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16 May 2012: Let Ti,(i = 1,2,3) denote a basis of su(2) with commutation relations [Ti,Tj] = ϵijkTk and TiT i := TiTjδij = 3412.

14 Aug 2013: where the matrices ti generate the Lie algebra su(2) with the commutation relations [ti, tj] =(1/2)εijktk, and the one-forms Pj are given by (2.3). ... where the Pauli matrices τj are related to the generators of su(2) by tj = (i/2)τj.

26 Feb 2014: 20131160, published 26 February 201411 2014 J. R. Soc. Interface Kirsty Y. Wan, Kyriacos C. Leptos and Raymond E. Goldstein Lag, lock, sync, slip: the many 'phases' of coupled flagella.

5 Oct 2020: 2. The Integer Quantum Hall Eect. In this section we discuss the integer quantum Hall eect. This phenomenon can be. understood without taking into account the interactions between electrons. This means. that we will assume that the quantum states

20 Jun 2011: Phys Rev E Stat Nonlin Soft Matter Phys 80:041922.22. Ishikawa T, Locsei JT, Pedley TJ (2008) Development of coherent structures in concen-. ... Science 325:487–490. 43. Pedley TJ, Kessler JO (1992) Hydrodynamic phenomena in suspensions of

6 Jul 2011: Phys Rev E Stat Nonlin Soft Matter Phys 80:041922.22. Ishikawa T, Locsei JT, Pedley TJ (2008) Development of coherent structures in concen-. ... Science 325:487–490. 43. Pedley TJ, Kessler JO (1992) Hydrodynamic phenomena in suspensions of

2 Sep 2012: Phys Rev E Stat Nonlin Soft Matter Phys 80:041922.22. Ishikawa T, Locsei JT, Pedley TJ (2008) Development of coherent structures in concen-. ... Science 325:487–490. 43. Pedley TJ, Kessler JO (1992) Hydrodynamic phenomena in suspensions of

6 Jul 2011: 1. Pedley TJ, Kessler JO (1992) Hydrodynamic phenomena in suspensions of swimmingmicroorganisms.

2 Sep 2012: J Fluid Mech 669:167–177.21. Ishikawa T, Locsei JT, Pedley TJ (2010) Fluid particle diffusion in a semidilute suspension.

5 Sep 2012: Science 317:105–108. 52. Pedley TJ (2010) Collective behaviour of swimming micro-organisms.

12 Feb 2018: G(ti, tj ) and further integrals, and so are again suppressed by higher powers of M.

10 Apr 2011: R E S E A R C H A R T I C L E. Fluid dynamics of self-propelled microorganisms,from individuals to concentrated populations. Luis H. Cisneros Æ Ricardo Cortez ÆChristopher Dombrowski Æ Raymond E. Goldstein ÆJohn O. Kessler. Received: 13 February

6 Feb 2019: Conf [J ] = KJ Lor (J ) D TJ. Lor (J ) is the 5D U-duality group that leaves the cubic norminvariant.

27 May 2019: Pkjd t tj. , where tj’s are delay timesand where the kj’s determine the intensity of the responsesubject to.

3 Jul 2008: Adiabatic limit and the slow motion of vortices in a. Chern-Simons-Schroedinger system. Sophia Demoulini and David StuartCentre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 OWB, England. email:sd290@cam.ac.uk, dmas2@cam.ac.uk.

22 Jul 2010: J. Fluid Mech. (1978), wol. 89, part 4 , p p. 609-646. Printed i n Great Britain 609. An exact theory of nonlinear waves on a Lagrangian-mean flow. By D. G. A N D R E W S U.K. Universities’ Atmospheric Modelling Group,. Reading, Berkshire,

6 Oct 2014: Anti–self–dual fields. and manifolds. Moritz F. Högner. Trinity College. Dissertation submitted for the Degree of Doctor of Philosophy. October 2012. Abstract. Anti–self–dual fields and manifoldsMoritz F. Högner. In this thesis we study

19 Oct 2013: 23 Nov 2004 1:27 AR AR235-FL37-11.tex AR235-FL37-11.sgm LaTeX2e(2002/01/18) P1: IBD10.1146/annurev.fluid.37.061903.175710. Annu. Rev. Fluid Mech. 2005. 37:263–93doi: 10.1146/annurev.fluid.37.061903.175710. Copyright c 2005 by Annual Reviews. All

10 May 2022: travel back to the position where they originated. Because Fj and Tj are the forces and.

25 Feb 2016: FL48CH05-Lauga ARI 24 November 2015 12:50. Bacterial HydrodynamicsEric LaugaDepartment of Applied Mathematics and Theoretical Physics, Center for MathematicalSciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom;email:

6 Nov 2019: uj = Φ1(tj) = erf. 1(. tj. α. 2. ),. where tjs are drawn randomly from the uniform distribution U([0, 1]). ... Let us discretise theinterval [0, 1] by points tj = j/N and write uj = f(tj).

2 Dec 2021: i. {avgj. ([Re(tj) RΞi (gtj)]. 2)}. i. , (S2). where i iterates over all datasets and j over all pointswithin the experimental dataset Re(tj) = Re(tj)/Re(0)enumerated by ... avgj. ([Re(tj) RΞ (gntj)]2. ). (S3). Here, all minimizations were performed

24 Nov 2006: K} such that. ti º tj , j = 1, 2,. , ... K. If ti tj for all j 6= i, we let (ti, ti1,. ,

16 Feb 2021: CAN STABLE AND ACCURATE NEURAL NETWORKS BE COMPUTED? – ON THEBARRIERS OF DEEP LEARNING AND SMALE’S 18TH PROBLEM. VEGARD ANTUN, MATTHEW J. COLBROOK†, AND ANDERS C. HANSEN†. ABSTRACT. Deep learning (DL) has had unprecedented success and is now

2 Sep 2012: FL43CH26-Koch ARI 15 November 2010 14:32. Collective Hydrodynamics ofSwimming Microorganisms:Living FluidsDonald L. Koch1 and Ganesh Subramanian21 School of Chemical and Biomolecular Engineering, Cornell University, Ithaca,New York 14853; email:

9 May 2019: Computational Projects. Lecture 5: Gaussian Elimination / LU decomposition. http://www.maths.cam.ac.uk/undergrad/catam/part-ia-lectures. Dr Rob Jack, DAMTP. 1. Motivation. So far we considered algorithms that correspond to very short MATLAB programs,

5 May 2020: Computational Projects. Lecture 6: Improving LU decomposition. http://www.maths.cam.ac.uk/undergrad/catam/part-ia-lectures. Dr Rob Jack, DAMTP. Recall. Suppose we want to solve Ax = b with. A =. 0 11 0. , b =. 23. <latexit

4 Feb 2022: 0/34. The finite-dimensional case. du. dt= Au, A Cnn, u(0) = u0 Cn u(t) = exp(tA)u0 =. j=0. tj. j!Aju0. E.g., if A = PDP1, with

1 Dec 2021: 0/34. The finite-dimensional case. du. dt= Au, A Cnn, u(0) = u0 Cn u(t) = exp(tA)u0 =. j=0. tj. j!Aju0. E.g., if A = PDP1, D =

1 Sep 2011: More details on the problems relevant to k;p can befound in [1],[2],[5].Recall that Nj(t) := (tjk tj) [tj; tj1; : : :; tjk] ( t)k1+ ;so that suppNj = (tj; tjk); ... degree p such thatsuppMj;p = (tj; tjp1); Z tjp1tj Mj;p(x)dx = 1;and by!

1 Sep 2011: 2. Condition number and related constantsLet fN̂jg be the B-spline basis of order k on a knot sequence t = (tj), tj < tjk,normalized with respect to the Lp-norm (1 ... p 1), i.e.,N̂j(x) = (k=(tjk tj))1=pNj(x);where fNjg is the B-spline basis which

10 Apr 2011: Continuum theory of critical phenomena in polymer solutions: Formalism and mean field approximation. Raymond E. Goldstein Laboratory of Atomic and Solid State Physics and Materials Science Center, Clark Hall, Cornell University, Ithaca, New York

18 May 2016: Coordinated beating of algal flagella is mediated bybasal couplingKirsty Y. Wana and Raymond E. Goldsteina,1. aDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom. Edited by Peter Lenz

31 Oct 2023: a) Prove [ti , tj] = iǫijktk. (b) Prove (nt)3 = |n|2nt.

2 Sep 2012: CURRENT TOPICS IN PLANT RESEARCH. The sliding theory of cytoplasmic streaming: fifty yearsof progress. Teruo Shimmen. Received: 18 August 2006 / Accepted: 22 November 2006 / Published online: 25 January 2007! The Botanical Society of Japan and

21 Nov 2007: k)tj of the expression. 2Λ(k)t =m. j=1 µ(k)tj (y. (k)j x̂) (y(k).

29 Jan 2008: Thus the orthogonality conditions. d Tj F (xk1) = 0, j = 1, 2,. ,

13 Apr 2011: F(x) = 12xT{ n. j=1 100(j1)/(n1) vj v. Tj. }x, xRn.

27 Aug 2014: Tj Hk v1) vj. ‖Hk v1 1. j=1 (vTj Hk v1) vj ‖. (2.14). is applied, the amount of work being only O(n), because equation (2.10) providesvTj Hkv1 = ... w =2Qredk w1. 1j=1 (w. Tj 2Qredk w1) wj. ‖2Qredk w1 1.

2 Jun 2016: 23. where we definet̃i = εij tj , ̃i = εijj , (7.3).

21 Feb 2022: Day et al. eLife 2022;11:e72707. DOI: https:// doi. org/ 10. 7554/ eLife. 72707 1 of 28. Cellular organization in lab- evolved and extant multicellular species obeys a maximum entropy lawThomas C Day1, Stephanie S Höhn2, Seyed A Zamani- Dahaj1,3,4

14 Jun 2014: Development/Plasticity/Repair. Developmental Modulation of Retinal Wave Dynamics:Shedding Light on the GABA Saga. Evelyne Sernagor,1 Carol Young,1 and Stephen J. Eglen21School of Neurology, Neurobiology, and Psychiatry, Medical Sciences, University

5 Dec 2007: J. Fluid Mech. (1986), vol. 161, p p. 449-492 Printed in &eat Britain. 449. Do Rossby-wave critical layers absorb, reflect, or over-reflect? By PETER D. KILLWORTH? A N D MICHAEL E. M c I N T Y R E Department of Applied Mathematics & Theoretical

2 Sep 2012: Due to the linearity of the Stokes equations, theirtranslational and rotational velocities, vi and ωi, dependlinearly on all external forces and torques, Fj and Tj [12,18]:.

12 Aug 2016: J. Fluid Mech. (2013), vol. 722, pp. 554–595. c Cambridge University Press 2013 554doi:10.1017/jfm.2013.122. Invariant recurrent solutions embedded in aturbulent two-dimensional Kolmogorov flow. Gary J. Chandler and Rich R. Kerswell†. School of

2 Jan 2024: Dow. nloa. ded. from. http. s://r. oyal. soci. etyp. ublis. hing. org. / on. 20 J. uly. 2023. royalsocietypublishing.org/journal/rsos. ResearchCite this article: Théry A, Maaß CC, Lauga E.2023 Hydrodynamic interactions between. squirmers near walls

18 May 2024: Montier, G Morgante, A Moss, S Mottet, M Münchmeyer, P Natoli, HU Nørgaard-Nielsen, CA Oxborrow, L Pagano, D Paoletti, B Partridge, G Patanchon, TJ Pearson, M Peel, HV Peiris, F

18 May 2024: Montier, G Morgante, A Moss, S Mottet, M Münchmeyer, P Natoli, HU Nørgaard-Nielsen, CA Oxborrow, L Pagano, D Paoletti, B Partridge, G Patanchon, TJ Pearson, M Peel, HV Peiris, F

18 May 2022: operate within the framework of Stokesflow, where the relationship between the dynamics (forcesFj and torques Tj) and kinematics (linear and angularvelocities Uj and Ωj) of rigid bodies is linear.

23 Sep 2015: elifesciences.org. RESEARCH ARTICLE. Cortical microtubule nucleation canorganise the cytoskeleton of Drosophilaoocytes to define the anteroposterior axisPhilipp Khuc Trong1,2, Hélène Doerflinger3, Jörn Dunkel1,4, Daniel St Johnston3,Raymond E