The study of the Mills ratio is much older than the work of Mills [1], and through its relation with the function (F x)=e^{x^{2}}int_{x}^{infty}e^{-t^{2}},dt) given by (R x)=sqrt{2}F(x/sqrt{2})), its introduction can be traced back to Laplace [2], Livre X, Chapter 1, no5, while he was analyzing different hypotheses related to the refraction of the light in the atmosphere.
To the best of our knowledge, this is the first study that explicitly associates smaller volumes of putamen and thalamus with Alzheimer's disease, and reveals their relation with cognitive functioning.
The mean squared displacement in relation with the correlation function of velocities is given by: 〈 [ R → ( t ) − R → ( 0 ) ] 2 〉 = 2 ∫ 0 t d t ′ ( t − t ′ ) 〈 v → ( t ′ ) · v → ( 0 ) 〉 (11).
Two hypotheses may explain our results: 1° a disturbance of the anterograde/retrograde transport, in relation with the MAP function of STOP protein [1] [3]; 2° a disturbance of synaptic vesicles turnover, in relation with the action of the phosphorylated form of STOP protein [26].
GPS cells also express E-cadherin and b-Catenin in a polarized manner (coronal vs. axial) surrounded by Vimentin+ cells, suggesting a putative relation with the known function of the Wnt/b-Catenin pathway together with E-cadherin to retain the stem cells within the niche confines [60].
Beside the involvement of PBPs and OBPs in chemical communication, it is possible that in Hymenoptera, some OBP-like proteins fulfil other roles in relation with the venomous functions.
Furthermore, to focus on other functions that may establish relations with the peroxisomal functions, FN were selected with NTS ≥ 60 and a core protein content of no more than one third.
We proceed to define in more detail the scattering relation and its relation with the boundary distance function.
We remark here that from the proof of Lemma 2.2 and Lemma 2.3 in [4], the existence and uniqueness of α and β for the initial value problem (2.1) and (2.2) have no relation with the sign of the functions a and b.
Then, the stresses and displacements are determined with the aid of the relations with the potential functions and the theorem of inverse of Hankel integral transforms.
