The phrase "a closed sphere" is correct and usable in written English.
It can be used in mathematical or scientific contexts to describe a three-dimensional object where all points on the surface are equidistant from a central point.
Example: "In topology, a closed sphere is defined as the set of all points in three-dimensional space that are at or below a certain distance from a given point."
Alternatives: "a solid sphere" or "a complete sphere".
Lemma 9 Let be an Euclidean space, let the dimension of satisfy dim E ≥ 3, and let B ( g, 1 ) be a closed sphere in.
Let be an Euclidean space, the dimension of dim E ≥ 3, P = ( p 1, p 2, …, p n ) and m = ( m 1, m 2, …, m n ) be the sequences of and R + +, respectively, and B ( g, r ) be a closed sphere in.
I think...that life is not a closed sphere.
The de novo-designed four-helix bundle, α4, was also used as a scaffold for the incorporation of a closed-sphere ZnCys2His2 site (Zα4), much like the structural site found in zinc finger (ZF) proteins.
Klemba et al. reported the redesign of the B1 domain of IgG-binding protein G (a 56-residue protein with a four-stranded β-sheet crossed by a single α-helix) to incorporate a closed-sphere His3Cys site for binding Zn II).
We used the Stokeslet approximation to the flow field of an isolated cell in Figure 3, to test the effect of force modulation on synchronization within the class of minimal models which abstract the beating flagellum as a sphere driven along a closed orbit (Niedermayer et al., 2008; Uchida and Golestanian, 2011, 2012).
In the simplest case, often used in models of synchronization (Vilfan and Jülicher, 2006; Niedermayer et al., 2008; Uchida and Golestanian, 2011), that would be just a single sphere tracing out a closed orbit in space under the action of internal driving forces.
Furthermore, PFC accumulated in chronic phase of infection like CLIO characterized by forming a closed hollow sphere around the edema pattern.
The authors demonstrate that mutating some of the surrounding residues to Glu results in a closed coordination sphere and a corresponding loss of activity (supporting a Zn OH– mechanism).
As you point out, the absence of complete reconstitution of a closed membrane sphere does not detract from the overall importance of your work; however, we feel that it is important for readers to know this limitation of your in vitro LC3 lipidation system.
Then the mapping (G x)=x-F'(x)^{-1}F x)) is well defined on S for the closed sphere (S=bar{S}(x^{-1}F xsubset S_{0}).
