Pauli-blocking Effect in a Quark Model

Pauli-Blocking effect on the kinetic term is investigated by employing the quark cluster model. The effect can be understood by the change of the degrees of the mixing between the incoming wave and the 0$\ell$ state of the inter-cluster wave function, which can be expressed by a potential which is highly nonlocal. We look into the properties of this effect by comparing equivalent local potentials. In the channel where the Pauli-blocking effect is small, the on-shell equivalent local potential simulates the nonlocal potential well even for the off-shell behavior. On the other hand, the off-shell behavior is very different from the original one where the effect is large. This off-shell behavior, however, can well be simulated by considering the nonlocal matrix elements only between the $0s$ state and the other states. The energy dependent potentials are also constructed and found to be helpful to understand the energy dependence of the effect.Comment: 14 pages, 12 figure

Coincidence sets in quasilinear elliptic problems of monostable type

This paper concerns the formation of a coincidence set for the positive solution of $p$-Laplacian elliptic problems of monostable type. It is proved that for any small parameter of diffusion term, the solution coincides with the stable zero-function $a(x)$ of reaction term in an open set if $a(x)$ is $p$-harmonic (but, not constant) and a zero of order less than 1. Inversely, it is also shown that the solution is less than $a(x)$ if $a(x)$ is a zero of order greater than or equal to 1. The proof rely on comparison theorems and an energy method for obtaining local comaprison functions.Comment: 18 page

Bifurcation values of polynomial functions and perverse sheaves

We characterize bifurcation values of polynomial functions by using the theory of perverse sheaves and their vanishing cycles. In particular, by introducing a method to compute the jumps of the Euler characteristics with compact support of their fibers, we confirm the conjecture of N\'emethi-Zaharia in many cases.Comment: 19 pages, to appear in Annales de l'Institut Fourie