Integer solutions of a sequence of decomposable form inequalities

In this paper, we prove the finiteness of the number of integer solutions of the decomposable form inequalities. We also study the number of integer solutions of a sequence of decomposable form inequalities

Entire functions sharing simple aa-points with their first derivative

We show that if a complex entire function $f$ and its derivative $f'$ share their simple zeroes and their simple $a$-points for some nonzero constant $a$, then $f\equiv f'$. We also discuss how far these conditions can be relaxed or generalized. Finally, we determine all entire functions $f$ such that for 3 distinct complex numbers $a_1,a_2,a_3$ every simple $a_j$-point of $f$ is an $a_j$-point of $f'$.Comment: v3: 11 pages, corrected a typo in Theorem 2', updated address; refereed version, but note that the journal version carries my old address and has a finer division into sections and a different numbering of the theorem

Studying Double Charm Decays of B_{u,d} and B_{s} Mesons in the MSSM with R-parity Violation

Motivated by the possible large direct CP asymmetry of \bar{B}^0_d \to D^+ D^- decay measured by Belle collaboration, we investigate double charm B_{u,d} and B_s decays in the minimal supersymmetric standard model with R-parity violation. We derive the bounds on relevant R-parity violating couplings from the current experimental data, which show quite consistent measurements among relative collaborations. Using the constrained parameter spaces, we explore R-parity violating effects on other observables in these decays, which have not been measured or have not been well measured yet. We find that the R-parity violating effects on the mixing-induced CP asymmetries of \bar{B}^0_d \to D^{(*)+} D^{(*)-} and \bar{B}^0_s \to D^{(*)+}_s D^{(*)-}_s decays could be very large, nevertheless the R-parity violating effects on the direct CP asymmetries could not be large enough to explain the large direct CP violation of \bar{B}^0_d \to D^{+} D^{-} from Belle. Our results could be used to probe R-parity violating effects and will correlate with searches for direct R-parity violating signals in future experiments.Comment: 28 pages and 6 figures, matches published versio