Sentence examples for explicit forms for from inspiring English sources

They both obtained some explicit forms for the eigensolutions of these problems and derived some useful spectral properties of the obtained eigensolutions.

They were the first authors who not only obtained some explicit forms for the eigensolutions of these problems but also derived some useful spectral properties of the obtained eigensolutions.

Moreover, we give an explicit form for it.

We first obtain a more explicit form for g δ CR.

The optimum shapes are given in explicit form for punches with rectangular bases.

Explicit form for the complex variable boundary integral equation (CVBIE) is derived.

We want to give an explicit form for the components of the heat flux vector (q_{i}).

We first give an explicit form for the proximity operator (text {prox}_{frac {1}{beta }iota _{mathcal {C}}}).

The closed form solution is established in an explicit form for this generalized Sylvester quaternion j-conjugate matrix equation.

Note that there is no explicit form for the quantile function Φ- 1. Larralde (2012) gave the maximum-entropy bivariate distribution with normal marginals.

H-tensors of cubical, octahedral and tetrahedral pores for several values of matrix Poisson's ratio are published in explicit form for the first time.