Cylindrical first-order superintegrability with complex magnetic fields

Primordial Magnetic Fields from Cosmological First Order Phase Transitions

We give an improved estimate of primordial magnetic elds generated during cosmological rst order phase transitions. We examine the charge distribution at the nucleated bubble wall and its dynamics. We consider instabilities on the bubble walls developing during the phase transition. It is found that damping of these instabilities due to viscosity and heat conductivity caused by particle di usio...

Non-magnetic simplified cylindrical cloak with suppressed zero order scattering

A type of simplified cloaks with matched exterior boundaries is proposed. The cloak uses nonmagnetic material for the TM polarization and can function with a relatively thin thickness. It is shown that the zero order scattering of such cloak is dominant among all cylindrical scattering terms. A gap is added at the cloak’s inner surface to eliminate the zero order scattering, through the mechani...

Superintegrability with third-order integrals in quantum and classical mechanics

We consider here the coexistence of firstand third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable systems are found that have no classical analog, i.e. the potentials are proportional to h̄, so their classical limit is free motion.

First-order Definitions in Function Fields over Anti-mordellic Fields

Theorem 1.5. For each of the following classes of fields, there is a sentence that is true for fields in that class and false for fields in the other five classes: (1) finite and anti-Mordellic fields (2) number fields (3) function fields over finite fields (4) function fields over anti-Mordellic fields of characteristic > 0 (5) function fields over anti-Mordellic fields of characteristic 0 (6)...

First-order Definitions in Function Fields over Anti-mordellic Fields