Related papers: Fat Shellable Spheres

Using a hydrogen molecule as a test system we demonstrate how to compute the effective potential according to the formalism of the new density functional theory (DFT), in which the basic variable is the set of spherically averaged densities…

We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that their barycentric subdivisions are simplicial polytopes. The…

We construct infinite families of topologically isotopic but smoothly distinct knotted spheres in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with $S^2 \times S^2$, and as a…

The Behrend function of a $\mathbb C$-scheme $X$ is a constructible function $\nu_X\colon X(\mathbb C) \to \mathbb Z$ introduced by Behrend, intrinsic to the scheme structure of $X$. It is a (subtle) invariant of singularities of $X$,…

For $3$-dimensional convex polytopes, inscribability is a classical property that is relatively well-understood due to its relation with Delaunay subdivisions of the plane and hyperbolic geometry. In particular, inscribability can be tested…

We consider the combinatorial question of how many convex polygons can be made by using the edges taken from a fixed triangulation of n vertices. For general triangulations, there can be exponentially many: we show a construction that has…

We consider the van der Waals energy of an atom near the infinitely thin sphere with finite conductivity which model the fullerene. We put the sphere into spherical cavity inside the infinite dielectric media, then calculate the energy of…

An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of $R^3$ into polyhedra. The polyhedra are divided…

We study the elliptic curves given by $y^2 = x^3 + b x + t^{3^n+1}$ over global function fields of characteristic $3$; in particular we perform an explicit computation of the $L$-function by relating it to the zeta function of a certain…

This paper proves that given a doubling weight $w$ on the unit sphere $\mathbb{S}^{d-1}$ of $\mathbb{R}^d$, there exists a positive constant $K_w$ such that for each positive integer $n$ and each integer $N\geq \max_{x\in \mathbb{S}^{d-1}}…

We improve the previously best known upper bounds on the sizes of $\theta$-spherical codes for every $\theta<\theta^*\approx 62.997^{\circ}$ at least by a factor of $0.4325$, in sufficiently high dimensions. Furthermore, for sphere packing…

It is proved that the equality $\Delta\ln|\kappa-\lambda|=6\kappa$, where $\kappa$ is the Gaussian curvature of a metric tensor g on a 2-dimensional manifold is a sufficient and necessary condition for local realizability of the metric as…

Composed of square particles, the tetratic phase is characterised by a four-fold symmetry with quasi-long-range orientational order but no translational order. We construct the elastic free energy for tetratics and find a closed form…

We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a tangent space on a 4-dimensional differentiable manifold. The manifold is equipped with a positive definite metric and an additional tensor structure of…

Shell model calculations with the neutron effective charge as single free parameter describe well the \bet and \bef rates for $N\le 64$ in the Cd and Sn isotopes. The former exhibit weak permanent deformation corroborating the prediction of…

We calculate the low-energy spectral weight of a holographic superfluid coupled to a Chern-Simons term in IR radial scaling geometries characterized by a parameter $\eta$. This work was motivated by previous results where an unexpected…

This article is concerned with the problem of placing seven or eight points on the unit sphere $\mathbb{S}^2$ in $\mathbb{R}^3$ so that the surface area of the convex hull of the points is maximized. In each case, the solution is given for…

Facets of the convex hull of $n$ independent random vectors chosen uniformly at random from the unit sphere in $\mathbb{R}^d$ are studied. A particular focus is given on the height of the facets as well as the expected number of facets as…

In the present work, we have discussed the four dimensional spherically symmetric steller system in the framework of modified $f(T)$ gravity theory with electro-magnetic field. The field equations have been written for two cases, either…

For $n \geq 1$, the twistor space $\mathfrak{Z}(\mathbb{S}^{2n})$ of the conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the complex Grassmannian manifold $\mathbf{G}(n+1, 2n+2)$, of the set of graphs of…