Virtual contributions from D∗(2007)0D^{\ast}(2007)^0 and D∗(2010)±D^{\ast}(2010)^{\pm} in the B→DπhB\to D\pi h decays

We study the quasi-two-body decays $B\to D^*h \to D\pi h$ with $h=(\pi, K)$ in the perturbative QCD approach and focus on the virtual contributions from the off-shell $D^{\ast}(2007)^0$ and $D^{\ast}(2010)^{\pm}$ in the four measured decays $\bar B^0 \to D^0\pi^+\pi^-$, $\bar B^0\to D^0\pi^+K^-$, $B^- \to D^+\pi^-\pi^-$ and $B^- \to D^+\pi^-K^-$. For the $\bar B^0 \to D^{*+}\pi^-\to D^0\pi^+\pi^-$ and $\bar B^0\to D^{*+}K^-\to D^0\pi^+K^-$ decays, their branching fractions concentrate in a very small region of $m_{D^0\pi^+}$ near $D^{*+}$ pole mass, and the virtual contributions from $D^{*+}$, in the region $m_{D^0\pi^+}>2.1$ GeV, are about $5\%$ of the corresponding quasi-two-body results. We define two ratios $R_{D^{*+}}$ and $R_{D^{*0}}$, from which we conclude that the flavor-$SU(3)$ symmetry will be maintained for the $B\to D^* h\to D\pi h$ decays with very small breaking at any physical value of the $m_{D\pi}$. The $B^-\to D^{*0}\pi^-\to D^0\pi^0\pi^-$ and $B^-\to D^{*0}K^-\to D^0\pi^0K^-$ decays can be employed as a constraint for the $D^{*0}$ decay width, with preferred values consistent with previous theoretical predictions for this quantity.Comment: 12 pages, 5 figures. Published versio

Relationship between CYP1A1 polymorphisms and invasion and metastasis of breast cancer

AbstractObjectiveTo investigate the relationship between CYP1A1 genetic polymorphisms and the invasion and metastasis of breast cancer.MethodsThe CYP1A1 gene polymorphism (an T-C transversion at nucleotide position 3801) was detected by the polymerase chain reaction and restriction fragment length polymorphism in 80 cases with breast cancer and 60 samples of normal breast tissue. The difference in genotypic distribution frequency between the groups, the correlation between the genotypes and the factors related to prognosis were analyzed.ResultsThe incidence of homozygous and variant genotypes had no difference between the breast cancer group and controls group (P=0.746). The proportion of variant genotype increased as clinical stage (P=0.006) advanced, as well as with increased numbers of lymph node metastases (P=0.010).ConclusionsIn patients with breast cancer there is a correlation between the CYP1A1 CC allele and some factors indicating poor prognosis, including more lymph node metastases as well as a more advanced clinical stage

Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007)