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t2r} (j1i=1 Mi)such that w2µj = max{w. 2ti : ti Tj}, and let Mj be a minimally even subset of. ... Tj containing µj. Let s be the largest j for which µj is defined above.

T11 T12 ηj,. η123j =Tj [T13 (T. 11 T. 12 η3)T3][T. ... N}, (4.7). in terms of whichη1.ij =. Tj Ai 1T1j Ai 1.

Tj.  ,where ei is the i-th canonical basis unit vector. ... Gij. eTi TUej beie. Tj.  β(U η).The minimizer of J with respect to U satisfies J(U) = 0.

as. Qm(β) : C0(Γ) R, Qm(β) =. 1iN. Qm(βi), Qm(β)[v] =#m(β)j=1. v(tj)ωj,. ... where tj are points in the Cartesian grid. 1iN{zβi,j}m(βi)j=1 , ωj are the corresponding products of weights.

h+ C1. ). exp. (. C. (. tj. tjτ. τ. ‖vτh‖2H1 ds. (. ... tj τ). ϕ0. H1. )2q̄)). for all 1 j N.

ts). > a treatment in T, then Vi(u) = ui and Aj(t) = tj.

Keeping 39modes (corresponding to the 99% threshold) ensures the two Modes of half period Tj/2 = π/Imλj 6.5years and 3.2 years, whilst their growth rates, Reλj, and so ... This is consistentwith their periods: Tj/2 for Mode 2 is approximately half of

Then. for some partition of the index set {1,. ,N} = J tJ c, we have x = (xJ , xJc )with dist(ΠxJ , ΠxJc ) (x) := R/(N 1), and, respectively,. ... N} = J tJ c, denote. J (u) = dist(uJ , uJc ). Then for all x, w ZN the following inequality holds (cf.

Johnstone St John’s CollegeProfessor Sir John Kingman FRS Director, Newton InstituteProfessor PV Landshoff (Chair) General Board Professor WBR Lickorish Head of Department, DPMMS, CambridgeProfessor TJ Pedley Head of Department, DAMTP,

Machado et al. BMC Biology (2015) 13:98 DOI 10.1186/s12915-015-0200-y. RESEARCH ARTICLE Open Access. Emergent material properties of developingepithelial tissuesPedro F. Machado1, Julia Duque2, Jocelyn Étienne3,4, Alfonso Martinez-Arias1, Guy B.