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Then (5.1) can be rewritten into the abstract form (4.1) with (alpha=beta=1).

Hence the impulsive boundary value problem (5.1) can be rewritten into the abstract form (3.5).

end{aligned} Then the fractional parabolic equation (4.1) can be rewritten into the abstract fractional nonlocal evolution equation (1.1).

The control system (1.4) can be rewritten into the abstract form (1.1) with A and B given by (1.5).

Using this, system (1) can be rewritten into the vector form d x (t) = f (x), dt + h (x), d w (t), quad tgeq0.

The query has to be rewritten into the query Q AI ( x 1, x 2, x 3, y, y ′ ) = Fracture ( x 1, y ) ∧ Respiratory ( x 1, y ∧ ) ∧ Info ( x 1, x 2, x 3 ).

Your current quadratic equation will need to be rewritten into this form, and in order to do that, you'll need to complete the square.

Thus, the problem (2) is rewritten into the form of abstract evolution equation (3).

With these notations, system (3) is rewritten into the form L x = N x, x ∈ Dom L ∩ X.

Then the necessity optimal condition (5.1) is rewritten into the form begin{aligned} int_{0}^{T}bigl( u v_{0} -z_{d},z bigr)_{2},d t+(Nv_{0} -z_{d},z_{U} geq0,quad text{for all }vin U_{mathrm{ad}}.

For this method the system of DSEs is rewritten into the following form: (6) E (i, k ) = − A i (x k ) + A bare i (x k ) + ∑ l Z i, l ∫ R d l d d l y F l (y, x k, { A }, { A model } ), where i labels the dressing functions of all DSEs and x k denotes the external momenta.