Sentence examples for minimal sphere from inspiring English sources

Briefly, for each cell i at location r i =[x i,y i,z i ], we find the minimal sphere centered at r i with radius r m that encloses exactly k cells.

The hydrodynamic radius, the translational diffusion coefficient, and the frictional ratio of the unhydrated particle can be directly computed using the Stokes Einstein relation (eq 3), and using the same equation, and the computed volume, the frictional coefficient of the minimal sphere can be calculated.

An arbitrary parametrization of the sedimentation and diffusion space can be obtained using the following six relationships: 1 2 3 4 5 6where V is the volume of a solvated particle (eq 1), N refers to Avogadro's number, r0 is the radius of the minimal sphere with frictional coefficient f0 (eq 2).

A soap bubble forms a sphere, a surface with minimal area — the smallest possible surface area for the volume enclosed.

Using the results, we established some new pinching theorems for minimal submanifolds in spheres.

Regardless of these differences, the overall catalytic efficiency for the metal complex of each sequence is retained, suggesting that this minimal first-coordination-sphere Zn II) site in a helical structure is all that is required to attain significant hydrolytic activity.

Open image in new window Figure 14 The cut applied on the connected sum of a minimal torus and a sphere.

Such solutions arise from variational min/max constructions, and examples include equatorial disks, the (critical) catenoid, as well as the cone over any minimal submanifold of the sphere.

For instance, the minimal graph for the sphere is made of two vertices, while the minimal graph for the solid 3-torus is in Figure 7. Open image in new window Figure 7 The minimal graph of the solid torus S 1 ⊗ S 2. As it has been shown recently [16], 3-spheres play a special role in three-dimensional group field theories, a role played indeed by 2-spheres in matrix models.

The minimal radius of the sphere that covers 80% of gene-days of the selected 37 genes in the 4-mer multi-scaling space is 2.6.

We will refer to this as Rmin, because it is the minimal radius of a sphere that could contain the given mass of protein (2.2) R min = (3 V / 4 π ) 1 / 3 = 0.066 M 1 / 3  (for  M  in Dalton,  R min  in nanometer).