Reduction of mm-Regular Noncrossing Partitions

In this paper, we present a reduction algorithm which transforms $m$-regular partitions of $[n]=\{1, 2, ..., n\}$ to $(m-1)$-regular partitions of $[n-1]$. We show that this algorithm preserves the noncrossing property. This yields a simple explanation of an identity due to Simion-Ullman and Klazar in connection with enumeration problems on noncrossing partitions and RNA secondary structures. For ordinary noncrossing partitions, the reduction algorithm leads to a representation of noncrossing partitions in terms of independent arcs and loops, as well as an identity of Simion and Ullman which expresses the Narayana numbers in terms of the Catalan numbers

Charmless two-body B decays: A global analysis with QCD factorization

In this paper, we perform a global analysis of $B \to PP$ and $PV$ decays with the QCD factorization approach. It is encouraging to observe that the predictions of QCD factorization are in good agreement with experiment. The best fit $\gamma$ is around $79^\circ$. The penguin-to-tree ratio $|P_{\pi \pi}/T_{\pi \pi}|$ of $\pi^+ \pi^-$ decays is preferred to be larger than 0.3. We also show the confidence levels for some interesting channels: $B^0 \to \pi^0 \pi^0$, $K^+ K^-$ and $B^+ \to \omega \pi^+$, $\omega K^+$. For $B \to \pi K^\ast$ decays, they are expected to have smaller branching ratios with more precise measurements.Comment: 20 pages, 4 figures, version to appear in Phys. Rev.

Quantum reliability

Quantum technology has led to increasingly sophisticated and complex quantum devices. Assessing their reliability (quantum reliability) is an important issue. Although reliability theory for classical devices has been well developed in industry and technology, a suitable metric on quantum reliability and its loss has not been systematically investigated. Since reliability-loss depends on the process, quantum fidelity does not always fully depict it. This study provides a metric of quantum reliability by shifting the focus from state-distinguishing to trajectory-distinguishing. In contrast to the conventional notion of classical reliability, which is evaluated using probabilistic measurements of binary logical variables, quantum reliability is grounded in the quantum probability amplitude or wave function. This research provides a universal framework for reliability theory encompassing both classical and quantum devices. It offers a new perspective on quantum engineering by elucidating how intensely the real quantum process a device undergoes influences its performance.Comment: 5 pages, 3 figures. Comments welcome

Testing QCD factorisation and charming penguins in charmless B→PV{\boldsymbol{B\to PV}}

We try a global fit of the experimental branching ratios and CP-asymmetries of the charmless $B\to PV$ decays according to QCD factorisation. We find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. The main reason for this failure is the difficulty to accomodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in $\bar {B^0}\to\rho^+ \pi^-$, which is predicted very small by QCD factorisation. Trying a fit with QCD factorisation complemented by a charming-penguin inspired model we reach a best fit which is not excluded by experiment (CL of about 8 %) but is not fully convincing. These negative results must be tempered by the remark that some of the experimental data used are recent and might still evolve significantly.Comment: 21 pages, 4 figures; several typos corrected, added one footnote and two references, comments added about PQCD. To appear in Phys.Rev.

Boundary States in Graphene Heterojunctions

A new type of states in graphene-based planar heterojunctions has been studied in the envelope wave function approximation. The condition for the formation of these states is the intersection between the dispersion curves of graphene and its gap modification. This type of states can also occur in smooth graphene-based heterojunctions.Comment: 5 pages, 3 figure