Dessins, their delta-matroids and partial duals

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how delta-matroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of delta-matroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial duals and tropical curves arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14 Conference Proceeding

High Energy Theorems at Large-N

Sum rules for products of two, three and four QCD currents are derived using chiral symmetry at infinite momentum in the large-N limit. These exact relations among meson decay constants, axialvector couplings and masses determine the asymptotic behavior of an infinite number of QCD correlators. The familiar spectral function sum rules for products of two QCD currents are among the relations derived. With this precise knowledge of asymptotic behavior, an infinite number of large-N QCD correlators can be constructed using dispersion relations. A detailed derivation is given of the exact large-N pion vector form factor and forward pion-pion scattering amplitudes.Comment: 34 pages TeX and mtexsis.tex, 10 figures (uses epsf

Catalog of dessins d'enfants with \le 4 edges

In this work all the dessins d'enfant with no more than 4 edges are listed and their Belyi pairs are computed. In order to enumerate all dessins the technique of matrix model computations was used. The total number of dessins is 134; among them 77 are spherical, 53 of genus 1 and 4 of genus 2. The orders of automorphism groups of all the dessins are also found. Dessins are listed by the number of edges. Dessins with the same number of edges are ordered lexicographically by their lists of 0-valencies. The corresponding matrix model for any list of 0-valencies is given and computed. Complex matrix models for dessins with 1 -- 3 edges are used. For the dessins with 4 edges we use Hermitian matrix model, correlators for which are computed in [1].Comment: 64 pages, 134 figure

Stimulated radiative laser cooling

Building a refrigerator based on the conversion of heat into optical energy is an ongoing engineering challenge. Under well-defined conditions, spontaneous anti-Stokes fluorescence of a dopant material in a host matrix is capable of lowering the host temperature. The fluorescence is conveying away a part of the thermal energy stored in the vibrational oscillations of the host lattice. In particular, applying this principle to the cooling of (solid-state) lasers opens up many potential device applications, especially in the domain of high-power lasers. In this paper, an alternative optical cooling scheme is outlined, leading to radiative cooling of solid-state lasers. It is based on converting the thermal energy stored in the host, into optical energy by means of a stimulated nonlinear process, rather than a spontaneous process. This should lead to better cooling efficiencies and a higher potential of applying the principle for device applications

Anti-Stokes laser cooling in bulk Erbium-doped materials

We report the first observation of anti-Stokes laser-induced cooling in the Er^{3+}:KPb_{2}Cl_{5} crystal and in the Er^{3+}:CNBZn (CdF_{2}-CdCl_{2}-NaF-BaF_{2}-BaCl_{2}-ZnF_{2}) glass. The internal cooling efficiencies have been calculated by using photothermal deflection spectroscopy. Thermal scans acquired with an infrared thermal camera proved the bulk cooling capability of the studied samples. Implications of these results are discussed.Comment: 4 pages, 4 figures. The figures enclosed with this submission are low quality ones. Versions of this paper with high quality figures are available upon reques

Notes for genera: basal clades of Fungi (including Aphelidiomycota, Basidiobolomycota, Blastocladiomycota, Calcarisporiellomycota, Caulochytriomycota, Chytridiomycota, Entomophthoromycota, Glomeromycota, Kickxellomycota, Monoblepharomycota, Mortierellomycota, Mucoromycota, Neocallimastigomycota, Olpidiomycota, Rozellomycota and Zoopagomycota)

Compared to the higher fungi (Dikarya), taxonomic and evolutionary studies on the basal clades of fungi are fewer in number. Thus, the generic boundaries and higher ranks in the basal clades of fungi are poorly known. Recent DNA based taxonomic studies have provided reliable and accurate information. It is therefore necessary to compile all available information since basal clades genera lack updated checklists or outlines. Recently, Tedersoo et al. (MycoKeys 13:1--20, 2016) accepted Aphelidiomycota and Rozellomycota in Fungal clade. Thus, we regard both these phyla as members in Kingdom Fungi. We accept 16 phyla in basal clades viz. Aphelidiomycota, Basidiobolomycota, Blastocladiomycota, Calcarisporiellomycota, Caulochytriomycota, Chytridiomycota, Entomophthoromycota, Glomeromycota, Kickxellomycota, Monoblepharomycota, Mortierellomycota, Mucoromycota, Neocallimastigomycota, Olpidiomycota, Rozellomycota and Zoopagomycota. Thus, 611 genera in 153 families, 43 orders and 18 classes are provided with details of classification, synonyms, life modes, distribution, recent literature and genomic data. Moreover, Catenariaceae Couch is proposed to be conserved, Cladochytriales Mozl.-Standr. is emended and the family Nephridiophagaceae is introduced