Groupoids satisfying the equation x(yz) = (xy)(xz) are called left distributive, or LD-groupoids. We give an algorithm for their enumeration and prove several results on the collection of LD-groupoids extending a given monounary algebra.

Integration of human immunodeficiency virus (HIV-1) DNA into the genome of an infected cell is one of the key steps in the viral replication cycle. The viral enzyme integrase (IN), which catalyzes the integration, is an attractive target for the development of new antiviral drugs. However, the HIV-1 therapy often results in the IN gene mutations inducing viral resistance to integration inhibito...

The spin-orbit entangled quantum states in $4d/5d$ compounds, e.g., the ${J}_{\mathrm{eff}}=\frac{1}{2}$ and ${J}_{\mathrm{eff}}=\frac{3}{2}$ states, have attracted great interests for their unique physical roles unconventional superconductivity topological states. Here, key role of tetragonal distortion is clarified, which determines ground $4{d}^{1}/5{d}^{1}$ systems to be one (e.g., ${\mathr...

Nematic elastomers exhibit a rich elastic response to external stresses. Of particular interest is the semisoft response of elastomers with an anisotropy direction (z) frozen in by a double cross-linking process. This response is characterized by a stress-strain curve for stresses along x perpendicular to z that rises initially, exhibits a nearly flat plateau between two critical values of stra...

Kagome magnets are believed to have numerous exotic physical properties due the possible interplay between lattice geometry, electron correlation and band topology. Here, we report large anomalous Hall effect in kagome ferromagnet LiMn$_6$Sn$_6$, which has a Curie temperature of 382 K easy plane along with lattice. At low temperatures, unsaturated positive magnetoresistance opposite signs ordin...