Related papers: Lattice packings with gap defects are not complete…
We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the…
The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195-200) proved that the Hamiltonian Cycle Problem is NP-Complete even for…
In this paper, we prove a gap result for a locally conformally flat complete non-compact Riemannian manifold with bounded non-negative Ricci curvature and a scalar curvature average condition. We show that if it has positive Green function,…
The present article is concerned with a group of problems raised by J. Noguchi and M. Jarnicki/P. Plug, namely whether the envelopes of holomorphy of truncated tube domains are always schlicht, i.e. subdomains of $\mathbb{C^n}$, and how to…
In this paper we prove an asymptotic lower bound for the sphere packing density in dimensions divisible by four. This asymptotic lower bound improves on previous asymptotic bounds by a constant factor and improves not just lower bounds for…
This paper is concerned with a covering problem of Euclidean space by a particular arrangement of cones that are not necessarily full and are allowed to overlap. The problem provides an equivalent geometric reformulation of the solvability…
We survey recent developments on the structure of complemented subspaces of Banach lattices, including in particular the construction of a complemented subspace of a $C(K)$-space which is not linearly isomorphic to any Banach lattice.…
A real 3- or 4-manifold has by definition an orientation preserving smooth involution acting on it. We consider Lefschetz fibrations of 4-dimensional manifolds-with-boundary and open book decompositions on their boundary in the existence of…
The following two results are shown. 1) Let $G$ be the $k$-rational points of a simple algebraic group over a local field $k$ and let $H$ be a lattice in $G.$ Then the regular representation of $G$ on $L^2(G/H)$ has a spectral gap (that is,…
A linear cycle in a hypergraph $H$ is a cyclic sequence of hyperedges such that two consecutive hyperedges intersect in exactly one element and two nonconsecutive hyperedges are disjoint and $\alpha(H)$ denotes the size of a largest…
We consider a Kondo-like impurity interacting with fermions on a honeycomb lattice at half-filling, as in the case of graphene. We derive from the lattice model an effective one-dimensional continuum theory which has, in general, four…
We study the sphere packing problem in Euclidean space where we impose additional constraints on the separations of the center points. We prove that any sphere packing in dimension $48$, with spheres of radii $r$, such that no two centers…
We address the question of which convex shapes, when packed as densely as possible under certain restrictions, fill the least space and leave the most empty space. In each different dimension and under each different set of restrictions,…
We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb lattice compounds under trigonal compression. Our method utilizes a systematic algorithm to identify all dual…
We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…
We provide a novel setup for generalizing the two-dimensional pseudospin S=1/2 Dirac equation, arising in graphene's honeycomb lattice, to general pseudospin-S. We engineer these band structures as a nearest-neighbor hopping Hamiltonian…
We study packings of bidispersed spherical particles on a spherical surface. The presence of curvature necessitates defects even for monodispersed particles; bidispersity either leads to a more disordered packing for nearly equal radii, or…
A linear isometry $R$ of $\mathbb{R}^d$ is called a similarity isometry of a lattice $\Gamma \subseteq \mathbb{R}^d$ if there exists a positive real number $\beta$ such that $\beta R\Gamma$ is a sublattice of (finite index in) $\Gamma$. The…
Circle packings are arrangement of circles satisfying specified tangency requirements. Many problems about packing of circles and spheres occur in nature particularly in material design and protein structure. Surprisingly, little is known…
Unconventional superconductivity on a honeycomb lattice has received increasing interest since the discovery of graphene primarily due to the similarities between materials with a honeycomb lattice and cuprate superconductors. Many…