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 powers of the infrared behaviour of the propagators are changed substantially. We find the very intriguing result that the gluon propagator vanishes in the infrared exactly like p 2 , whilst the ghost propagator is exactly as singular as 1/p 4 . We also find that the value of the infrared fixed point of the QCD coupling is much decreased from the y-max estimate: it is now equal to 4π/3. Schwinger equations for the gluon and ghost form factors F and G. The approximations were two-fold: firstly the vertices were taken bare, and secondly angular averaging was introduced (the so-called y-max approximation). Deferring to later work an improvement of the vertices, in this paper we seek to remove the deficiency of the y-max approximation. On the one hand the results might be regarded simply as quantitative adjustments to the y-max calculations; but on the other hand they are far from negligible. The numerical value of the infrared fixed point is reduced by a factor of almost three; and the finding that the gluon propagator has a simple zero, while the ghost propagator has a double pole, might perhaps be deemed a qualitatively new result.As an improvement on the y-max approximation used in Ref.[2], we now solve the coupled integral equations for the gluon and ghost propagators with an exact treatment of the angular 1 atkinson@phys.rug.nl 2 bloch@phys.rug.nl 1

A recent claim that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole, is investigated analytically and numerically. This picture is shown to be supported even at the level in which the vertices in the Dyson-Schwinger equations are taken to be bare. The running coupling is shown to be uniquely determined by the equations and to have a large finite infrared limit.

The resistance between two arbitrary nodes in an infinite square lattice of identical resistors is calculated. The method is generalized to infinite triangular and hexagonal lattices in two dimensions, and also to infinite cubic and hypercubic lattices in three and more dimensions.

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Somatosensation as a proximal sense can have a strong impact on our attitude toward physical objects and other human beings. However, relatively little is known about how hedonic valence of touch is processed at the cortical level. Here we investigated the electrophysiological correlates of affective tactile sensation during caressing of the right forearm with pleasant and unpleasant textile fabrics. We show dissociation between more physically driven differential brain responses to the different fabrics in early somatosensory cortex – the well-known mu-suppression (10–20 Hz) – and a beta-band response (25–30 Hz) in presumably higher-order somatosensory areas in the right hemisphere that correlated well with the subjective valence of tactile caressing. Importantly, when using single trial classification techniques, beta-power significantly distinguished between pleasant and unpleasant stimulation on a single trial basis with high accuracy. Our results therefore suggest a dissociation of the sensory and affective aspects of touch in the somatosensory system and may provide features that may be used for single trial decoding of affective mental states from simple electroencephalographic measurements.