Books: Kaleidoscopes

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Kaleidoscopes, Chessboards, and Symmetry

This paper describes the n-queens problem on an n × n chessboard. We discuss the possible symmetries of n-queens solutions and show how solutions to this classical chess question can be used to create examples of colorful artwork.

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Modular curves, raindrops through kaleidoscopes

Hoping for a richer supply of phenomena, we should wonder about limits of two-dimensional things (surfaces). It was convenient that all the circles in the solenoids were uniformized compatibly, that is, were compatibly expressed as quotients of R. For ease of description, we choose to look at surfaces X which are quotients of the upper half-plane H in C, with quotient mappings H→ X that fit tog...

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Unstable cavity lasers – from kaleidoscopes to snowflakes

Unstable cavity lasers have linear resonators with inherent magnification whose mode patterns possess fractal characteristics (proportional levels of detail across decimal orders of spatial scale) [1]. The origin of fractality in strip resonators has been explained by considering repeated diffraction of the circulating field at the feedback mirror (which subsequently plays a key role in determi...

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Books, books, books.

IAPR Fellow, shares a personal sketch of his career in statistical pattern recognition. At the end, he poses questions to entice further research. Chart of some upcoming IAPR and non-IAPR workshops, conferences, and summer schools of interest to the I APR community. The views expressed in this newsletter represent the personal views of the authors and not necessarily those of their host institu...

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Spin Singularities: Clifford Kaleidoscopes and Particle Masses

Are particles singularitiesvortex lines, tubes, or sheets in some global ocean of dark energy? We visit the zoo of Lagrangian singularities, or caustics in a spin(4,C) phase flow over compactifed Minkowsky space, M# ≡ S1 × S3, and find that their varieties and energies parallel the families and masses of the elementary particles. Singularities are classified by tensor products of Coxeter groups...

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ژورنال

عنوان ژورنال: British Journal of General Practice

سال: 2020

ISSN: 0960-1643,1478-5242

DOI: 10.3399/bjgp20x712073