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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 portion of the knowle…

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. Preliminary general 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 to elaborate upon the…

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 anywhere in this theory…

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 quantum pumps always have…

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 and N. Kumar [Curre…

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. It is shown that a …

We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \emph{do not} use any kind of semiclassic approximation or limiting procedures for $\hbar \to 0$. Harmonic os…