Quasi Regular Polyhedra and Their Duals with Coxeter Symmetries Represented by Quaternions I

In two series of papers we construct quasi regular polyhedra and their duals which are similar to the Catalan solids. The group elements as well as the vertices of the polyhedra are represented in terms of quaternions. In the present paper we discuss the quasi regular polygons (isogonal and isotoxal polygons) using 2D Coxeter diagrams. In particular, we discuss the isogonal hexagons, octagons and decagons derived from 2D Coxeter diagrams and obtain aperiodic tilings of the plane with the isogonal polygons along with the regular polygons. We point out that one type of aperiodic tiling of the plane with regular and isogonal hexagons may represent a state of graphene where one carbon atom is bound to three neighboring carbons with two single bonds and one double bond. We also show how the plane can be tiled with two tiles; one of them is the isotoxal polygon, dual of the isogonal polygon. A general method is employed for the constructions of the quasi regular prisms and their duals in 3D dimensions with the use of 3D Coxeter diagrams.Comment: 22 pages, 16 figure

Leaf trichomes and foliar chemistry mediate defence against glasshouse thrips; Heliothrips haemorrhoidalis (Bouché) in Rhododendron simsii

Herbivore defence mechanisms are a costly diversion of resources away from growth and reproduction. Thus time-limited and tissue specific expression in critical plant parts is more efficient as defined by optimal defence theory. Surprisingly little is known about Rhododendron herbivore defence but it may be mediated by combined chemical and physical mechanisms. Rhododendron simsii Planch. survives cyclic infestations of a leaf-feeding thrips, Heliothrips haemorrhoidalis, which severely damage mature leaves but avoid terminal young leaves suggesting specific, localised defence expression. We examined correlations between the distribution of thrips and feeding damage with density of trichomes and the concentration of the diterpenoid, grayanotoxin I, a compound implicated in but not previously reported to meditate invertebrate defence in Rhododendron. Our data show that as leaves matured the number of thrips and area of feeding damage increased as trichome density and grayanotoxin I concentration decreased, this inverse correlation 10 suggesting trichomes and grayanotoxin I mediate defence in younger leaf tissue. Grayanotoxin I was tested against H. haemorrhoidalis and was toxic to immature life stages and repellent to the adult thrips, reducing numbers of first instars emerging on leaves when applied at ecologically relevant concentrations. This work demonstrates that the pattern of defensive traits in foliage of a species of Rhododendron is key to its ability to tolerate cyclic infestations of a generalist herbivore, effectively conserving vital tissues required for growth and reproduction

Of the importance of a leaf: the ethnobotany of sarma in Turkey and the Balkans

BACKGROUND: Sarma - cooked leaves rolled around a filling made from rice and/or minced meat, possibly vegetables and seasoning plants - represents one of the most widespread feasting dishes of the Middle Eastern and South-Eastern European cuisines. Although cabbage and grape vine sarma is well-known worldwide, the use of alternative plant leaves remains largely unexplored. The aim of this research was to document all of the botanical taxa whose leaves are used for preparing sarma in the folk cuisines of Turkey and the Balkans. Methods: Field studies were conducted during broader ethnobotanical surveys, as well as during ad-hoc investigations between the years 2011 and 2014 that included diverse rural communities in Croatia, Bosnia and Herzegovina, Serbia, Kosovo, Albania, Macedonia, Bulgaria, Romania, and Turkey. Primary ethnobotanical and folkloric literatures in each country were also considered. Results: Eighty-seven botanical taxa, mainly wild, belonging to 50 genera and 27 families, were found to represent the bio-cultural heritage of sarma in Turkey and the Balkans. The greatest plant biodiversity in sarma was found in Turkey and, to less extent, in Bulgaria and Romania. The most commonly used leaves for preparing sarma were those of cabbage (both fresh and lacto-fermented), grape vine, beet, dock, sorrel, horseradish, lime tree, bean, and spinach. In a few cases, the leaves of endemic species (Centaurea haradjianii, Rumex gracilescens, and R. olympicus in Turkey) were recorded. Other uncommon sarma preparations were based on lightly toxic taxa, such as potato leaves in NE Albania, leaves of Arum, Convolvulus, and Smilax species in Turkey, of Phytolacca americana in Macedonia, and of Tussilago farfara in diverse countries. Moreover, the use of leaves of the introduced species Reynoutria japonica in Romania, Colocasia esculenta in Turkey, and Phytolacca americana in Macedonia shows the dynamic nature of folk cuisines. Conclusion: The rich ethnobotanical diversity of sarma confirms the urgent need to record folk culinary plant knowledge. The results presented here can be implemented into initiatives aimed at re-evaluating folk cuisines and niche food markets based on local neglected ingredients, and possibly also to foster trajectories of the avant-garde cuisines inspired by ethnobotanical knowledge

Quaternion-Octonion Analyticity for Abelian and Non-Abelian Gauge Theories of Dyons

Einstein- Schroedinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex, quaternion and octonion spaces in internal gauge groups are shown to describe the consistent field equations and generalized Dirac equation of dyons. It is also shown that quaternion and octonion representations extend the so-called unified theory of gravitation and electromagnetism to the Yang-Mill's fields leading to two SU(2) gauge theories of internal spaces due to the presence of electric and magnetic charges on dyons

CMS physics technical design report : Addendum on high density QCD with heavy ions

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