Excluding a precise list of groups like alternating, symmetric, cyclic and dihedral, from 1st year algebra (§7.2.3), we expect there are only finitely many monodromy groups of primitive genus 0 covers. Denote this nearly proven genus 0 problem as Problem 2 . We call the exceptional groups 0-sporadic. Example: Finitely many Chevalley groups are 0-sporadic. A proven result: Among polynomial 0-spo...

Schnyder woods are a well-known combinatorial structure for plane triangulations, which yields a decomposition into 3 spanning trees. We extend here definitions and algorithms for Schnyder woods to closed orientable surfaces of arbitrary genus. In particular, we describe a method to traverse a triangulation of genus g and compute a so-called g-Schnyder wood on the way. As an application, we giv...

The species of the genus Charisius Champion, from Mexico and Central America are reviewed. The flightless genus Narses Champion, with one included species, N. subalatus Champion, is placed in synonymy with the genus Charisius. Four new species are described and illustrated, C. granulatus and C. punctatus (from Guatemala) and C. apterus and C. howdenorum (from Mexico). Charisius subalatus (Champ...

The genus Chalcasthenes Arrow (Dynastinae: Oryctoderini), a scarab beetle genus endemic to the Solomon Islands, is reviewed. Based on examination of type specimens, the genus Strehlia Frey (Rutelinae: Rutelini: Parastasiina) is a new junior synonym of Chalcasthenes. The historical classification of these genera (either in the subfamily Dynastinae or Rutelinae) and character-based criteria for a...

A compact hyperbolic surface of genus g is said to be extremal if it admits an extremal disc, a disc of the largest radius determined only by g. We discuss how many extremal discs are embedded in non-orientable extremal surfaces of genus 6. This is the final genus in our interest because it is already known for g = 3, 4, 5, or g > 6. We show that non-orientable extremal surfaces of genus 6 admi...

Surface parameterization establishes bijective maps from a surface onto a topologically equivalent standard domain. It is well known that the spherical parameterization is limited to genus-zero surfaces. In this work, we design a new parameter domain, two-layered sphere, and present a framework for mapping high genus surfaces onto sphere. This setup allows us to transfer the existing applicatio...

A new genus and species, Undulopsychopsis alexigen. et sp. n., is described from the Early CretaceousYixian Formation of western Liaoning Province, China. This genus is probably most closely related to the Asian Cretaceous genus Kagapsychops Fujiyama, 1978. The family affinity of Undulopsychopsisgen. n. is discussed. The genus is preliminarily assigned to Psychopsidae, although it shares some c...

Molecular and morphological evidence is presented to support the description of a second species of Pseudophilothrips from Brazil in association with Schinus terebinthifolius, an invasive weedy tree in North America. Pseudophilothrips is here recognized as a weakly defined genus comprising 13 described species from the Americas. This genus is presumably derived from within, rather than sister-g...

BACKGROUND The records of genus Bubopsis McLachlan, 1898 with species Bubopsis tancrei Weele, 1908 and the genus Nousera Navás, 1923 with species Nousera gibba Navás, 1923 have not been published in China. NEW INFORMATION The genus Bubopsis McLachlan, 1898 with species Bubopsis tancrei Weele, 1908 and the genus Nousera Navás, 1923 with species Nousera gibba Navás, 1923 are recorded for the fi...