29 research outputs found
A new Hardy–Mulholland-type inequality with a mixed kernel
By the use of weight coefficients and techniques of real analysis, we establish a new Hardy–Mulholland-type inequality with a mixed kernel and a best possible constant factor in terms of the hypergeometric function. Equivalent forms, an operator expression with the norm and reverses are also considered
Vector Centrality in Hypergraphs
Identifying the most influential nodes in networked systems is of vital
importance to optimize their function and control. Several scalar metrics have
been proposed to that effect, but the recent shift in focus towards network
structures which go beyond a simple collection of dyadic interactions has
rendered them void of performance guarantees. We here introduce a new measure
of node's centrality, which is no longer a scalar value, but a vector with
dimension one lower than the highest order of interaction in a hypergraph. Such
a vectorial measure is linked to the eigenvector centrality for networks
containing only dyadic interactions, but it has a significant added value in
all other situations where interactions occur at higher-orders. In particular,
it is able to unveil different roles which may be played by the same node at
different orders of interactions -- information that is otherwise impossible to
retrieve by single scalar measures. We demonstrate the efficacy of our measure
with applications to synthetic networks and to three real world hypergraphs,
and compare our results with those obtained by applying other scalar measures
of centrality proposed in the literature.Comment: 10 pages, 9 figure
Discrete mathematics and applications
Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research. Each chapter presents new methods and techniques by leading experts. Unifying interdisciplinary applications, problems, and approaches of discrete mathematics, this book connects topics in graph theory, combinatorics, number theory, cryptography, dynamical systems, finance, optimization, and game theory. Graduate students and researchers in optimization, mathematics, computer science, economics, and physics will find the wide range of interdisciplinary topics, methods, and applications covered in this book engaging and useful
Trigonometric sums and their applications
This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research