Dimer models and the special McKay correspondence

We study the behavior of a dimer model under the operation of removing a corner from the lattice polygon and taking the convex hull of the rest. This refines an operation of Gulotta, and the special McKay correspondence plays an essential role in this refinement. As a corollary, we show that for any lattice polygon, there is a dimer model such that the derived category of finitely-generated modules over the path algebra of the corresponding quiver with relations is equivalent to the derived category of coherent sheaves on a toric Calabi-Yau 3-fold determined by the lattice polygon. Our proof is based on a detailed study of relationship between combinatorics of dimer models and geometry of moduli spaces, and does not depend on the result of math/9908027.Comment: 56 pages, v2: major revisio

Enhancement of hydrogen response by forming an Au submonolayer on nanogap Pd nanoparticles

Nakamura Nobutomo, Yoshikawa Kazushi, Ishii Akio. Applied Physics Letters 125, 021902 (2024) https://doi.org/10.1063/5.0204024.When Pd nanoparticles dispersed on a glass substrate with nanometer order gaps are exposed to H2 gas, H atoms are adsorbed on the nanoparticle surface, and the electrical resistance between the nanoparticles increases because of the tunneling current suppression. In contrast, when Au nanoparticles are exposed to H2 gas, the resistance remains unchanged because H atoms are not adsorbed on the Au surface. Considering these behaviors, the change ratio of the electrical resistance is expected to be smaller when the surface of Pd nanoparticles is partially covered with Au. However, the experimental results show the opposite resistance change. Density functional theory simulation indicates that H atoms are adsorbed and absorbed on the pure Pd surface, but H atoms are adsorbed and tend to remain on the partially covered Pd surface. These results indicate that the decrease in the resistance due to the gap narrowing by hydrogen absorption occurs in Pd nanoparticles, but it does not occur in Au/Pd nanoparticles, resulting in a larger resistivity increase compared with the Pd nanoparticles. This result implies that in certain cases, the low reactivity of Au to H2 contributes to the enhancement of the electrical resistance response

Dimer models and group actions

We construct a consistent dimer model having the same symmetry as its characteristic polygon. This produces examples of non-commutative crepant resolutions of non-toric non-quotient Gorenstein singularities in dimension 3.Comment: 23 pages, 5 figure

Vaginoplasty with an M-Shaped Perineo- Scrotal Flap in a Male-to-female Transsexual

To date, many techniques have been reported for vaginoplasty in male-to-female trans-sexual (MTFTS) patients, such as the use of a rectum transfer, a penile-scrotal flap and a reversed penile flap. However, none of these procedures is without its disadvantages. We developed a newly kind of flap for vaginoplasty, the M-shaped perineo-scrotal flap (M-shaped flap), using skin from both sides of the scrotum, shorn of hair by preoperative laser treatment. We applied this new type of flap in 7 MTFTS patients between January 2006 and January 2007. None of the flaps developed necrosis, and the patients could engage in sexual activity within 3 months of the operation. The M-shaped flap has numerous advantages: it can be elevated safely while retaining good vascularity, it provides for the construction of a sufficient deep vagina without a skin graft, the size of the flap is not influenced entirely by the length of the penis, and it utilizes skin from both sides of the scrotal area, which is usually excised.</p