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1. Challenges for modelling interventions for future pandemics 1 2 Mirjam E. Kretzschmar1, Ben Ashby2, Elizabeth Fearon3,4, Christopher E. Overton5,6,7, Jasmina 3 Panovska-Griffiths8,9, Lorenzo Pellis5,6,10, Matthew Quaife11, Ganna Rozhnova1,12,

Professor KA Brown University of Glasgow. Professor EB Davies, FRS Kings College London.

National Advisory Board and UK Mathematics. Professor Sir Michael Berry FRS University of BristolProfessor J Brindley University of LeedsProfessor KA Brown FRSE University of GlasgowProfessor P Grindrod Lawson Software, OxfordProfessor J

The vector ω is an interior point (since a‖ω‖ωTω = a1 < 0), and thus Ka issolid. ... Consider x Ka and y Kb, which we take to have unit norm without lossof generality.

B(x)dx. 1. For any a (0,Bm/BM) there exists Ka > 0 such that. ... x 0 G(x) Ka min{1,x}ea Λ(x). (62). 2. For any δ > 0 there exists Kδ > 0 such that.

compact quantum graph Γ (acting in Λ0(Γ) and Λ1(Γ) respectively), KK and KA be the. ... 33). Then. index d = Tr KK Tr KA = V E, (34)the Euler characteristic of Γ.

Soliton-mean field interaction in Korteweg-de Vriesdispersive hydrodynamics. Mark J. Ablowitz1, Justin T. Cole2, Gennady A. El3, Mark A. Hoefer1, andXu-dan Luo4. 1Department of Applied Mathematics, University of Colorado, Boulder2Department of

19] JC Crocker, MT Valentine, ER Weeks, T Gisler, PD Ka-plan, AG Yodh, and DA Weitz Phys Rev Lett 85, 888(2000).

5.1) jyA(m,k) = kA(m1,k1) (0 k m),. (5.2) divA(m,k) = (2m 2k 1)(n 2m 2k 3)A(m,k1) (0 k m).12. ... By (3.63.6), the right-hand side of this formula is equal to kA(m1,k1).

Since K H+ {0},we have θHa θ. Ka and p. Ha p. ... Ka , and therefore pg p. Ha by Theorem 5. We pose two questions.