Predicting coiled coils by use of pairwise residue correlations.

A method is presented that predicts coiled-coil domains in protein sequences by using pairwise residue correlations obtained from a (two-stranded) coiled-coil database of 58,217 amino acid residues. A program called PAIRCOIL implements this method and is significantly better than existing methods at distinguishing coiled coils from alpha-helices that are not coiled coils. The database of pairwise residue correlations suggests structural features that stabilize or destabilize coiled coils.

Repacking protein cores with backbone freedom: structure prediction for coiled coils.

Progress in homology modeling and protein design has generated considerable interest in methods for predicting side-chain packing in the hydrophobic cores of proteins. Present techniques are not practically useful, however, because they are unable to model protein main-chain flexibility. Parameterization of backbone motions may represent a general and efficient method to incorporate backbone relaxation into such fixed main-chain models. To test this notion, we introduce a method for treating explicitly the backbone motions of alpha-helical bundles based on an algebraic parameterization proposed by Francis Crick in 1953 [Crick, F. H. C. (1953) Acta Crystallogr. 6, 685-689]. Given only the core amino acid sequence, a simple calculation can rapidly reproduce the crystallographic main-chain and core side-chain structures of three coiled coils (one dimer, one trimer, and one tetramer) to within 0.6-A root-mean-square deviations. The speed of the predictive method [approximately 3 min per rotamer choice on a Silicon Graphics (Mountain View, CA) 4D/35 computer] permits it to be used as a design tool.

A bound on the error in a general quadrature formula with equidistant ordinates /

"October 20, 1954"

Numerical quadrature over a rectangular domain in two or more dimensions /

"This work was supported in part by the Office of Naval Research under Contract Nonr-1834(27)."

Rempe engineering data book, prepared for the engineer and draftsman as a guide in the design of pipe coils and fin coils, with specific data on the subjects of dimensional limitations, coil development formula and heat transfer factors.

Mode of access: Internet.

Famous problems of elementary geometry; the duplication of the cube, the trisection of an angle; the quadrature of the circle;

Lettered on cover: Problems in geometry. Beman and Smith. 1922.

Tarif de quadrature pour le mesurage du sciage des bois, d'après le système métrique, calculé pour toutea les longueurs de madriers, de 1 à 162 décimètres, et les largeurs de 1 à 64 centimètres,

Mode of access: Internet.

Elements of geometry: containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids: to which are added Elements of plane and sherical trigonometry.

Mode of access: Internet.

Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids : to which are added, elements of plane and spherical trigonometry /

Mode of access: Internet.

Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids: to which are added elements of plane and spherical trigonometry /

Mode of access: Internet.

Elements of geometry; : containing the first six books of Euclid, with a supplement on the quadrature of the circle and the geometry of solids; to which are added, Elements of plane and spherical trigonometry. /

"Errata"--P. [xvi]

Elements of geometry: containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids: to which are added, elements of plane and spherical trigonometry,

Mode of access: Internet.

Higher geometry and trigonometry : being the third part of a series on elementary and higher geometry, trigonomentary and mensuration : containing many valuable discoveries and improvements in mathematical science, especially in relation to the quadrature of the circle, and some other curves, as well as the cubature of certain curvilinear solids : designed as a text-book for collegiate and academic instruction, and as a practical compendium of mensuration /

With: Higher geometry and mensuration / by Nathan Scholfield.

A distributed equivalent magnetic current based FDTD method for the calculation of E-fields induced by gradient coils

This paper evaluates a new, low-frequency finite-difference time-domain method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretization of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modelling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multi-layered spherical phantom model and a complete body model. (C) 2004 Elsevier Inc. All rights reserved.