Banks-Zaks fixed point analysis in momentum subtraction schemes

The Banks - Zaks Expansion and “ Freezing ” in Perturbative QCD

The recent calculation of the four-loop β-function in QCD provides further evidence that the Banks-Zaks expansion in 16 1 2 −nf is sufficiently well behaved to be useful even for nf ≈ 2 light flavours. This expansion inherently predicts “freezing” of the QCD couplant at low energies as a perturbative effect. We consider the e+e− and Bjorken-sum-rule cases as examples.

Fixed-Point Arithmetic in SHE Schemes

The purpose of this paper is to investigate fixed point arithmetic in ring-based Somewhat Homomorphic Encryption (SHE) schemes. We provide three main contributions: Firstly, we investigate the representation of fixed point numbers. We analyse the two representations from Dowlin et al, representing a fixed point number as a large integer (encoded as a scaled polynomial) versus a polynomial-based...

Termination criteria for inexact fixed-point schemes

We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point iteration. Important applications are the Picard iteration and partitioned fluid structure interaction. We prove that the iteration converges irrespective of ho...

Fixed-analysis adaptive-synthesis filter banks

S parameter and parity doubling below the conformal window