It is discussed how the ideas of entropy and the second law of thermodynamics, conceived long ago during the nineteenth century, underly why cosmological dark matter exists and originated in the first three years of the universe in the form of primordial black holes, a very large number of which have many solar masses including up to the supermassive black holes at the centres of galaxies. Certain upper bounds on dark astrophysical objects with many solar masses based on analysis of the CMB spectrum and published in the literature are criticised. For completeness we discuss WIMPs and axions which are leading particle theory candidates for the constituents of dark matter. The PIMBHs (Primordial Intermediate Mass Black Holes) with many solar masses should be readily detectable in microlensing experiments which search the Magallenic Clouds and measure light curves with durations of from one year up to several years. *

A simple phenomenological model motivated by a two-component duality-like picture is able to fit simultaneously both the scaling breakdown in muoproduction and the high-y anomaly and related effects in neutrino scattering; this suggests that the two are merely different manifestations of the same phenomenon.Recent high-energy experiments at Fermilab, with both muon' and neutrino2 beams, indicate departures from predictions based on exact scaling. Some authors have attempted to compare the data with models based on asymptotic freedom;= others4 have suggested that the anomalies observed for neutrinos a r e due to new-particle production with right-handed currents. The first suggestion does not appear to be completely satisfactory because the magnitude of the scaling breakdown predicted by asymptotically free theories seems to be too small to account for the observed violation^;^ a s for the second suggestion, the presence of large scale breaking in muoproduction i s unaccounted for. In this paper we propose a model of scaling breakdown free from any of the above-mentioned difficulties, providing a satisfactory simultaneous fit for both muon and neutrino scattering data.In 1972 Schildknecht and one of us (J.J.S.) considered a model6 of electroproduction (Model A of Ref. 6) where the Q2 dependence of the Regge residue function i s the same for Pomeron exchange a s for Regge exchange V,A2,. . .) at asymptotically high values of Q2. In that model scaling is broken in such a way that ordinary Regge exchange becomes increasingly unimportant relative to Pomeron exchange by a factor 1 / (~~) ' /~; for example, the en-to-ep ratio approaches unity as Q2 -with x = Q2/2m,v fixed. Even though the argument presented was motivated by generalized vector dominance,' we believe that it is more general. By extending the same line of reasoning and identifying the contribution due to the sea of qq pairs with Pomeron exchange and the valence-quark contribution with Regge exchange, we construct a model of scaling breakdown where the relative importance of the sea vs the valence quarks increases a s Q2 i s raised.To be quantitative, let us first recall how scaling is achieved in scale-invariant Regge models.' In the Regge asymptotic region the structure function F2(Q2, v) can be expanded a swhere ai stands f o r the intercept at t = O of the Regge trajectory of type i. We obtain a scale-invariant structure function by adjusting the Q~ dependence of the residue function 0,(Q2) in such a way that the product fl,(Q2)vat'l becomes a function of v/Q2 only, specifically Suppose we require, instead, that the Q2 dependence of P,(Q2) be the same for Pomeron exchange (a! = 1) as for ordinary Regge exchange (a! = g). This possibility, first suggested within the framework of generalized vector dominance, may perhaps be reasonable if we subscribe to the point of view that it is the amplitude for the current to go into hadronic vector or axial-vector states that determines the Q2 dependence, irrespective of what i s being exchanged in the t channel. Wi...

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A possible strong-interaction Born term for pion-pion scattering is suggested and discussed.The purpose of this paper is to point out the existence of a class of narrow resonance approximations, related to Euler B function models, one of which can provide a realistic Born term for AK scattering.