He established analogous results for the sphere showing that the volume of a sphere is equal to that of a cone whose height equals the radius of the sphere and whose base equals its surface area; the surface area of the sphere he found to be four times the area of its greatest circle.
In this picture, Poe's "broad belt of gleaming spray" is exactly analogous to a photon sphere around a black hole.
Specifically, we will show that, under the conditions on the C and B tensors, the Green's tensors can be exactly expressed as a simple line integral over a unit circle, and that the Eshelby's tensors for a general ellipsoidal inclusion can be derived as surface integrals over a unit sphere, entirely analogous to those of the classical elasticity.
The comparison of a group of crystal structures is carried out in a pairwise fashion and is accomplished by generating a set of neighbouring molecules, analogous to a coordination sphere, around a central molecule from the symmetry operations of the space groups of each structure.
In the crystal structure of oxidized pterin (BH2) in complex with rat tyrosine hydroxylase, the cofactor adopts a flipped conformation such that the dihydroxpropyl chain of the cofactor is oriented toward Glu332 (the second-coordination sphere residue analogous to Asp139 in cPAH) and the water molecules seen bridging pterin and the acidic amino acid are thus lost.
Analogous to the MCF7 MMO culture, secondary spheres were generated, which required 5 days.
The universe is, as it were, one machine, wherein the celestial spheres are analogous to the interlocking wheels and the particular beings are like the things moved by the wheels and all events are determined by an inescapable necessity.
Analogous results are established for normalized L2 functions on the sphere Sn.
As Halpern has pointed out, the reversible Co C bond cleavage in B12-dependent reactions is formally an inner-sphere redox process analogous to reactions of reversible dioxygen carriers such as hemoglobin and myoglobin.
Analogous to MPI_Alltoallv.
