Let K be a closed convex cone with dual K∗ in a finite-dimensional real Hilbert space V . A positive operator on K is a linear operator L on V such that L (K) ⊆ K. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. We say that L is a Z-operator on K if 〈L (x), s〉 ≤ 0 for all (x, s) ∈ K ×K such that 〈x, s〉 = 0. The Z-operators are generalizat...

We describe the development of Analytic Perturbation Theory (APT) in QCD, called Fractional APT (FAPT), which has been suggested to apply the renormalization group evolution and QCD factorization technique in the framework of APT. 1 Basics of APT in QCD In the standard QCD Perturbation Theory (PT) we have: ✔ the Renormalization Group (RG) equation das(L)/dL = −as − c1 as − . . . for the effecti...

Let E be an elliptic curve over Q, with L-function LE(s). For any primitive Dirichlet character χ, let LE(s, χ) be the L-function of E twisted by χ. In this paper, we use random matrix theory to study vanishing of the twisted L-functions LE(s, χ) at the central value s = 1. In particular, random matrix theory predicts that there are infinitely many characters of order 3 and 5 such that LE(1, χ)...

Abstract This paper details the theory of edge shear layer collapse as density approaches Greenwald limit. It significantly extends earlier work, which was restricted in applicability. The zonal flow screening length is calculated for banana, plateau and Pfirsch–Schluter regimes. Poloidal field scaling persists regime. Neoclassical drift wave–zonal dynamics are combined a theory, then reduced t...