Temperature-dependent cross sections for meson–meson nonresonant reactions in hadronic matter

We present a potential of which the short-distance part is given by one gluon exchange plus perturbative one- and two-loop corrections and of which the large-distance part exhibits a temperature-dependent constant value. The Schrödinger equation with this temperature-dependent potential yields a temperature dependence of the mesonic quark–antiquark relative-motion wave function and of meson masses. The temperature dependence of the potential, the wave function and the meson masses brings about temperature dependence of cross sections for the nonresonant reactions $\pi \pi \to \rho \rho$ for $I=2$, $KK\to K^{*}{K}^{*}$ for $I=1$, $K{K}^{*}\to K^{*}{K}^{*}$ for $I=1$, $\pi K\to \rho K^{*}$ for $I=3/2$, $\pi K^{*}\to \rho K^{*}$ for $I=3/2$, $\rho K\to \rho K^{*}$ for $I=3/2$ and $\pi K^{*}\to \rho K$ for $I=3/2$. As the temperature increases, the rise or fall of peak cross sections is determined by the increased radii of initial mesons, the loosened bound states of final mesons, and the total-mass difference of the initial and final mesons. The temperature-dependent cross sections and meson masses are parametrized.     

Zeros of Wronskians of Hermite polynomials and Young diagrams

For a certain class of partitions, a simple qualitative relation is observed between the shape of the Young diagram and the pattern of zeros of the Wronskian of the corresponding Hermite polynomials. In the case of the two-term Wronskian $W(H_n,H_{n+k})$, we give an explicit formula for the asymptotic shape of the zero set as $n\to \infty$. Some empirical asymptotic formulas are given for the zero sets of three-term and four-term Wronskians.     

Numerically anticanonical divisors on Kato surfaces

The compact curves of an intermediate Kato surface $S$ form a basis of $H^2(S,\mathbb{Q})$. We present a way to compute the associated rational coefficients of the first Chern class $c_1\left(S\right)$. We get in particular a simple geometric obstruction for $c_1\left(S\right)$ to be an integral class, or equivalently index $\left(S\right)=1$. In the final part we discuss relations with some recent work of Dloussky (2011) and Oeljeklaus and Toma (2009).