In this paper, Betti numbers are evaluated for several classes of graphs whose complements are bipartite graphs. Relations are established for the general case, and counting formulae are given in several particular ca...In this paper, Betti numbers are evaluated for several classes of graphs whose complements are bipartite graphs. Relations are established for the general case, and counting formulae are given in several particular cases, including the union of several mutually disjoint complete graphs.展开更多
Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral ...Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of aK（n）,This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sumwhere K1 and K2 are two different quadratic fields.展开更多
文摘提出了基于AFS(Axiomatic Fuzzy Set)理论的模糊聚类分析算法(FCA_AFS),并且给出了聚类有效性指标。该指标能够判断合理的聚类数,而且能给出达到最高准确率的参数值。与其他算法比较:FCA_AFS算法主要通过模糊概念及其逻辑运算求出描述每类特征的模糊集,然后用这些具有确切语义的模糊集来确定每个样本归属的类。规避了其他模糊聚类算法涉及的复杂优化问题,同时不需要事先给出聚类数。在著名数据集-Iris、Wine、Wisconsin Breast Cancer的应用说明该算法实用、有效。
基金This research was supported by the National Natural Science Foundation of China （Grant No. 11271250）.
文摘In this paper, Betti numbers are evaluated for several classes of graphs whose complements are bipartite graphs. Relations are established for the general case, and counting formulae are given in several particular cases, including the union of several mutually disjoint complete graphs.
基金supported by the Fundamental Research Funds for the Central Universities(No.14QNJJ004)
文摘Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of aK（n）,This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sumwhere K1 and K2 are two different quadratic fields.
