We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code all relevant domain concepts. These concepts encode a large p…
In the framework of the crystal basis model of the genetic code, where each codon is assigned to an irreducible representation of $U_{q \to 0}(sl(2) \oplus sl(2))$, single base mutation matrices are introduced. The strength of the mutation is assumed to depend on the "distance" between the codons. P…
For the eight-dimensional Riemannian manifold comprised by the three-level quantum systems endowed with the Bures metric, we numerically approximate the integrals over the manifold of several functions of the curvature and of its (anti-)self-dual parts. The motivation for pursuing this research is t…
This short note contains an explicit proof of the Jacobi identity for variational Schouten bracket in $Z_2$-graded commutative setup. For the reasoning to be rigorous, it refers to the product bundle geometry of iterated variations (see arXiv:1312.1262 [math-ph]); no ad hoc regularizations occur any…
In a recent Letter, Avron et. al (math-ph/0105011) introduced a notion of optimal quantum pumps. These are adiabatic quantum pumps which work without dissipation. In particular, they produce neither entropy nor noise. In the present Comment we show that in the absence of magnetic field optimal quant…
For the first time the kinetic description of Landau diamagnetism for degenerate collisional plasma is given. The correct expression for transverse electric conductivity of the quantum plasma, found by authors (see arXiv:1002.1017 [math-ph] 4 Feb 2010) is used. In work S. Dattagupta, A.M. Jayannavar…
The asymptotic properties at future null infinity of the solutions of the relativistic Vlasov-Maxwell system whose global existence for small data has been established by the author in a previous work are investigated. These solutions describe a collisionless plasma isolated from incoming radiation.…