Then a pointwise bound on ν ( t ) ∈ L 2 ( D ), i.e., a constant C such that | ν ( t, x ) | ≤ C for almost all x ∈ D and all t ≥ 0, are then easily obtained by an approximation argument, that is, approximating the less regular solution by solutions of higher regularity.
Therefore, Taylor series of the first order are used to approximate the argument of the Q-function, (g(gamma)=frac {lambda -bgamma }{sqrt {V_{0}+cgamma }}), around γ 0=λ/b as follows (see Appendix 6): begin{array}{*{20}l} g_{1}(gamma)& = g(gamma_{0})+g'(gamma_{0})(gamma - gamma_{0}) &=g'(gamma_{0})(gamma-gamma_{0}) end{array} (49).
It is of course recognized that the conclusions made in the present work are based on approximate scaling arguments and on highly simplified stress fiber network topologies.
To be more rigorous, we use a density argument to approximate in by a sequence of smooth maps.
JH carried out the problem formulation and mean-field backward-forward system analysis, participated in the arguments of approximate Nash equilibrium and fixed-point analysis of certainty principle.
Optimal recovery of the synchronization parameters (timing, phase and frequency offsets) is analytically intractable and, as a consequence, most existing synchronization methods are either heuristic or based on approximate maximum likelihood (ML) arguments.
Employing the geometrically exact theory of rods with appropriate kinematic assumptions and asymptotic arguments, two approximate models are obtained a relaxed model and its constrained version that describe extensional and bending motions and neglect shear deformations.
While the actin network mesh size did alter the absolute values of ∆ T for a given k F / k s, ∆ T does significantly increase with k F / k s supporting the underlying argument for approximating 2D conditions with a 1D track.
As for their critique of atomic theories of magnitude, they came in two general forms: arguments attempting to show that atomism cannot even approximate our best mathematics and arguments attempting to show that the notion of minimal parts that are not even conceptually divisible is inadequate to describe certain basic natural phenomena.
A probabilistic argument provides an approximate bounding of the plastic displacement process of the bilinear EPO.
