Algorithms to test open set condition for self-similar set related to P.V. numbers

Fix a P.V. number $\lambda ^{-1}>1.$ Given $\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}$, \mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}, for the self-similar set $E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(\lambda ^{p_{i}}E_{\mathbf{p},\mathbf{b}}+b_{i})$ we find an efficient algorithm to test whether $E_{\mathbf{p},\mathbf{b}}$ satisfies the open set condition (strong separation condition) or not

Study of the weak annihilation contributions in charmless Bs→VVB_s\to VV decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless $B_s\to VV$ (where $V$ stands for a light vector meson) decays, we perform the $\chi^2$-analyses for the end-point parameters within the QCD factorization framework, under the constraints from the measured $\bar B_{s}\to$$\rho^0\phi$, $\phi K^{*0}$, $\phi \phi$ and $K^{*0}\bar K^{*0}$ decays. The fitted results indicate that the end-point parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless $B\to PP$ and $PV$ (where $P$ stands for a light pseudo-scalar meson) decays observed in the previous work. Moreover, the abnormal polarization fractions $f_{L,\bot}(\bar B_{s}\to K^{*0}\bar K^{*0})=(20.1\pm7.0)\%\,,(58.4\pm8.5)\%$ measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of $\bar B_{s}\to\phi K^{*0}$ decay exhibits a tension between the data and theoretical result, which dominates the contributions to $\chi_{\rm min}^2$ in the fits. Using the fitted end-point parameters, we update the theoretical results for the charmless $B_s\to VV$ decays, which will be further tested by the LHCb and Belle-II experiments in the near future.Comment: 31 pages, 4 figures, 6 table

Qubit state tomography in superconducting circuit via weak measurements

The standard method of "measuring" quantum wavefunction is the technique of {\it indirect} quantum state tomography. Owing to conceptual novelty and possible advantages, an alternative {\it direct} scheme was proposed and demonstrated recently in quantum optics system. In this work we present a study on the direct scheme of measuring qubit state in the circuit QED system, based on weak measurement and weak value concepts. To be applied to generic parameter conditions, our formulation and analysis are carried out for finite strength weak measurement, and in particular beyond the bad-cavity and weak-response limits. The proposed study is accessible to the present state-of-the-art circuit-QED experiments.Comment: 7 pages,5figure

Production of single-charm hadrons by quark combination mechanism in pp-Pb collisions at sNN=5.02\sqrt{s_{NN}}=5.02 TeV

If QGP-like medium is created in $p$-Pb collisions at extremely high collision energies, charm quarks that move in the medium can hadronize by capturing the co-moving light quark(s) or anti-quark(s) to form the charm hadrons. Using light quark $p_{T}$ spectra extracted from the experimental data of light hadrons and a charm quark $p_{T}$ spectrum that is consistent with perturbative QCD calculations, the central-rapidity data of $p_{T}$ spectra and the spectrum ratios for $D$ mesons in the low $p_{T}$ range ($p_{T}\lesssim7$ GeV) in minimum-bias $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV are well described by quark combination mechanism in equal-velocity combination approximation. The $\Lambda_{c}^{+}/D^{0}$ ratio in quark combination mechanism exhibits the typical increase-peak-decrease behavior as the function of $p_{T}$, and the shape of the ratio for $p_{T}\gtrsim3$ GeV is in agreement with the preliminary data of ALICE collaboration in central rapidity region $-0.96<y<0.04$ and those of LHCb collaboration in forward rapidity region $1.5<y<4.0$. The global production of single-charm baryons is quantified using the preliminary data and the possible enhancement (relative to light flavor baryons) is discussed. The $p_{T}$ spectra of $\Xi_{c}^{0}$, $\Omega_{c}^{0}$ in minimum-bias events and those of single-charm hadrons in high-multiplicity event classes are predicted, which serves as the further test of the possible change of the hadronization characteristic for low $p_{T}$ charm quarks in the small system created in $p$-Pb collisions at LHC energies.Comment: 13 pages, 8 figure

Migrativity properties of 2-uninorms over semi-t-operators

summary:In this paper, we analyze and characterize all solutions about $\alpha$-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$, $C^{0}_{k}$, $C^{1}_{k}$, $C^{0}_{1}$, $C^{1}_{0}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha$-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^{k}$, the $\alpha$-migrativity of $G$ over a semi-t-operator $F_{\mu,\nu}$ is closely related to the $\alpha$-section of $F_{\mu,\nu}$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_{\mu,\nu}$. But for the other four categories, the $\alpha$-migrativity over a semi-t-operator $F_{\mu,\nu}$ is fully determined by the $\alpha$-section of $F_{\mu,\nu}$