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‘Let us assume that, when stretched, the toroidal polymer becomes an ellipse, with equation’
‘Surrounding the pulsar is a bright doughnut-shaped, or toroidal, structure, with jet-like features extending in a perpendicular direction away from the torus.’
‘The element after the polygon can be a toroidal or cylindrical lens incorporated into the scan lens, or it can be a cylindrical lens or mirror located near the image plane.’
‘This cylinder has about 5 fringes of toroidal curvature.’
‘In this paper, we will use melittin as an example to see if the proposed theory also describes peptides that form toroidal pores.’
‘Briefly, four replicate 25 m diameter toroidal plenum rings constructed from 0.305 m diameter pipe were placed in the field shortly after planting.’
‘Instead, they are consistent with the toroidal model that was first proposed to describe magainin-induced pores.’
‘If the two circular ends of the cylinder are now glued together then it becomes a toroidal ring, like a doughnut.’
‘Pore-forming mechanisms that have been proposed to explain the mode of action of Î-helical membrane peptides include the transmembrane-helical bundle, the carpet-like, and the toroidal models.’
‘To see, using modern mathematics, why this works we note that the cylindrical surface has equation the toroidal surface has equation and the conical surface has equation’
‘Free oscillations are literally the ringing of the Earth like a large bell after it has been struck (by an earthquake) There are two basic types of free oscillation: toroidal, or torsional, and spheroidal.’
‘The analytical solutions of the Poisson equation in toroidal coordinates are, unfortunately, very complicated and it is not possible to extract the [epsilon] dependence of the potential energy of an ion from them.’
‘Other curvature geometries such as elliptical, logarithmic parabolic, and log spiral can be used to accommodate different source or image geometries, though we'll restrict this discussion to the symmetrical toroidal geometry.’
‘The transmit winding is wound along the diameter of the toroidal core and the receive winding is wound along the circumference of the toroidal core.’
‘The observed invariance of melittin-induced leakage with differences in bilayer hydrocarbon thickness is also evidence in favor of the toroidal pore over the barrel stave pore.’
‘In this case, the toroidal surface has become an off-axis segment of an ellipsoid.’
‘EUV radiation from a slit or a slot passes through another thin aluminum filter and then illuminates a 9-cm diameter, ion-etched, holographic toroidal grating.’
‘At lower concentrations, the peptide altered the morphology of the bilayer in a way consistent with the formation of a toroidal pore.’
‘Expected values from Equations 4 and 6 (for toroidal and rectangular habitats, respectively) are indicated by solid lines.’
‘If we assume that POPC has a cross-sectional area of 65 [Angstrom] 2, the surface area of a toroidal pore equals that of 105 lipids.’