Abstract The reaction rates of the beta processes for all particles at arbitrary degeneracy are derived, and an analytic steady state equilibrium condition μn = μp + 2μe which results from the equality of electron and positron capture rates in the hot electron-positron plasma with nucleons is also found, if the matter is transparent to neutrinos. This simple analytic formula is valid only if el...

We demonstrate a degenerate parametric oscillator in a silicon nitride microresonator. We use two frequency-detuned pump waves to perform parametric four-wave mixing and operate in the normal group-velocity dispersion regime to produce signal and idler fields that are frequency degenerate. Our theoretical modeling shows that this regime enables generation of bimodal phase states, analogous to t...

Hyperfine coupling in non-rigid molecular systems with several equivalent nuclei is very interesting because of the averaging due to the large amplitude motion(s). For instance, in the cases of the non-rigid (D O) and (C D ) dimers, the molecule behaves as if quadrupole coupling was identical for all four deuterium atoms. This result, only valid for nondegenerate tunneling levels, disagrees ind...

A decomposition problem in geometry is the following: given a C manifold M on which is defined an affine connection without torsion, under what conditions in terms of the holonomy group will M be affinely diffeomorphic to a direct product of two other affinely connected manifolds? Here, we give a complete solution to the problem in the case the connection is one induced by a (definite or indefi...

Leaky dominant mode propagation regimes of a conductor-backed coplanar strip line are rigorously analyzed using the concept of critical or equilibrium points from catastrophe and bifurcation theories, in conjunction with a full-wave integral equation solution. The existence of nondegenerate or Morse critical points (MCP’s) and degenerate or fold (turning) critical points (FP’s) in coupling and ...

The primary function of the disc is mechanical; therefore, degenerative changes in disc mechanics and the interactions between the annulus fibrosus (AF) and nucleus pulposus (NP) in nondegenerate and degenerate discs are important to functional evaluation. The disc experiences complex loading conditions, including mechanical interactions between the pressurized NP and the surrounding fiber-rein...

core of quantum decoding network and is also the key step of recovery. The definitions of the bit-flip error syndrome matrix and the phase-flip error syndrome matrix were presented, and then the error syndromes of quantum errors were expressed in terms of the columns of the bit-flip error syndrome matrix and the phase-flip error syndrome matrix. It also showed that the error syndrome matrices o...

We give a unified approach to analysing, for each positive integer s, a class of finite connected graphs that contains all the distance transitive graphs as well as the locally s-arc transitive graphs of diameter at least s. A graph is in the class if it is connected and if, for each vertex v, the subgroup of automorphisms fixing v acts transitively on the set of vertices at distance i from v, ...