We prove that every projectively normal Fano manifold in Pn+r of index 1, codimension r, and dimension n≥10r is birationally superrigid K-stable. This result was previously proved by Zhuang under the complete intersection assumption.

The paper [Howard E. Brandt, ”Conclusive eavesdropping in quantum key distribution,” J. Opt. B: Quantum Semiclass. Opt. 7 (2005)] is generalized to include the full range of error rates for the projectively measured quantum cryptographic entangling probe, and also the full range of inconclusive rates for the entangling probe measured with the POVM receiver.

In this paper, we will introduce a projectively natural iteration on polygons which has a construction similar to the pentagram map but very different dynamical behavior. We will prove several results about the action of this map and also discuss some experimental observations on its interaction with the pentagram map.

We study several exotic systems, including the X-cube model, on a flat three-torus with twist in $xy$-plane. The ground state degeneracy turns out to be sensitive function of various geometrical parameters. Starting from lattice, depending how we take continuum limit, find different values degeneracy. Yet, there is natural limit well-defined (though infinite) value that also uncover surprising ...

‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...