Search for sterile neutrinos in holographic dark energy cosmology: Reconciling Planck observation with the local measurement of the Hubble constant

We search for sterile neutrinos in the holographic dark energy cosmology by using the latest observational data. To perform the analysis, we employ the current cosmological observations, including the cosmic microwave background temperature power spectrum data from the Planck mission, the baryon acoustic oscillation measurements, the type Ia supernova data, the redshift space distortion measurements, the shear data of weak lensing observation, the Planck lensing measurement, and the latest direct measurement of $H_0$ as well. We show that, compared to the $\Lambda$CDM cosmology, the holographic dark energy cosmology with sterile neutrinos can relieve the tension between the Planck observation and the direct measurement of $H_0$ much better. Once we include the $H_0$ measurement in the global fit, we find that the hint of the existence of sterile neutrinos in the holographic dark energy cosmology can be given. Under the constraint of the all-data combination, we obtain $N_{\rm eff}= 3.76\pm0.26$ and $m_{\nu,\rm sterile}^{\rm eff}< 0.215\,\rm eV$, indicating that the detection of $\Delta N_{\rm eff}>0$ in the holographic dark energy cosmology is at the $2.75\sigma$ level and the massless or very light sterile neutrino is favored by the current observations.Comment: 10 pages, 4 figures; typos corrected, published in PR

The signless Laplacian spectral radius of graphs without trees

Let $Q(G)=D(G)+A(G)$ be the signless Laplacian matrix of a simple graph of order $n$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix of $G$, respectively. In this paper, we present a sharp upper bound for the signless spectral radius of $G$ without any tree and characterize all extremal graphs which attain the upper bound, which may be regarded as a spectral extremal version for the famous Erd\H{o}s-S\'{o}s conjecture.Comment: 12 page

A novel tread model for tire modelling using experimental modal parameters

Modal parameter model acts as an analytical model of tire, because it can represent the entire tire characteristics, when applied to the tire modelling. However, without considering the effect of transfer characteristics of adjacent tread spring elements, the accuracy of modal parameter model may be limited in previous studies. Based on contact mechanics and the modal parameter model, a novel tread model is proposed considering tread transfer characteristics, and then a modified model using the modal parameters was obtained using the novel tread model. The effects of tire external characteristics were analyzed by modifying the modal parameter static vertical model. Finally, the experimental and calculated data were compared, the proposed tread model improved the accuracy of calculation. The results show that the tread transfer characteristics significantly affect contact length, i.e., by improving the predictive accuracy by 50 %, and the effect on improving the squat of tire can be ignored. The developed model may help to optimize tire modelling