Tikhonov regularization is a popular and effective method for the approximate solution of illposed problems, including Fredholm equations of the first kind. The Tikhonov method works well when the solution of the equation is well-behaved, but fails for solutions with irregularities, such as jump discontinuities. In this paper we develop a method that overcomes the limitations of the standard Ti...

Previously, people thought the effects of quantum corrections on neutrino mass matrix may be negligible, since the Yukawa couplings of neutrinos are much much smaller than other quarks and leptons. However, is it true?? Besides, are “maximal” mixings in the lepton flavor mixing matrix stable against quantum corrections? My talk is concentrating on these topics in the framework of the minimal su...

Recently, sum rules were derived for the inverse eigenvalues of the Dirac operator. They were obtained in two different ways: i) starting from the low-energy effective Lagrangian and ii) starting from a random matrix theory with the symmetries of the Dirac operator. This suggests that the effective theory can be obtained directly from the random matrix theory. Previously, this was shown for thr...