论文标题
经典统计力学中功率序列系数表示的复杂性。他们的分类和复杂性标准
Complexity of representations of coefficients of power series in classical statistical mechanics. Their classification and complexity criteria
论文作者
论文摘要
宣布，简化电源系列经典统计力学系数的表示的目的是简化使用其简化表示的系数估算的过程。本文的目的是：为这些表示形式的复杂性（从上述角度）制定标准，并通过比较病毒系数的REE-HOOVER表示的示例来证明其应用，以及基于标记图框架分类的概念的功率系数的这种表示。 为了解决这些问题，引入了数学概念（例如基本产品，基础积分，积分的基础线性组合，积分的基础线性组合，具有可忽略不计的复杂性系数，一组积分的基础线性组合，具有可忽略不可综合性的系数的基础线性组合）；并提出了一系列经典统计力学系数系数的表示。在此分类中，具有可忽略的复杂性系数的积分的基础线性组合是最重要的类。它包括经典统计力学功率系列系数的最著名表示。 制定了三个标准，以估计积分的基础线性组合的比较复杂性，具有可忽略不计的复杂性系数及其扩展到具有可忽略的复杂性系数的积分基碱基线性组合的总数。所有构建标准的应用是通过相互比较的示例来证明的。获得的结果在表中显示并评论。
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 these representations and to demonstrate their application by examples of comparing Ree-Hoover representations of virial coefficients and such representations of power series coefficients that are based on the conception of the frame classification of labeled graphs. To solve these problems, mathematical notions were introduced (such as a base product, a base integral, a base linear combination of integrals, a base linear combination of integrals with coefficients of negligible complexity, a base set of base linear combinations of integrals with coefficients of negligible complexity); and a classification of representations of coefficients of power series of classical statistical mechanics is proposed. In this classification the class of base linear combinations of integrals with coefficients of negligible complexity is the most important class. It includes the most well-known representations of the coefficients of power series of classical statistical mechanics. Three criteria are formulated to estimate the comparative complexity of base linear combinations of integrals with coefficients of negligible complexity and their extensions to the totality of base sets of base linear combinations of integrals with coefficients of negligible complexity are constructed. The application of all the constructed criteria is demonstrated by examples of comparing with each other of the above power series coefficients representations. The obtained results are presented in the tables and commented.
