相关论文: Plane Geometry: An Elementary School Textbook (ca.…

The author recalls general tendencies of the "mathematization" of the sciences and derives challenges and tentative obstructions for a successful merger of mathematics and physics on fancied steps towards "Quantum Gravity". This is an…

The utilization of time reversal symmetry in designing and implementing (quantum) optical experiments has become more and more frequent over the past years. We review the basic idea underlying time reversal methods, illustrate it with…

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…

Weihrauch complexity is now an established and active part of mathematical logic. It can be seen as a computability-theoretic approach to classifying the uniform computational content of mathematical problems. This theory has become an…

We develop an inversive geometry for anisotropic quadradic spaces, in analogy with the classical inversive geometry of a Euclidean plane.

In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early…

Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…

This book is intended for teaching Signal Analysis methods and Inverse Problems theory. It is completely open access and will remain free. It is currently illustrated with examples that we have actually encountered in geophysics, but will…

We recall major findings of a systematic investigation of the mathematization of the individual sciences, conducted by the author in Bielefeld some 35 years ago under the direction of Klaus Krickeberg, and confront them with recent…

Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…

In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and…

Lectures by the author at the 1986 Cargese summer school modestly corrected and uploaded for greater accessibility. Some of the author's views on the quantum mechanics of cosmology have changed from those presented here but may still be of…

It is the purpose of the present article to collect arguments for, that there should exist in fact -- although not necessarily yet found -- some law, which imply an adjustment to special features to occur in the future. In our own "complex…

Aerocapture is a technique which uses atmospheric drag to decelerate a spacecraft and achieve nearly fuel-free orbit insertion from an interplanetary trajectory. The present study performs a historical review of the field, and a…

In this paper we discuss how teaching of mathematics for middle school and high school students can be improved dramatically when motivation of concepts and ideas is done through the classical problems and the history of mathematics. This…

The kinematics of particles and rigid bodies in the plane are investigated up to higher-order accelerations. Discussion of point trajectories leads from higher-order poles to higher-order Bresse circles of the moving plane. Symplectic…

The rapid advances in technology over the last decade have significantly altered the nature of engineering knowledge and skills required in the modern industries. In response to the changing professional requirements, engineering…

A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have…

In the mathematical tradition, reversibility requires that the evolution of a dynamical system be a bijective function. In the context of graph rewriting, however, the evolution is not even a function, because it is not even deterministic…

"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers…