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7 Jan 2004: n̂m̂. j=1. sj zj z. Tj = Z. SZ+ T , (5.1). ... 2 zn̂m̂ zTn̂m̂. sn̂m̂ (eTt zn̂m̂)2. =n̂m̂1. j=1. sj zj zTj =. n̂m̂1. j=1. sj zj z. Tj. (5.9). We see that is the sum of the matrix

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

4 Feb 2020: Then for each time interval tj–tj 1 with1ojoM, predictions of the beach profile for tj 1 were made usingK̄(x)k in place of K in Eq. ... 14) can be written as. hðxi; tjþ1ÞffiðexpðDtÞ 1ÞD1GþexpðDtÞhðxi; tjÞ ð15Þ. where t= tj 1tj.The

13 Dec 2018: dx8,. Tj ,n5 2 Exj 21. ... xjGr1;r28!dx8,. Sj ,n8 5 Exj 21. xjGr2;r18!dx8,. Tj ,n8 5 2 Exj 21.

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

30 May 2018: ,. where tj = 1 0.5(sin(j) i cos(j)) for j 4.

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 =

16 Mar 2022: APP. LIED. MAT. HEM. ATIC. S. The difficulty of computing stable and accurate neuralnetworks: On the barriers of deep learning andSmale’s 18th problemMatthew J. Colbrooka,1,2 , Vegard Antunb,1,2, and Anders C. Hansena,b,2. aDepartment of Applied

23 Sep 2020: i] x2[i]N[i]1. j=0b̃[i]j Tj. (x[i]d[i]. ). =. d2[i] x2[i].

21 Feb 2023: 2022 European Mathematical SocietyPublished by EMS Press. J. Eur. Math. Soc. (Online first) DOI 10.4171/JEMS/1289. Matthew J. Colbrook Anders C. Hansen. The foundations of spectral computations via theSolvability Complexity Index hierarchy. Received