That works in dimension three but in higher dimensions the modified determinants grow faster than (2.30)—see [278].
Analytically, the PIP can facilitate a richer understanding of the mediating and modifying determinants of intervention impact than would be possible from an intention-to-treat analysis alone.
The modified perturbation determinant, which we will just call the perturbation determinant, is given by begin{aligned} D zeta ):=det (mathbbm {1}+sqrt{V}R_0 zeta ^2)sqrt{|V|}),quad mathfrak {I}zeta >0, end{aligned}where (sqrt{V}:= {text {sgn}} V sqrt{|V|}).
In our case, we will actually need to look at the modified perturbation determinant (see [7, 8] for details).
end{aligned}In the half-line case and under suitable conditions on the potential, the (modified) perturbation determinant (D zeta )) (Sect. 2) is simply given by (D zeta )=omega (zeta )) and is analytic in (zeta ) for (mathfrak {I}zeta >0) and continuous up to (mathfrak {I}zeta =0) except possibly at (zeta =0).
As a result, we succeed in reducing a certain ratio of modified Fredholm perturbation determinants associated with operators in L2(Ω dnx), n∈N, to modified Fredholm determinants associated with operators in L2(∂Ω dn−1σ), n⩾2.
Moreover after the 2003 heat wave in Europe the introduction of prevention programs may have modified the determinants of the population's susceptibility to high temperature [ 15, 16].
The many possibilities for modifying the determinant hydrophobic fragment between the C12H25/C14H29 and C16H33/C18H37 structural variants require additional information (the mutual interchain mass ratio of 7/3).
At the start of this study, little was known about the specific effect of psychosocial determinants in SCs, although interventions aiming to modify these determinants, such as cognitive behavioural programs were considered to be promising for musculoskeletal pain in general [ 4- 8].
By modifying cytomegaloviral determinants that control unconventional T cell priming it is possible to uniquely tailor the CD8+ T cell response for each individual disease target in order to maximize prophylactic or therapeutic protection.
