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Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk-edge correspondence and symmetry-related to ...
We study the elliptic curves given by y(2) = x(3) + bx + t(3n+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 superelliptic curve u(3) ...
We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn-Triantafillou to the case of odd weight and no ...
We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...
In this note, we demonstrate direct high-temperature growth of single-crystalline GaN on c-plane ScAlMgO4 substrates by metalorganic chemical vapor deposition, without using low-temperature buffers. We found that a trimethylaluminium preflow was crucial to ...
We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...
In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...
We construct a new family of lattice packings for superballs in three dimensions (unit balls for the l(3)(p) norm) with p epsilon (1, 1.58]. We conjecture that the family also exists for p epsilon (1.58, log(2) 3 = 1.5849625 ...]. Like in the densest latti ...
Magnetic anisotropy is anticipated to govern the formation of exotic spin textures reported recently in cubic chiral magnets, like low-temperature tilted conical and skyrmion lattice (SkL) states and metastable SkLs with various lattice geometry. Motivated ...
We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of d/2 in dimension d, achieved by the "standard terminal simplices" and direct sums of them. We prove this conjecture up to ...