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Guide rails’ nonlinear dynamic response to the collision process between gangues and the suspended buffer is the basis for its intensity examination and fatigue prediction. This paper established a numerical model for simulating the dynamic response of buffer’s guide rails using Pro/E and Femap based on an analysis of the basic structural components of the suspended buffer. The effects of the gangues diameter and feeding rate on the guide rails’ dynamic response were investigated, which were mainly revealed by a tension in guide rails. Simulation results showed that the tension in guide rails rapidly increased to a peak value after the suspended buffer was impacted by gangues, followed by a periodic vibration. The peak tension, maximum and minimum tensions within the periodic vibration were exponential functions of the gangues diameter. And they depended linearly on the feeding rate. The vibration frequency of the tension in guide rails was an exponential function of the gangues diameter but did not depend on the feeding rate. Based on the backfilling workface parameters used in D.Ping coal miner’s 15601 working panel, the feeding rate of 500 t/h was selected. The diameter of the crushed gangues was selected to be 50 mm based on the strength of guide rails. Their expected service life is 54.2 years. Finally, an industrial test was performed in D.Ping coal miner’s 15601 working panel and the guide rails operated steadily. The measured vibration parameters of the tension in guide rails agree well with that of numerical predictions, which verified the reliability of the numerical model to some extent. [ABSTRACT FROM AUTHOR]

The atom-bond connectivity index (or, for short, ABC index) is a molecular structure descriptor bridging chemistry to graph theory. It is probably the most studied topological index among all numerical parameters of a graph that characterize its topology. For a given graph G = (V, E), the ABC index of G is defined as , where di denotes the degree of the vertex i, and ij is the edge incident to the vertices i and j. A combination of physicochemical and the ABC index properties are commonly used to foresee the bioactivity of different chemical composites. Additionally, the applicability of the ABC index in chemical thermodynamics and other areas of chemistry, such as in dendrimer nanostars, benzenoid systems, fluoranthene congeners, and phenylenes is well studied in the literature. While finding of the graphs with the greatest ABC-value is a straightforward assignment, the characterization of the tree(s) with minimal ABC index is a problem largely open and has recently given rise to numerous studies and conjectures. A B1-branch of a graph is a pendent path of order 2. In this paper, we provide an important step forward to the full characterization of these minimal trees. Namely, we show that a minimal-ABC tree contains neither 4 nor 3 B1-branches. The case when the number of B1-branches is 2 is also considered. [ABSTRACT FROM AUTHOR]