We present the analytic expressions for two-loop form factors production or decay of pseudo-scalar quarkonia, in a scheme where quarks are produced at threshold. consider amplitude process $\gamma \gamma \leftrightarrow {^1S_0^{[1]}}$, that was previously known only numerically, as well processes $gg g {^1S_0^{[8]}}$ and {^1S_0^{[8]}}$, which have not been computed before. The corrections to {^...

This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...

In 1985 Goode and Wainwright devised the concept of an isotropic singularity. Since that time, numerous authors have explored the interesting consequences, in mathematical cosmology, of assuming the existence of this type of singularity. In this paper, we collate all examples of cosmological models which are known to admit an isotropic singularity, and make a number of observations regarding th...

Global visibility of naked singularities is analyzed here for a class of spherically symmetric spacetimes, extending previous studies limited to inhomogeneous dust cloud collapse to more physical valid situations in which pressures are non-vanishing. Existence of nonradial geodesics escaping from the singularity is shown, and the observability of the singularity from far-away observers is discu...

Holographic aspects of 2D Fresnel type memory patterns with 3D couplings and mutual diffractions are considered. Encoding topological charges and spin, the nonlinear interaction potentials are assigned to a shared holographic memory phase space with limited information storage density. Neutral intermediate structures arise in the overlap region. The neutralizing process is regarded as a generat...

The Landau equation and the Boltzmann are connected through limit of grazing collisions. This has been proved rigorously for certain families operators concentrating on In this contribution, we study collision kernels associated to two-particle scattering via a finite range potential $ \Phi(x) in three dimensions. We then consider weak interaction given by \Phi_ \epsilon(x) = \epsilon $. Here \...

The multiaxial Mises-Schleicher and Drucker-Prager unified (MSDPu) criterion has been shown to exhibit several specific features compared other yield failure criteria, including a nonlinear mean stress dependency, influence of the Lode angle, use independent uniaxial compressive tensile strength values absence an apex (singularity) on envelope surface in negative quadrant. However, MSDPu seldom...

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a γ-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show ...