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8 Jan 2018: Nonlinear NonmodalStability Theory. R. R. Kerswell,School of Mathematics, Bristol University, Bristol, U.K., BS8 1TW; email:. R.R.Kerswell@bris.ac.uk. Xxxx. Xxx. Xxx. Xxx. YYYY. AA:1–30. This article’s doi:. 10.1146/((please add article doi)).

11 Jan 2018: coli) [24], and also Salmonella typhimurium [23], Halobacteriumsalinarium [25], and Bacillus subtilis [26] [see Fig. ... 24). The terms on the left-hand side can be simplified by noting that.

19 Jan 2018: absolutely impossible for a course of 24 lectures to do so). ... showing that the quantity. =. Z. N dd1x (1.24). is conserved under evolution via the classical equations.

22 Jan 2018: and slender-body theory (SBT)24,25 to model the flow induced by the rotating flagellar filamentsof the trapped bacteria. ... Mater. 24, 811–816 (2012).33X. Chen and H. C. Berg, “Torque-speed relationship of the flagellar rotary motor of Escherichia

23 Jan 2018: qq′). (1.24). Upon the substitution p′ = p m(qq′). t this becomes. ... Z0[J] =. d[ϕ] e. i2. ddx (µϕ(x)µϕ(x)m. 2ϕ2(x))iddx J(x)ϕ(x). (2.24). This is an integral with a highly oscillating integrand; if

26 Jan 2018: S k log G = kαN log E const. (1.24). and hence.

12 Feb 2018: Z. CT [y0,y1]Dx eS[x]/. nY. i=1. Oi(x(ti)). (3.24). – 47 –. for the n–point correlation function. The hats on the Ôi remind us that the

27 Feb 2018: Resource-explicit models of bacterial mutualismscompare well with experiments in which mutualists are wellmixed [5,6,23,24].

10 Mar 2018: A different approach was developed by Painlevé, Kowalevskaya, and Gambier who studied 2ndorder ODEs in the complex domain.16,24. ... Proc. Cambridge Philos. Soc. 156, 99–113. (2014).24 Painlevé, P., “Sur les équations différentielles du

3 Apr 2018: with (2.17).Finally, equation (2.24) is satisfied upon eliminating fww in the sameway and using w. ( ... 24. motion of N-vortices. There are several ways to obtain the metric forboth flat and curved backgrounds [46, 16].