Power-partible Reduction and Congruences for Schr\"oder Polynomials

In this note, we apply the power-partible reduction to show the following arithmetic properties of large Schr\"oder polynomials $S_n(z)$ and little Schr\"oder polynomials $s_n(z)$: for any odd prime $p$, nonnegative integer $r\in\mathbb{N}$, $\varepsilon\in\{-1,1\}$ and $z\in\mathbb{Z}$ with $\gcd(p,z(z+1))=1$, we have $$\sum_{k=0}^{p-1}(2k+1)^{2r+1}\varepsilon^k S_k(z)\equiv 1\pmod {p}\quad \text{and} \quad \sum_{k=0}^{p-1}(2k+1)^{2r+1}\varepsilon^k s_k(z)\equiv 0\pmod {p}.$$Comment: 1

Effect of Explosive Sources on the Elastic Wave Field of Explosions in Soils

A seismic wave is essentially an elastic wave, which propagates in the soil medium, with the strength of initial elastic wave being created by an explosion source that has a significant effect on seismic wave energy. In order to explore the explosive energy effect on output characteristics of the elastic wave field, four explosives with different work capacity (i.e., TNT, 8701, composition B and THL) were used to study the effects of elastic wave pressure and rise time of stress wave to the peak value of explosions in soils. All the experimental data was measured under the same geological conditions using a self-designed pressure measuring system. This study was based on the analysis of the initial pressure of elastic waves from the energy output characteristics of the explosives. The results show that this system is feasible for underground pressure tests, and the addition of aluminum powder increases the pressure of elastic waves and energy release of explosions in soils. The explosive used as a seismic energy source in petroleum and gas exploration should have properties of high explosion heat and low volume of explosion gas products.Defence Science Journal, 2013, 63(4), pp.376-380, DOI:http://dx.doi.org/10.14429/dsj.63.277

The Study of the Composite Material Go/CF/PTFE Tribological Property

In this paper, the composite material Go/CF/PTFE tribological property was studied. The test of its mechanical property, and the fabrication of the filled PTEE composite material sample which is based on the technology of cold press molding and sinter molding proved that adding Go and CF moderately to the composite material was an efficient way to improve its mechanical property. Meanwhile the process of friction and wear trial and SEM analysis results of the micro-structure of wear pattern proved that the addition of the Go and CF tremendously improved the anti-wear property and that after the addition the plowing effect which took place on the material surface would turn into a kind of mixed wear effect that includes plowing effect and fatigue wear. Working as pinning and bridging, the Go which distributing uniformly in the matrix was able to improve the resistance and substantially resisted the crack propagation, therefore to a certain degree enhanced the intensity of composite material and prolong its lifespan

Edge Charge Asymmetry in Top Pair Production at the LHC

In this brief report, we propose a new definition of charge asymmetry in top pair production at the LHC, namely the edge charge asymmetry (ECA). ECA utilizes the information of drifting direction only for single top (or anti-top) with hadronically decay. Therefore ECA can be free from the uncertainty arising from the missing neutrino in the $t\bar{t}$ event reconstruction. Moreover rapidity $Y$ of top (or anti-top) is required to be greater than a critical value $Y_{\rm C}$ in order to suppress the symmetric $t\bar{t}$ events mainly due to the gluon-gluon fusion process. In this paper ECA is calculated up to next-to-leading order QCD in the standard model and the choice of the optimal $Y_{\rm C}$ is investigated.Comment: 10 pages, 6 figure

Discriminating Different Z′Z^\primes via Asymmetries at the LHC

In practice the asymmetry, which is defined based on the angular distribution of the final states in scattering or decay processes, can be utilized to scrutinize underlying dynamics in and/or beyond the standard model (BSM). As one of the possible BSM physics which might be discovered early at the LHC, extra neutral gauge bosons $Z^\prime$s are theoretical well motivated. Once $Z^\prime$s are discovered at the LHC, it is crucial to discriminate different $Z^\prime$s in various BSM. In principle such task can be accomplished by measuring the angular distribution of the final states which are produced via $Z^\prime$-mediated processes. In the real data analysis, asymmetry is always adopted. In literature several asymmetries have been proposed at the LHC. Based on these works, we stepped further on to study how to optimize the asymmetries in the left-right model and the sequential standard model, as the examples of BSM. In this paper, we examined four kinds of asymmetries, namely rapidity-dependent forward-backward asymmetry, one-side forward-backward asymmetry, central charge asymmetry and edge charge asymmetry (see text for details), with $\ell^+\ell^-$ ($\ell=e,\mu$), $b\bar b$ and $t\bar t$ as the final states. In the calculations with $b\bar b$ and $t\bar t$ final states, the QCD-induced higher order contributions to the asymmetric cross section were also included. For each kind of final states, we estimated the four kinds of asymmetries and especially the optimal cut usually associated with the definition of the asymmetry. Our numerical results indicated that the capacity to discriminate $Z^\prime$ models can be improved by imposing the optimal cuts.Comment: 17 pages, 20 ps file