81. (IUCr) WHEATSHEAF: An Algorithm To Average Protein Structure Ensembles The iteration is a multidimensional extension of the famous method of JosephRaphson, almost universally misattributed to Isaac Newton (Thomas Smith, http://journals.iucr.org/d/issues/2005/01/00/dz5023/dz5023bdy.html

short communications Volume 61 Part 1 Pages 112-116 January 2005 Received 15 June 2004 Accepted 28 October 2004 WHEATSHEAF : an algorithm to average protein structure ensembles David Thomas a and Annalisa Pastore b a Biological NMR Unit, Institute for Clinical Research, University of Birmingham Medical School, Birmingham B15 2TT, England, and b Division of Molecular Structure, National Institute for Medical Research, The Ridgeway, Mill Hill, London NW7 1AA, England Correspondence e-mail: apastor@nimr.mrc.ac.uk A new algorithm is described that forms a single structure representative of ensembles of structures from files in the format used by the Protein Data Bank. A first attempt is made by averaging in the space spanned by bond lengths, inter-bond rotations and symmetry-multiplied dihedral rotations. This normally produces well formed regular secondary-structure elements, but the intervening less well ordered regions are often distorted because of the invalidity of averaging large rotations about divergent axes. For this reason, the algorithm includes a second stage that pulls the interatomic distances towards more fully representative values. Results produced by this method have proved better as judged by conventional quality checks than any input structure in nearly all cases tested so far, especially for the backbone, and much better than those produced by commonly used alternative methods. Keywords: protein structure; structural ensemble; representative structure; averaging rotations; dihedral bond symmetry.

82. Fraktalni Oblici U Numerièkim Aproksimacijama razvio je takvu specificnu iteracijsku metodu, koju je kasnije usavršio JosephRaphson (17.st.). Neka je ? rješenje jednadžbe f(x) = 0 na segmentu a, http://www.math.hr/~mathe/fraknum/

Broj 5 Mario Matijeviæ Fraktalni oblici u numerièkim aproksimacijama Sadržaj: 1. Priroda iteracijske metode 2. Cayleyjev problem 3. Koraci algoritma 4. Primjeri fraktalnih bazena ... download 1. Priroda iteracijske metode Problem traženja rješenja jednadžbe f x ) = prastar je, same metode koje mogu rješavati jednadžbe u formi a x bx c = poznate su veæ tisuæama godina. U šesnaestom stoljeæu talijanski matematièari razvili su egzaktne formule za rješavanje polinomijalnih jednadžbi stupnja tri i èetiri, a poèetkom devetnaestog stoljeæa dokazano je kako ne postoje opæenite relacije u radikalima za jednadžbe stupnja pet ili više ( Niels Abel ). Unatoè tome, numerièke metode za rješavanje polinomijalnih jednadžbi bilo kojeg stupnja tijekom povijesti sustavno su razvijane. Sir Isaac Newton (17.st.) razvio je takvu specifiènu iteracijsku metodu, koju je kasnije usavršio Joseph Raphson (17.st.). f x ) = na segmentu [ a b ] i neka su i neprekidne funkcije koje ne mijenjaju predznak na segmentu [ a b ]. Ako je

83. Title The summary for this English page contains characters that cannot be correctly displayed in this language/character set. http://gu.wikipedia.org/wiki/વિકિપીડિà�

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