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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.

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.

ds. ). We next obtain bounds on Hj(t), under the assumption that t 6 Tj, where. ... 25|u0t (z0)|and. |δjt | 64|u0t (z0)eiξ. 0T t 1|. 25. for all t 6 Tj.