Let $$(R,\mathfrak {m})$$ be a Noetherian local ring of prime characteristic p and Q an $$\mathfrak {m}$$ -primary parameter ideal. We give criteria for F-rationality R using the tight Hilbert function $$H^*_Q(n)=\ell (R/(Q^n)^*)$$ coefficient $$e_1^*(Q)$$ polynomial $$P^*_Q(n)=\sum _{i=0}^d(-1)^ie_i^*(Q)\left( {\begin{array}{c}n+d-1-i\\ d-i\end{array}}\right) .$$ obtain lower bound equidimensi...

The unmixed gamma distribution has been used extensively in fitting precipitation data. After the author [l] proposed a mixed distribution for precipitation series where zeros occur this distribution also began to be widely employed. Since it is often necessary to add precipitation, i.e. June plus July, for example, it is a great convenience to be able to accomplish this analytically and so avo...

We discuss our results on scalar glueball decay in the top-down holographic Witten-SakaiSugimoto model for low-energy QCD and compare with available experimental data, which appear to disfavor the glueball candidate f0(1500) but seem to be perfectly consistent with interpreting f0(1710) as a nearly unmixed glueball. The holographic model moreover makes definite predictions for future experiments.