On Jessen's Inequality for Convex Functions, III

Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

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Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

The principle and models of dynamic programming, V

Inequalities of the Rado-Popoviciu type for functions and their applications

On inverses of the Hölder inequality

This paper presents a survey of the development of inverses of the Cauchy and Hlder inequalities, an approach to establishing bounds for the ratio of weighted means, a proof of equivalence of quoti...

WangChung-Lie

Papers

On Development of Inverses of the Cauchy and Hlder Inequalities