Mathematical analysis of the Anderson localization has been facilitated by the use of suitable fractional moments of the Green function. Related methods permit now a readily accessible derivation of a number of physical manifestations of localization, in regimes of strong disorder, extreme energies, or weak disorder away from the unperturbed spectrum. The present work establishes on this basis ...

The multiplicity of a point in the joint numerical range W (A1, A2, A3) ⊆ R is studied for n×n Hermitian matrices A1, A2, A3. The relative interior points of W (A1, A2, A3) have multiplicity greater than or equal to n−2. The lower bound n−2 is best possible. Extreme points and sharp points are studied. Similar study is given to the convex set V (A) := {xT Ax : x ∈ R, x x = 1} ⊆ C, where A ∈ Cn×...

Based on universal arguments it is believed that there is a critical point (E) in QCD on the temperature (T) versus chemical potential (µ) plane, which is of extreme importance for heavy-ion experiments. Using finite size scaling and a recently proposed lattice method to study QCD at finite µ we determine the location of E in QCD with n f =2+1 dynamical staggered quarks with semi-realistic mass...

This paper is concerned with the existence of extreme solutions of the three-point boundary value problem for a class of second order functional differential equations. We introduce new concept of lower and upper solutions. By using the method of upper and lower solutions and monotone iterative technique, we obtain the existence of extreme solutions.