Related papers: Kissing number in spherical space

We have studied the packing of congruent disks on a spherical cap, for caps of different size and number of disks, $N$. This problem has been considered before only in the limit cases of circle packing inside a circle and on a sphere…

We introduce the notion of p-adic spherical codes (in particular, p-adic kissing number problem). We show that the one-line proof for a variant of the Delsarte-Goethals-Seidel-Kabatianskii-Levenshtein upper bound for spherical codes,…

In this paper, let $n\geq2$ be an integer, $P=diag(-I_{n-\kappa},I_\kappa,-I_{n-\kappa},I_\kappa)$ for some integer $\kappa\in[0, n-1)$, and $\Sigma \subset {\bf R}^{2n}$ be a partially symmetric compact convex hypersurface, i.e., $x\in…

The density, denoted by $\kappa(n,r)$, of permutations having no cycles of length less than $r+1$ in a symmetric group $\mathrm{S}_n$ is explored. New asymptotic formulas for $\kappa(n,r)$ are obtained using the saddle-point method when…

We prove that the kissing number in 19 dimensions is at least 11948, improving the bound of Cohn and Li by 256. By the odd-sign construction of Cohn and Li, it is enough to find a binary code of length 19 and minimum distance 5 inside the…

We give an estimate for Manolescu's $\kappa$-invariant of a rational homology 3-sphere $Y$ by the data of a spin 4-orbifold bounded by $Y$. By an appropriate choice of a 4-orbifold, sometimes we can restrict and determine the value of…

We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $N\sim n^\alpha, 0<\alpha\le 2.$ The bounds are derived by specializing recent general, universal bounds on energy of spherical…

This paper concerns the coherent states on spheres studied by the authors in [J. Math. Phys. 43 (2002), 1211-1236]. We show that in the odd-dimensional case the coherent states on the sphere approach the classical Gaussian coherent states…

Given a sphere of any radius $r$ in an $n$-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the lowest covering density, which defines the average…

We study stable immersed capillary hypersurfaces $\Sigma$ in domains B of R n+1 bounded by hyperplanes. When B is a half-space, we show $\Sigma$ is a spherical cap. When B is a domain bounded by k hyperplanes P 1 ,. .. , P k , 2 $\le$ k…

We study the Riemann curvature tensor of (\kappa,\mu,\nu)-spaces when they have almost cosymplectic and almost Kenmotsu structures, giving its writing explicitly. This leads to the definition and study of a natural generalisation of the…

The set of all error-correcting codes C over a fixed finite alphabet F of cardinality q determines the set of code points in the unit square with coordinates (R(C), delta (C)):= (relative transmission rate, relative minimal distance). The…

Measurements of ellipticities of background galaxies are sensitive to the reduced shear, the cosmic shear divided by $(1-\kappa)$ where $\kappa$ is the projected density field. We compute the difference between shear and reduced shear both…

We provide analogues of the results from [FMR11, CMMR13] in the reference list (which correspond to the case $\kappa = \omega$) for arbitrary $\kappa$-Souslin quasi-orders on any Polish space, for $\kappa$ an infinite cardinal smaller than…

We obtain lower bounds on the rank of the kappa ring of the Delign-Mumford compactification of the moduli space of curves in different degrees. For this purpose, we introduce a quotient of the kappa ring, the combinatorial kappa ring, and…

In this paper, we obtain new asymptotic lower bounds for the chromatic numbers of spheres.

Motivated by the $1/N_c$ expansion, we study a simple model in which the pi-K scattering amplitude is the sum of a current-algebra contact term and resonance pole exchanges. This phenomenological model is crossing symmetric and, when a…

We present a classification of the complete, simply connected, contact metric $(\kappa,\mu)$-spaces as homogeneous contact metric manifolds, by studying the base space of their canonical fibration. According to the value of the Boeckx…

We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) $\Omega_{\kappa\mu}(\mathbf{n})$ used in relativistic atomic, molecular, and solid state…

Envelopes of parameterized families of plane curves is an important topic, both for the mathematics involved and for its applications. Nowadays, it is generally studied in a technology-rich environment, and automated methods are developed…