The existence of an interior extension with critical points on the boundary is proved for a given closed normal curve and for nonnormal curves of specific kind. 2000 Mathematics Subject Classification: 30G12.

We prove a multidimensional extension of Selberg’s central limit theorem for the logarithm of the Riemann zeta function on the critical line. The limit is a totally disordered process, whose coordinates are all independent and Gaussian.

This paper presents an extension of the Poincaré-Hopf theorem to generalized critical points of a function on a compact region with nonsmooth boundary, M , defined by a finite number of smooth inequality constraints. Given a function F M → , we define the generalized critical points of F over M , define the index for the critical point, and show that the sum of the indices of the critical point...

Distinguished selfadjoint extension of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, −|x|. The method uses Hardy-Dirac inequalities and quadratic form techniques.

Journal of Anaesthesia and Critical Care Case Reports 2016 May-Aug;2(2):13-15 Department of anesthesiology, Max Superspeciality Hospital, I.P Extension, Patparganj, New Delhi, India. Address of Correspondence

Fractals at T = T c due to instanton-like configurations Abstract We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter at the critical point (T = T c) we show that instanton-like configurations, corresponding to...