经典统计力学中幂级数系数的表示。它们的分类和复杂性标准
Representations of coefficients of power series in classical statistical mechanics. Their classification and complexity criteria
摘要：
指出经典统计力学幂级数系数简化表示的目的是简化利用其简化表示求系数估计的过程。文章的目的是：制定复杂性的标准，（从上述观点出发）对经典统计力学幂级数系数的表示进行了研究，并通过比较维里系数的Ree-Hoover表示的例子来说明它们的应用（简称RH表示）与基于标号图的框架分类概念的幂级数系数表示进行了比较（缩写-- FC）。为了解决这些问题，引入了数学概念（如基本乘积、基本积分、基本线性组合、具有不显著复杂系数的基本线性组合（简称BLC with CIC）），并提出了经典统计力学幂级数系数表示的分类。在分类中，具有CIC的BLC类是最重要的。它包含了经典统计力学幂级数系数的上述所有表示。给出了BLC与CIC比较复杂性的三个判据。这些标准按其准确性排序。基于这些准则，我们构造了一个BLC与CIC的有限集的比较复杂性准则。所构造的准则按其准确性排序。通过比较RH表示与基于FC概念的幂级数系数表示的例子，证明了所有构造的准则的应用。所获得的结果列于表中并进行了评论。
英文摘要：
It is declared that the aim of simplifying representations of coefficients of power series of classical statistical mechanics is to simplify a process of obtaining estimates of the coefficients using their simplified representations. The aim of the article is: to formulate criteria for the complexity (from the above point of view) of representations of coefficients of the power series of classical statistical mechanics and to demonstrate their application by examples of comparing the Ree-Hoover representations of virial coefficients (briefly -- the RH representations) with such representations of power series coefficients that are based on the conception of the frame classification of labeled graphs (the abbreviation -- FC). To solve these problems, mathematical notions were introduced (such as a basic product, a basic integral, a basic linear combination, a basic linear combination with coefficients of insignificant complexity(the abbreviation -- BLC with CIC) and the classification of representations of the coefficients of power series of classical statistical mechanics is proposed. In the classification, the class of BLC's with CIC is the most important. It includes all the above representations of the coefficients of power series of classical statistical mechanics. Three criteria are formulated for estimate the comparative complexity of BLC's with CIC. These criteria are ordered by their accuracy. Based on each of these criteria, a criterion for the comparative complexity of finite sets of BLC's with CIC is constructed. The constructed criteria are ordered by their accuracy. The application of all the constructed criteria is demonstrated by examples of comparing RH representations with the representations of the power series coefficients based on the concept FC. The obtained results are presented in the tables and commented.
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