degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...

We investigate the effect of degenerate atomic states on exciton delocalization dipole-dipole interacting Rydberg assemblies. Using a frozen gas and regular one-, two-, three-dimensional lattice arrangements as examples, we see that degeneracies can enhance compared to situation when there is no degeneracy. Zeeman splitting provided by magnetic field, controllably lift degeneracy study in detai...

We present an analytic study of the dispersion relation for isotropic magnetized plasma interacting with axions. provide a quantitative picture electromagnetic oscillations in both ultrarelativistic and nonrelativistic regimes considering non-degenerate degenerate media, accounting curves as function temperature ratio phase velocity to characteristic particles. include modifications on Landau d...

The degenerate regimes and individuals have been a neglected topic in the literature on Plato’s moral psychology in the Republic. This thesis contributes to the currently limited literature on degradation, and explores the following issues in the interpretation of Plato: the validity of the city-soul analogy across all regimes, including both the just city and the unjust cities, the cause of de...

We, for the first time, report the detection and the size measurement of single nanoparticles (i.e. polystyrene) in aquatic environment using mode splitting in a whispering gallery mode (WGM) optical resonator, namely a microtoroid resonator. Using this method we achieved detecting and measuring individual synthetic hemozoin nanocrystals--a hemoglobin degradation by-product of malarial parasite...

In this paper, the system of Fredholm integral equations of the second kind is investigated by using a modified degenerate kernel  method (MDKM). To construct a MDKM the source function is approximated by the same way of producing degenerate kernel. The interpolation is used to make the needed approximations. Lagrange polynomials are adopted for the interpolation. The equivalency of  proposed m...

In the study of quantum mechanical energy operators, particular attention is paid to the question of whether the bottom of the spectrum is an eigenvalue and whether that eigenvalue is simple. The corresponding eigenvector is usually called the gound state. Throughout our discussion we will say that a self-adjoint operator H has no ground state degeneracy when either E inf spectrum H is not an e...