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The aim of this paper is to examine the topological entropy for a free semigroup action defined by Bufetov using separated and spanning sets. First, this study reveals that such entropy is a topological conjugacy invariant and also can be equivalently defined using open covers. Furthermore, a quantitative analogue of Bowen's theorem for semiconjugacy is provided and we compared the topological entropies presented by Bufetov and Biś. Finally, a formula for the entropy of skew-product transformation with respect to the subshift is obtained. [ABSTRACT FROM PUBLISHER]

Quartz vein-type wolframite deposits are a key type of tungsten deposit that are widely found in the Nanling Metallogenic Belt and surrounding areas of South China. In this contribution, we present an in-situ laser ablation-inductively coupled plasma-mass spectrometry (LA – ICP – MS) analysis of U – Pb isotopes and trace elements of wolframites from the Nanling Region. We generated new wolframite U – Pb ages of 216.49 ± 4.08 Ma (2σ, MSWD = 3.07) and 213.16 ± 4.80 Ma (2σ, MSWD = 1.30) for the Shuiximiao deposit, 163.87 ± 1.36 Ma (2σ, MSWD = 2.46) for the Yaogangxian deposit, and 153.16 ± 5.04 Ma (2σ, MSWD = 1.03) for the Dayishan deposit. On this basis, augmented by published compositional data for wolframites from various deposits in South China, we divided the Nanling Region into three areas with distinctive geochemical fingerprints, i.e. northeastern Guangxi, southern Hunan-eastern Hunan, and southern Jiangxi-northern Guangdong. Further, wolframites from the western part of the Nanling Metallogenic Belt are distinct from those of the eastern part, suggesting heterogeneous ore-forming fluids and variable metallogenic conditions. Wolframites from the Wuyishan Metallogenic Belt bear a strong resemblance to those of similar age from the Nanling Region, suggesting that W mineralization in South China during the Late Jurassic was a region-wide process spanning the Nanling to Wuyishan metallogenic belts. Moreover, differences in the trace-element contents of wolframites in ore-bearing quartz veins and greisen can be used as an effective indicator of genetic evolution and forecaster of the presence of wolframite-bearing quartz veins in the deeper parts of deposits. In summary, the findings of the present study allow us to better identify and comprehend the source of ore-forming fluids and the metallogenic conditions of wolframite formation, providing insights into tungsten metallogenic events in South China. [ABSTRACT FROM AUTHOR]