subject to Dirichlet boundary conditions, provided that μ is not an eigenvalue of the p ( x ) -Laplacian.
We are concerned with the following nonlinear problem: − div ( w ( x ) | ∇ u | p ( x ) − 2 ∇ u ) + | u | p ( x ) − 2 u = μ g ( x ) | u | p ( x ) − 2 u + f ( λ, x, u, ∇ u ) in Ω, ∂ u ∂ n = 0 on ∂ Ω, which is subject to a Neumann boundary condition, provided that μ is not an eigenvalue of the p ( x ) -Laplacian.
The multiscale basis is shown to be efficient for finite PhC bands of any size, provided that boundary effects are resolved with a simple macroscopic boundary layer mesh.
Numerical experiments show that in fact nominal accuracy is attained in all cases for two advection diffusion problems, provided that curved boundaries are properly represented.
The treaty also provided that certain boundary disputes between Canada and the United States be referred to arbitration commissions, and both the U.S. and British governments agreed to use their best efforts to abolish the international slave trade.
Comparisons made between the measurements and simulations have shown the relevance of the method adopted, provided that suitable boundary conditions and soil parameters are taken into consideration.
In case of multiple cyclic martensitic transformations (CMT), additional sub-boundaries are formed in these alloys, provided that generation of new dislocations, their accumulation, and interaction occur during cycling.
Their enrichment in enhancer-like chromatin signatures, interactions with nearby trait-relevant protein-coding loci, and preferential location at topologically associated domain (TAD) boundaries provide evidence that TR-lincRNAs likely regulate proximal trait-relevant gene expression in cis by modulating local chromosomal architecture.
That's a collaborative process that transcends space, time, and boundaries, provided the ground is smooth enough to ride.
