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The goal of this paper is to extend the existence result of measure-valued solution to the Boltzmann equation in elastic interaction, given by Morimoto–Wang–Yang in (J Stat Phys 165:866–906, 2016), to the inelastic Boltzmann equation with moderately soft potentials, which is also an extensive work of our preceding result in the inelastic Maxwellian molecules case. We first prove the existence and uniqueness of measure-valued solution under Grad’s angular cutoff assumption, based on which, we further obtain the existence of non-cutoff solution, for both finite and infinite energy initial datum, by a delicate compactness argument. In addition, the moments propagation and energy dissipation properties are justified for the obtained measure-valued solution as well. [ABSTRACT FROM AUTHOR]

As an increasing number of scientific literature dataset are open access, more attention has gravitated to keyword analysis in many scientific fields. Traditional keyword analyses include the frequency based and the network based methods, both providing efficient mining techniques for identifying the representative keywords. The semantic meanings behind the keywords are important for understanding the research content. However, traditional keyword analysis methods pay scant attention to semantic meanings; the network based or frequency based methods as traditionally used, present limited semantic associations among the keywords. Moreover, the ways in which the semantic meanings behind the keywords are associated to the citations are not clear. Thus, we use the Google Word2Vec model to build word vectors and reduce them to a two-dimensional plane in a Voronoi diagram using the t-SNE algorithm, to link meanings with citations. The distance between semantic meanings of keywords in two-dimensional plane are similar to distances in geographical space, thus we introduce a geographic metaphor, “Ghost City” to describe the relationship between semantics and citations for hot topics that have recently become not so hot. Along with “Ghost City” zones, “Always Hot”, “Newly Emerging Hot”, and “Always Silent” areas are classified and mapped, describing the spatial heterogeneity and homogeneity of the semantic distribution of keywords cited in a domain database. Using a collection of “geographical natural hazard” literature datasets, we demonstrate that the proposed method and classification scheme can efficiently provide a unique viewpoint for interpreting the interaction between semantics and the citations, as “Ghost City”, “Always Hot”, “Newly Emerging Hot”, and “Always Silent” areas. [ABSTRACT FROM AUTHOR]

In bibliometric research, keyword analysis of publications provides an effective way not only to investigate the knowledge structure of research domains, but also to explore the developing trends within domains. To identify the most representative keywords, many approaches have been proposed. Most of them focus on using statistical regularities, syntax, grammar, or network-based characteristics to select representative keywords for the domain analysis. In this paper, we argue that the domain knowledge is reflected by the semantic meanings behind keywords rather than the keywords themselves. We apply the Google Word2Vec model, a model of a word distribution using deep learning, to represent the semantic meanings of the keywords. Based on this work, we propose a new domain knowledge approach, the Semantic Frequency-Semantic Active Index, similar to Term Frequency-Inverse Document Frequency, to link domain and background information and identify infrequent but important keywords. We adopt a semantic similarity measuring process before statistical computation to compute the frequencies of “semantic units” rather than keyword frequencies. Semantic units are generated by word vector clustering, while the Inverse Document Frequency is extended to include the semantic inverse document frequency; thus only words in the inverse documents with a certain similarity will be counted. Taking geographical natural hazards as the domain and natural hazards as the background discipline, we identify the domain-specific knowledge that distinguishes geographical natural hazards from other types of natural hazards. We compare and discuss the advantages and disadvantages of the proposed method in relation to existing methods, finding that by introducing the semantic meaning of the keywords, our method supports more effective domain knowledge analysis. [ABSTRACT FROM AUTHOR]