Sentence examples for satisfies exactly from inspiring English sources

M1 satisfies exactly the formulas satisfied by M without violating condition (iii), hence it is a characteristic normal matrix for S2 (M1 is the Lindenbaum algebra for S2).

The theory employs Fourier series representation for the displacement fields in the fiber and matrix phases in the cylindrical coordinate system that satisfies exactly the equilibrium equations and continuity conditions in the unit cell's interior.

In order to eliminate N i from Eq. (45), the stress function ϕ = ϕ r, θ, t) is introduced; this satisfies exactly Eqs.

Such an expansion satisfies exactly the mechanical equilibrium equations, Gauss law, the constitutive equations, two of the three displacement strain relations as well as one of the two electric field-electric potential relations.

In this work we propose a new unconditionally energy stable numerical scheme for a vesicle membrane model that satisfies exactly the conservation of volume constraint and penalizes the surface area constraint.

The function is also a wave-type solution that satisfies exactly the given governing differential equation and physically describes the displacement reponse of a point in an infinite membrane due to a unit displacement excited at another point.

According to this method, kinematic analysis is carried out in the sense that only constraint equations are satisfied exactly, while requirements are satisfied at best.

This approach allows to satisfy exactly the Piola compatibility condition.

When these requirements cannot be satisfied exactly, optimal (approximate) solutions are sought.

The states x1 and y1 satisfy exactly the same PDL formulas.

"So according to the retraction, the authors have satisfied exactly what NSF asked them to do".