相关论文: Special metrics

The last two decades have brought spectacular advances in astrophysics of cosmic rays (CRs) and space- and ground-based astronomy. Launches of missions that employ forefront detector technologies enabled measurements with large effective…

Natural Language Processing (NLP) is witnessing a remarkable breakthrough driven by the success of Large Language Models (LLMs). LLMs have gained significant attention across academia and industry for their versatile applications in text…

This is a non-technical survey of a recent theory of valuations on manifolds constructed in math.MG/0503397, math.MG/0503399, math.MG/0509512, math.MG/0511171 and actually a guide to this series of articles. We review also some recent…

This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…

Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.

Handwritten signatures are biometric traits at the center of debate in the scientific community. Over the last 40 years, the interest in signature studies has grown steadily, having as its main reference the application of automatic…

The search for dark matter is a very wide and active field of research. Many potential hints of dark matter have appeared recently which led to a burst of theoretical activity and model building. I necessarily concentrate here only in some…

In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…

This article is based on papers discussing different aspects of extra dimensional environments. In addition to the results, we review some of the concepts on which models with large extra dimensions are based.

Tracking physical activity reliably is becoming central to many research efforts. In the last years specialized hardware has been proposed to measure movement. However, asking study participants to carry additional devices has drawbacks. We…

We consider the problem of rescaling the lengths of a finite frame thereby transforming it into a tight one. Such frames are called scalable and have received a lot of attention in recent years. In this note we investigate the question in…

This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…

Scientific writing builds upon already published papers. Manual identification of publications to read, cite or consider as related papers relies on a researcher's ability to identify fitting keywords or initial papers from which a…

Ways to access transversity through asymmetry measurements are reviewed. The recent first extraction and possible near future extractions are discussed.

This is an update of, and a supplement to, a 1986 survey paper by the author on basic properties of strong mixing conditions.

Scientific research changed profoundly over the last 30 years, in all its aspects. Scientific publishing has changed as well, mainly because of the strong increased number of submitted papers and because of the appearance of Open Access…

This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…

This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlev\'e equations, for which the developments of the last two…

We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…