Sentence examples for be the inverse operator from inspiring English sources

For given u ∈ K, let M be the inverse operator of the state equation (12) such that y ( u ) = M B u is the solution of the state equation (12).

Given u ∈ K, let S 1, S 2 be the inverse operators of state equation (2.3) such that p ( u ) = S 1 B u and y ( u ) = S 2 B u are the solutions of state equation (2.3).

In particular, the β-backward integral is the inverse operator of (nabla_{beta}).

where Θ − 2 is the inverse operator of Θ 2 = 1 − k △.

We next show that (K_{P}) is the inverse operator of (L_{P}).

Now we prove that ({K_{P}}) is the inverse operator of (L|_{operatorname{dom}L cap operatorname{Ker}P}).

The last step is to prove that ({K_{P}}) is the inverse operator of (L| {_{operatorname{dom}L capoperatorname{Ker} P}} ).

Consequently, by applying the Riemann-Liouville fractional operator and to the above sets of linear equations, which is the inverse operator of Caputo derivative and respectively, the first few terms of the Homotopy perturbation method series for the system (1.1) are obtained as follows: (4.3).

Square matrix: this operator transforms a 2P th-order tensor R ∈ C I 1 × I 2 … × I P × I 1 × I 2 … × I P into a square matrix, SqMat ( R ) ∈ C I 1 … I P × I 1 … I P. S q M a t−1 is the inverse operator.

The above operator is the inverse operator of the proposed beta derivative and is called the Atangana-beta integral.

The source signals inside the brain can be described as projections of the sensor signals as: (2) where ϕ is the inverse operator.