Ethyl 1-(4-meth­oxy­benz­yl)-3-p-tolyl-1H-pyrazole-5-carboxyl­ate

In the title compound, C21H22N2O3, the pyrazole ring makes dihedral angles of 12.93 (8) and 69.38 (8)°, respectively, with the tolyl and meth­oxy­benzyl rings

Momentum-dependence of ρ−ω\rho-\omega mixing in the pion vector form factor and its effect on (g−2)μ(g-2)_\mu

The inclusion of the $\rho-\omega$ mixing effect is crucial for a good description of the pion electromagnetic form factor in the $e^+e^- \rightarrow \pi^+\pi^-$ process, which quantifies the two-pion contribution to the anomalous magnetic moment of the muon $a_\mu$. In this paper, we try to analyze the impact of the momentum-dependence of the $\rho-\omega$ mixing within the framework of resonance chiral theory. The momentum-dependence of the $\rho-\omega$ mixing is incorporated due to the calculation of loop contributions at the next-to-leading order in the $1/N_C$ expansion. The work of {[}Y. H. Chen, D. L. Yao, and H. Q. Zheng, Commun. Theor. Phys. 69 (2018) 1{]} is revisited taking into account the contribution due to the kaon mass splitting in the kaon loops and the latest experimental data. We perform two kinds of fits (with momentum-independent or momentum-dependent $\rho-\omega$ mixing amplitude) describing the $e^+e^-\rightarrow \pi^+\pi^-$ and $\tau\rightarrow \nu_{\tau}2\pi$ data in the energy region of 600$\sim$900 MeV and the decay width of $\omega \rightarrow \pi^+\pi^-$, and compare their results. It is found that taking account of the momentum-dependence of $\rho-\omega$ mixing can describe the pion vector form factor data a little better. For the contribution to the anomalous magnetic moment of the muon $a_\mu^{\pi\pi}|_{[0.6,0.9]\text{GeV}}$, the values of the results in the fits considering the momentum-dependent $\rho-\omega$ mixing amplitude are agree well with those in the fits without including the momentum-dependence of the $\rho-\omega$ mixing within errors. In addition, based on the fitted values of the involved parameters, we find that in the decay width of $\omega \rightarrow \pi^+\pi^-$ the contribution from the direct $\omega_I\pi\pi$ coupling is comparable with the contribution due to the $\rho-\omega$ mixing.Comment: 21 pages, 4 figures. arXiv admin note: text overlap with arXiv:1710.1144

TOWARDS A WORLD DISCIPLINE: INTERNATIONALIZING TRADITIONAL CHINESE MEDICINE IN UNIVERSITIES IN MAINLAND CHINA AND HONG KONG

Ph.DDOCTOR OF PHILOSOPH

Adaptive neural control of MIMO nonlinear systems with a block-triangular pure-feedback control structure

This paper presents adaptive neural tracking control for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. All subsystems within these MIMO nonlinear systems are of completely nonaffine purefeedback form and allowed to have different orders. To deal with the nonaffine appearance of the control variables, the mean value theorem (MVT) is employed to transform the systems into a block-triangular strict-feedback form with control coefficients being couplings among various inputs and outputs. A systematic procedure is proposed for the design of a new singularityfree adaptive neural tracking control strategy. Such a design procedure can remove the couplings among subsystems and hence avoids the possible circular control construction problem. As a consequence, all the signals in the closed-loop system are guaranteed to be semiglobally uniformly ultimately bounded (SGUUB). Moreover, the outputs of the systems are ensured to converge to a small neighborhood of the desired trajectories. Simulation studies verify the theoretical findings revealed in this work