We say that we are in the regular case whenever the strong Legendre condition holds along the extremal.
Our barrier constructions in [13] also permit some relaxation of the conditions on F in the regular case, as already indicated in Remark 3.2.
In the regular case, the tangent cone to the solution set coincides with the kernel of the first derivative of the map F. Recall the following theorem.
In the regular case of a latent Ari 1, 1) process cloaked in white noise, our results show that the finite sample size of the different tests is reliable.
For suitable s and (beta ) in the right norm (e^{-itH}) is (text {O}(t^{-3/2})) in the regular case, while in the resonance case, one can have (text {O}(t^{-1/2})) behavior.
By modifying the polynomial matrix equation for the filter in the regular case, a new simple polynomial matrix equation for a reduced order H∞ filter in the case of partially perfect measurements is obtained.
In the Regular Case, when neighborhood overlap and co-authorship frequency are in accordance indicating that a tie is strong, tieness also provides a high value that may represent a strong tie.
In the regular case, the leading term is (text {O}(t^{-2})), but when (beta ) and s are sufficiently large, the next term is (text {O}(t^{-3}log (t))) [unlike (nu =3) where the term after (text {O}(t^{-3/2})) is (text {O}(t^{-5/2}))].
But mathematically, the situation is unsatisfactory one would like the coefficients to uniquely determine (E(beta )) (as they do in the regular case) or even better, one would like to have an algorithm to compute (E(beta )) from ({a_n}_{n=0}^infty ).
Two additional clusters of vertices with high weights were formed at the lattice ridge, at a location where high weight vertices were also present in the regular case.
