In view of the boundary condition, we obtain (c_{1}=0) i (int_{0}^{2pi}y tau sintau,dthen0), then begin{aligned} operatorname{Im} overline{F}'_{x}(0,0,0)&=biggl{ yin mathcal{C}[0,2pi]: int _{0}^{2pi}y tau sintau,dtau=0biggr} &=bigl{ yinmathcal{C}[0,2pi]:langle y,sin t rangle=0,sin tin operatorname{Ker} overline{F}'_{x}(0,0,0 bigr}.
and in view of two mixed boundary conditions (4.57) and (4.58), together with (4.59) and (4.60), we have the following two simultaneous dual integral equations for the determination of the function : (4.61).
If u is the double layer potential with density ψ ∈ [W1,p] n, in view of (22) the boundary condition Lu = f turns into the equation R ′ ( d ψ ) = f, (57).
As to our specific case, in view of the homogeneous boundary conditions, (U X,y equiv0) (and hence also (u x,y equiv0)) is the unique function with such properties solving problem (15).
In view of the non-slip boundary condition (v|_{partialOmega}=0), we have (partialOmega=zeta(partialOmega, t)).
Although it is desirable to ascribe a single "effective" grain boundary diffusivity to a polycrystal, this quantity is a complex average over the grain boundary character distribution, in view of the network topology and connectivity among boundaries of different character.
In the following example we demonstrate that, in view of Theorem 3.1, the above boundary problems have univalent solutions in the unit disk with f ∗ ( z ) = ψ ( z 1 − α ).
However, in view of the conserved gene conversion boundaries, restriction of high sequence identity to the region 436 746 allowed (or favored) independent evolution of the N-terminal region and extreme C-terminal region of TLR1 and TLR6.
Kusky et al. (2010) have proposed an extension of plate boundaries from the East African Rift to the eastern side of Madagascar, but in view of the fact that the full boundary of any additional plate is not given, nor is there a relative motion pole, this result has not been added to my list.
In view of the importance of anti-periodic boundary conditions in the mathematical modeling of a variety of physical processes [26 28], the study of anti-periodic boundary value problems has received considerable attention.
