The S-integral is a generalized integral of Riemann type which is defined in terms of the Thomson＇s local systems. In this note we prove Gronwall-BeUman＇s inequality for the S-integral. As special cases we also obta...The S-integral is a generalized integral of Riemann type which is defined in terms of the Thomson＇s local systems. In this note we prove Gronwall-BeUman＇s inequality for the S-integral. As special cases we also obtain Gronwall-Bellman＇s inequalities for the Henstock integral and the BurkiU approximately continuous integral.展开更多
For a simple undirected graph G, denote by λ（G） the （0, 1）-adjacency matrix of G. Let the matrix S（G） = J-I-2A（G） be its Seidel matrix, and let SG（A） = det（AI-S（G）） be its Seidel characteristic polynomi...For a simple undirected graph G, denote by λ（G） the （0, 1）-adjacency matrix of G. Let the matrix S（G） = J-I-2A（G） be its Seidel matrix, and let SG（A） = det（AI-S（G）） be its Seidel characteristic polynomial, where I is an identity matrix and J is a square matrix all of whose entries are equal to 1. If all eigenvalues of SG（λ） are integral, then the graph G is called S-integral, In this paper, our main goal is to investigate the eigenvalues of SG（A） for the complete multipartite graphs G = Kn1,n2,...,n,. A necessary and sufficient condition for the complete tripartite graphs Km,n,t and the complete multipartite graphs Km,.... m,n,...,n to be S-integral is given, respectively.展开更多
基金the National Natural Science Foundation of China (10171035)the Natural Science Foundation of Gansu Province (ZS021-A25-004-Z).
文摘The S-integral is a generalized integral of Riemann type which is defined in terms of the Thomson＇s local systems. In this note we prove Gronwall-BeUman＇s inequality for the S-integral. As special cases we also obtain Gronwall-Bellman＇s inequalities for the Henstock integral and the BurkiU approximately continuous integral.
基金Supported by the National Natural Science Foundation of China (No.60863006)Program for New Century Excellent Talents in University (No.06-0912)
文摘For a simple undirected graph G, denote by λ（G） the （0, 1）-adjacency matrix of G. Let the matrix S（G） = J-I-2A（G） be its Seidel matrix, and let SG（A） = det（AI-S（G）） be its Seidel characteristic polynomial, where I is an identity matrix and J is a square matrix all of whose entries are equal to 1. If all eigenvalues of SG（λ） are integral, then the graph G is called S-integral, In this paper, our main goal is to investigate the eigenvalues of SG（A） for the complete multipartite graphs G = Kn1,n2,...,n,. A necessary and sufficient condition for the complete tripartite graphs Km,n,t and the complete multipartite graphs Km,.... m,n,...,n to be S-integral is given, respectively.
