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We introduce an all-optical system, termed the "lying mirror", to hide input information by transforming it into misleading, ordinary-looking patterns that effectively camouflage the underlying image data and deceive the observers. This…
We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-K\"{a}hler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the…
We give a survey on old and new results concerning Arnold's strange duality. We show that most of the features of this duality continue to hold for the extension of it discovered by C. T. C. Wall and the author. The results include…
We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations on a mirror surface which have interesting structure as seen…
We report on recent progress in understanding mirror symmetry. Some of more recent generalizations and applications are also presented. --- A contribution to the Proceedings of ``Strings 2001'' at Mumbai, India.
This is a survey on special metrics. We shall present some results and open questions on special metrics mainly appeared in the last 10 years
We propose a survey of the literature about archaeological and geophysical researches and on the paleoclimatology of the basin of Titicaca Lake, in connection with the agricultural system of the raised fields. Here again we discuss the use…
This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search for bodies that are, in a sense, close to invisible. We…
We review the discovery of reflection positivity. We also explain a new geometric approach and proof of the reflection positivity property.
Characterizations for Riemannian submersions to be harmonic or biharmonic are shown. Examples of biharmonic but not harmonic Riemannian submersions are shown.
Earthworks appear in the satellite images of deforested sections of the Amazon Basin. These images, and several other archaeological evidences, are showing that a lost civilization is waiting for further researches.
We describe the tropical mirror for complex toric surfaces. In particular we provide an explicit expression for the mirror states and show that they can be written in enumerative form. Their holomorphic germs give an explicit form of good…
A tomography experiment using muon cosmic rays was conducted on an archaeological site in Greece, a tumulus. This contribution presents issues related to the simulation of the experiment and of the site, using tools commonly used in…
Following previous works on ancient myths in Greek and Latin literature regarding Ursa Major, and the possible relation with the ancient shape of the constellation, we discuss further this case in the light of the evolution of Homo sapiens…
We construct a coordinate system fitting the geometry of a given, cylindrically symmetric, magnetic field.
We propose a conjecture on integrality property of the open-closed mirror maps of compact Calabi-Yau manifolds. Some examples are presented.
Almost 80 years have passed since Trumpler's analysis of the Galactic open cluster system laid one of the main foundations for understanding the nature and structure of the Milky Way. Since then, the open cluster system has been recognised…
We show the possibility to entangle radiation modes through a simple reflection on a moving mirror. The model of an optical cavity having a movable end mirror, and supporting different modes is employed. The mechanical motion of the mirror…
Advanced observational facilities allow to trace back the chemical evolution of the Universe, on the one hand, from local objects of different ages and, secondly, by direct observations of redshifted objects. The chemical enrichment serves…
The problem of localization of megalithic memorials on the Earth surface is investigated. It is pointed on existence of Great Belt of megalithic observatories - of con- centration of astronomically significant objects near geographical…