We introduce an algorithm that is able to find the facets of Coulomb diamonds in quantum dot arrays. simulate these arrays using constant-interaction model, and rely only on one-dimensional raster scans (rays) learn a model device regularized maximum likelihood estimation. This allows us determine, for given charge state device, which transitions exist what compensated gate voltages are. For sm...

The geometry of causal diamonds or Alexandrov open sets whose initial and final events p and q respectively have a proper-time separation τ small compared with the curvature scale is a universal. The corrections from flat space are given as a power series in τ whose coefficients involve the curvature at the centre of the diamond. We give formulae for the total 4-volume V of the diamond, the are...

This note derives the characteristic polynomial of a graph that represents nonjump moves in a generalized game of checkers. The number of spanning trees is also determined.

In the eleventh paper in series on MacMahon’s partition analysis, Andrews and Paule introduced [Formula: see text]-elongated diamonds. Recently, they revisited topic. Let text] count partitions obtained by adding links of plane diamonds length text]. several generating functions congruences for text], Da Silva et al. further found many modulo 4, 5, 7, 8, 9, 11 this paper, we extend some individ...

We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order n has exactly 2()/ domino tilings. In this, the first half of a two-part paper, we give two proofs of this formula. The first proof exploits a connection between domino tilings and the alternating-sign matrices of Mills, Robbins, and ...

In addition to the four grain size fractions of diamonds separated from the Efremovka (CV3) meteorite reported earlier [1], six more diamond size-fractions from the same meteorite have been generated with sizes both coarser and finer than the original set. Isotope analyses of C, N and noble gases in the new fractions confirmed most of the trends observed earlier for concentrations and isotopic ...

We introduce a family of planar regions, called Aztec diamonds, and study the ways in which these regions can be tiled by dominoes. Our main result is a generating function that not only gives the number of domino tilings of the Aztec diamond of order n but also provides information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from anoth...