Diophantine approximation by special primes

We show that whenever $\delta>0$, $\eta$ is real and constants $\lambda_i$ satisfy some necessary conditions, there are infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality $|\lambda_1p_1 + \lambda_2p_2 + \lambda_3p_3+\eta|<(\max p_j)^{-1/12+\delta}$ and such that, for each $i\in\{1,2,3\}$, $p_i+2$ has at most $28$ prime factors

Left-handed nuclei

The orientation of the angular momentum vector with respect to the triaxial density distribution selects a left-handed or right-handed system principal axes. This breaking of chiral symmetry manifests itself as pairs of nearly identical $\Delta I=1$-bands. The chiral structures combine high-j particles and high-j holes with a triaxial rotor. Tilted axis cranking calculations predict the existence of such configurations in different mass regions. There is experimental evidence in odd-odd nuclei around mass 134. The quantized motion of the angular momentum vector between the left- and right-handed configurations, which causes the splitting between the chiral sister bands, can be classified as tunneling (chiral rotors) or oscillation (chiral vibrators).Comment: Invited lecture at the Conference on Frontiers of Nuclear Structure, Berkeley, 200