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Nevertheless, finding the effective medium requires one to solve the so-called "cell problem", which corresponds to an elasto-static equation with a finite set of distinct loadings.
This approach requires the numerical approximations for the flow (i.e. primal) problem and the adjoint (i.e. dual) problem which corresponds to a particular simulation objective output of interest.
For the groundwater flow problem (which corresponds to the Darcy flow model), we show how to produce a scheme with one unknown per element, starting from a mixed formulation discretized with the Raviart Thomas triangular elements of lowest order.
It is natural to say that a point (x_{epsilon}in X) satisfying the above inequality is an ((epsilon)) -approximate solution of the feasibility problem which corresponds to the tuple ((C_{1},ldots,C_{n})).
Consider two external data systems L , which act on the thermoelastic-microstretch material, defined by L = { F i , G i , L , S , u ˜ i , φ ˜ i , t ˜ i , m ˜ i , q ˜ , a i 0 , a i 1 , b i 0 , b i 1 , ω 0 , ω 1 , θ 0 , η 0 }, α = 1, 2, and denote by p a solution of the mixed problem which corresponds to L p = { u i , φ i }.
In order to remove redundant SNPs, we employ a simple algorithm (presented in [37]) for the Column Subset Selection Problem, which corresponds to the theoretical formulation of the redundancy removal problem.
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The most important changes concerned conduct problems, which corresponds well with the problem description given by the parents at the outset.
Connor et al. [ 3] suggest that the effects of pharmacotherapy are similar in children with ADHD, both with and without comorbid conduct problems, which corresponds with our findings.
These problems, which correspond to mixed-integer linear programs, are solved to generate approximate solutions with improved objective value.
Delay problems, which correspond to differential equations of the form x'(t) = f t, x t), x(t - r)) along with a functional start condition, are included in the framework of problem (1).
Let ( u i ( α = 1, 2 ) be two solutions of our mixed problem which correspond to the same initial and boundary data but to different body force and different heat supply, ( F i , P ( α = 1, 2 ), where F i = f i 2 − f i 1, P = r 2 − r 1.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com