We clearly see that our results in Corollary 2.6(a), (b), and (d) are exactly corresponding to the results in Theorems B, C, and D, respectively.
The limit of the perturbed Riemann solution of (1.3) and (3.1) or (3.7) is exactly the corresponding Riemann solution of (1.3) and (1.4).
However, it is not obvious under which conditions there is exactly one CPN corresponding to a system of ODEs (even if we assume minimal arc weights), and especially whether certain biologically reasonable conditions on the CPN enforce its uniqueness.
We start by assuming \(W=S\), so there is exactly one possible world corresponding to each state of nature.
Theoretical and experimental analyses show that the frequency of TSVS is exactly twice that of the corresponding intrinsic structure.
When there is a signal in the presence of ( {overline{theta}}_i ), the element h i is not zero, and its size is exactly the size of the corresponding peak after the FRFT transformation.
For the details, we refer the reader to the Appendix A. With this technical approximation in place, all eigenvalues λ i (i = 1,..., N) are real, and the largest eigenvalue of W is exactly one (λ1 = 1), with corresponding eigenvector v 1 = ( 1 / N ) [ 1, 1, …, 1 ] T = ( 1 / N ) 1 N as shown in Figure 6.
From Proposition 6.2, the public key of the extended HS scheme is exactly equal to that of the corresponding Rainbow.
However, the results presented by VD were limited to the case when the Hall angle (theta_{H}equivtan^{-1}sigma_{xy}/sigma_{xx}) is exactly at its maximal value (pi/2), corresponding to parameter values (magnetic field, carrier density) for which the material conductance is on a quantum Hall plateau and the Landau level filling parameter ν is an integer.
Besides, according to Proposition 1, this distribution for model (3.1) is exactly the same as for the corresponding linear model with λ i = λ (i + a), δ i = λ (i + b), which was studied in detail in [12].
