The phrase "assumptions are established" is correct and usable in written English.
It can be used in contexts where you are discussing the formation or acceptance of certain beliefs or premises in a discussion, analysis, or argument.
Example: "Before we proceed with the experiment, it is crucial that all assumptions are established to ensure accurate results."
Alternatives: "assumptions are set" or "assumptions are defined".
The lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems under more weaker assumptions is established.
According to the capillary model and boundary layer theory, the following assumptions were established for the fluid flow in low-permeability reservoir: 1.
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.
Several new fixed-point theorems for multivalued generalized -hemicontractive mappings without generalized Lipschitz assumption are established in -uniformly smooth real Banach spaces.
A kinetic model without the pseudo-steady state assumption was established according to the generally accepted elementary reactions in UV/H2O2 advanced oxidation process.
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.
Under appropriate assumptions, sufficient conditions are established for the existence and exponential convergence of positive almost periodic solutions of this model.
Under the assumptions A.1-A.3, sufficonditionsitions are established for the existence and exponential convergence of positive almost periodic solutions of (1.3).
Generalizing the Heisenberg uncertainty principle, lower bounds for the variance of the measure ¦ƒ(x)¦2dx are established under assumptions on the Fourier transform \̂tf.
