Momentum space conformal three-point functions of conserved currents and a general spinning operator

We construct conformal three-point functions in momentum space with a general tensor and conserved currents of spin $1$ and $2$. While conformal correlators in momentum space have been studied especially in the connection with cosmology, correlators involving a tensor of general spin and scaling dimension have not been studied very much yet. Such a direction is unavoidable when we go beyond three-point functions because general tensors always appear as an intermediate state. In this paper, as a first step, we solve the Ward-Takahashi identities for correlators of a general tensor and conserved currents. In particular we provide their expression in terms of the so-called triple-$K$ integrals and a differential operator which relates triple-$K$ integrals with different indices. For several correlators, closed forms without the differential operator are also found.Comment: 24+16 page

Synaptic contribution to the production of the plateau formation of the biopotential of somatic neuromembranes treated with convulsants: experiment on the identified giant neurone of a snail's subesophageal ganglion-complex

I) On an identified giant neurone of the right parietal ganglion in a snail's subesophageal ganglion-complex, the synaptic contribution to the production of the plateau formation of biopotential or grouped spike discharges of the soma has been studied in the presence of a convulsant. 2) The orthodromic stimulation of a peripheral nerve (the intestinal nerve) can elicit the plateau formation of biopotential, instead of normal spike discharges, in the identified neurone treated with a convulsant. 3) With the application of a convulsant, for example bemegride which was in a concentration less than that necessary to produce the plateau formation, an EPSP accompanied a spike with a constant delay. This EPSP is a product of a proprioceptive reflex arc consisting of two excitatory synapses with a certain subordinate neurone. 4) Later, in the presence of a convulsant, spontaneously conveyed multiple EPSP's were observed on the biopotential of the identified neurone. These multiple EPSP's produced grouped spike discharges or the plateau formation of biopotential of the neurone. 5) The multiple EPSP's may be produced by the grouped spike discharges of the subordinate neurone, the membrane property of which would be changed by a convulsant. It is presumed that the grouped spike discharges or the plateau formation of biopotential often occurs synchron. ously in many neighboring neurones by means of synaptic triggering in the presence of a convulsant.</p

Ternary and quaternary Lennard-Jones atomic clusters : The effects of atomic sizes on the compositions, geometries, and relative stability

Global-minimum geometries of ternary and quaternary Lennard-Jones clusters have been calculated with constraints on atomic compositions of the clusters. In the present study, the constraints were removed to obtain optimal compositions. The size ratios of the largest-sized atom to the smallest-sized one ranged from 1.1 to 1.6 whereas the depths of the interatomic potentials were constant. The heuristic method combined with the geometrical perturbations and atom-type conversion was used to search for the global minima of the clusters with up to 50 atoms. The smallest-sized and largest-sized atoms usually occupy cores and outer shells, respectively, and the atoms with intermediate sizes are often lacking. The size ratio has pronounced effects on the compositions, structures, and relative stability of the clusters