Tree–level scattering amplitudes of particles have a geometrical description in terms intersection numbers pairs twisted differential forms on the moduli space Riemann spheres with punctures. We customize catalog containing both already known and new forms. By pairing elements from this list various theories can be furnished to compute their amplitudes. Some latter are familiar through CHY desc...

The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function.

Self-energy corrections involving logarithms of the parameter Zα can often be derived within a simplified approach , avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by α the fine-structure constant). For some logarithmic corrections, it is sufficient to ...

Self-energy corrections involving logarithms of the parameter Zα can often be derived within a simplified approach , avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by α the fine-structure constant). For some logarithmic corrections, it is sufficient to ...

In this talk, I survey several Q-linear relations for multiple L-values of Arakawa-Kaneko type. T. Arakawa and M. Kaneko proved in 2004 the so-called derivation relation, which is proved as a corollary of the regularized double shuffle relation. Kaneko firstly formulated an extension of the derivation relation by modeling a Hopf algebra introduced by A. Connes and H. Moscovici. G. Kawashima and...

In this paper, the derivation of likelihood function for parameter estimation based on double ranked set sampling (DRSS) designs used by Sabry el.al.; (2019) parameters power generalized Weibull distribution is considered. The developed then exponential Pareto parameters. maximum estimators (MLEs) are investigated and compared to corresponding ones simple random (SRS) (RSS) designs. A Monte Car...