr-Rao inequality, and the minimum uncertainty condition can give a smaller error than that implied by the usual Kennard-Robertson lower limit.

The above mentioned mapping is assumed to be defined from one set A to the other set B. Then under suitable conditions, by applying fixed point methodologies, we obtained a best proximity point of the above mentioned mapping which realizes the minimum distance.

To realize the minimum system energy at equilibrium, the state transition is performed stochastically with biological noise such as cytoskeletal fluctuations in the following: (8 where β represents the magnitude of the biological noise.

If you're living in a large American city, you might be forgiven for not realizing the federal minimum wage in America remains just $7.25 an hour, the level set back in the throes of recession in 2009.

A novel approach to realize the smart, minimum energy, green building is taken in this work.