The nature of this wave packet depends on the flow rate and on the two cases that are identified for the kinetic parameter μ, namely a generic case for general values of μ and when μ is close to the value which gives a Hopf bifurcation in the kinetic system.
As discussed in Section 3.1, that problem is not convex for general values of the weights.
For general values of these fields, the system is then approximated as a light-cone quantized string with a field dependent effective string tension Teff.
Note that in the following analysis we assume for simplicity but the similar results will hold for general values of and.
We find that for general values of the parameters α, β and γ, the solution only exists for a particular value of the permeability A 0. This is also a feature of the approximate solutions which are given in the appendices.
To provide bounds on the DMT d 2(r) for general values of n r, let U be an (n r ×n r ) unitary matrix such that ( U, underline {h}_{1} =; [! begin {array}{cccc} ||{underline {h}_{1}}||&0&cdots &0 end {array} ]^{top } := underline {h}. ).
Wheeler and Hughey (2000) also discuss (L, L−1, … -level algorithms and an optimal checkpointing algorithm, but do not provide a quick computation for choosing optimal checkpoints, nor do they give formulae to compute the number of stage computations for general values of M and N. The choice of the stages to checkpoint can be framed as an optimization problem.
At the separator equilibrium, the expression for the S-allele density is more complicated for general values of the fitnesses of RS and SS individuals in the crop, but it is readily verified that when, and, the value is close to the value at the control equilibrium (as exemplified in Fig. 5) and is, at least in these circumstances, a balance between S-allele immigration and reproduction/poisoning.
The authors developed novel in-nucleus single molecule imaging approaches and corresponding analyzing tool sets that are of general value for live cell single molecule studies.
Since (t_1) and (t_0) are assumed to be of diagonal form, the statement holds true for a general value of n if it does so for the special case of (n = 1).
