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The resistance between two arbitrary nodes in an innnite square lattice of identical resistors is calculated. The method is generalized to innnite triangular and hexagonal lattices in two dimensions, and also to innnite cubic and hypercubic lattices in three and more dimensions.
In a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging , but in the current paper we go beyond this approximation and perform an exact calculation of the angular integrals. The(More)
The theoretical principles lying behind phase-shift analysis and its ambiguities are explained, rst in the inelastic and then in the elastic cases. Fixed-point theorems are used to show the existence of solutions, while an iterative method is employed to construct alternative solutions. Argand diagrams of some numerical results are presented and references(More)
Motion compensated gated PET image reconstruction methods include joint-reconstruction (JR) and indirect reconstruction (IR) with pre-estimated motion from MRI (MRI-IR). JR suffers from poor PET data quality whereas MRI-IR requires high-quality MRI volumes at each gate. We propose a penalised maximum-likelihood approach combining JR and MRI-IR. Our method(More)
The coupled Dyson-Schwinger equations for the gluon and ghost propagators in QCD are shown to have solutions that correspond to a unique running coupling that has a nite infrared xed point and the expected logarithmic decrease in the ultraviolet. The infrared coupling is large enough to support chiral symmetry breaking; and quarks are not connned, but they(More)
We analyze an equation that arises out of the bifurcation analysis of an improvement of the nonperturbative equations for the electron mass function in quenched quantum electrodynamics. In quasilinear approximation, the integral equation is solved by Mellin transformation, followed by the calculation of the Muskhelishvili index of the resultant singular(More)
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