Sentence examples for assumptions were established from inspiring English sources

According to the capillary model and boundary layer theory, the following assumptions were established for the fluid flow in low-permeability reservoir: 1.

Some weaker assumptions are established.

The lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems under more weaker assumptions is established.

Then, by mixing the properties of the nonlinear scalarization mapping and the maximal element lemma, an existence theorem for the generalized symmetric vector equilibrium problem (GSVEP), by relaxing or weakening some assumptions, is established.

A kinetic model without the pseudo-steady state assumption was established according to the generally accepted elementary reactions in UV/H2O2 advanced oxidation process.

Several new fixed-point theorems for multivalued generalized -hemicontractive mappings without generalized Lipschitz assumption are established in -uniformly smooth real Banach spaces.

Then quarter vehicle-electric wheel system (QV-EWS) dynamics model based on the rigid ring tire assumption is established and the main parameters of the model are identified according to tire free modal test.

Firstly, a numerical model under the incompressible potential assumption is established for 3D bubble dynamics, and the traditional technique for the vortex ring induced potential at the reference point in axisymmetric model is extended to arbitrary location in 3D model.

Instead of subjective assumptions, prior probabilities were established from evidence that was identified through systematic literature search [ 1, 10].

Furthermore, strong convergence theorems of this method were established under suitable assumptions imposed on the algorithm parameters.

Since then, optimality conditions of Fritz John and Karush-Kuhn-Tucker type for differentiable or nondifferentiable nonconvex multiobjective programming problems were established under different assumptions.