Sentence examples for additional assumptions for from inspiring English sources

Based on Theorem 6.4 of Thieme [16], additional assumptions for more realistic, sigmoid-like growth of individuals are specified.

First of all, we need the following additional assumptions for f: (F7) (pF t) - f(t t > 0) for (tneq0).

We remark that if in the above result is, in particular, a pointwise contraction then the fixed point problem is well-posed without additional assumptions for.

We can obtain a formula that gives a concrete value of (C_{p}' (Omega )) with additional assumptions for Ω and p (see Corollary D.1).

This avoids the need for additional assumptions, for example, having to specify the stimulus reduction (task performance efficiency) as a function of the number of active individuals working [8], [47].

The definitions of the functions, vectors, matrices and equations (see Notation in Appendix S1) used for the simulations are given with the following additional assumptions: For t0 = 0 the initial state of the system is the reliability state R. The algorithm is applied until the system enters the maintenance state.

To show the fast time decay under the additional assumption, for this, we need to show the propagation of the solutions in (dot{B}^{-varrho}_{2,infty}).

However, while parsimony is relatively easy to justify in the original tree-building problem (in which homoplasy represents additional assumptions of evolutionary changes) a justification for its use as a supertree construction method is not quite as obvious.

With additional assumptions or for balanced designs, terms for a and b simplify and simple solutions for the sampling variance of h ^ 2 can be derived.

The additional assumption of conditions for radial symmetry allows the derivation of an integral equation that relates the scalar flux to the description of the beam source as function of the angle between the direction of the source particles and the normal to the sphere.

−Are additional assumptions applied for this modification?