The consistency of estimator under fixed design regression model with NQD errors

In this article, basing on NQD samples, we investigate the fixed design nonparametric regression model, where the errors are pairwise NQD random errors, with fixed design points, and an unknown function. Nonparametric weighted estimator will be introduced and its consistency is studied. As special case, the consistency result for weighted kernel estimators of the model is obtained. This extends the earlier work on independent random and dependent random errors to NQD case

Prediction of a missing higher charmonium around 4.26 GeV in J/ψJ/\psi family

Inspired by the similarity of mass gaps of $J/\psi$ and $\Upsilon$ families, the prediction of missing higher charmonium with mass $4263$ MeV and very narrow width is made. In addition, the properties of two charmonium-like states, $X(3940)$ and $X(4160)$, and charmonium $\psi(4415)$ are discussed. Here, $X(3940)$ as $\eta_c(3S)$ is established while the explanation of $X(4160)$ to be $\eta_c(4S)$ is fully excluded and $\eta_c(4S)$ is typically a very narrow state. These predictions can be accessible at BESIII, Belle and BelleII in near future.Comment: 5 pages, 5 figures and 1 table. More discussions added. Accepted by Eur. Phys. J.

Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach

From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method