Andreev's Theorem on hyperbolic polyhedra

In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of Andreev's Theorem, because Andreev's paper has the reputation of being ``unreadable''.Comment: To appear les Annales de l'Institut Fourier. 47 pages and many figures. Revision includes significant modification to section 4, making it shorter and more rigorous. Many new references include

Effects of diversity on beneficial and pest arthropods

Vegetational diversity within agroecosystems can vary in in three basic ways; the species richness of plants, the spatial arrangement of species and the temporal relationship among species. Agroecosystems with greater vegetational diversity are associated with decreased pest abundance and increased natural enemy abundance. The objectives of this dissertation were to test the effect of farming practices that alter vegetational diversity on beneficial arthropod communities and pest insects. Farming practices investigated included the addition rye cover crop (Secale cereale L.) to corn (Zea mays L.) and the use of extended crop rotations. Two separate studies were conducted on experimental plots to compare the effects of the addition of a rye cover crop and extended crop rotations against practices that lacked diversity on epigeal and canopy, beneficial arthropod communities. In both studies we hypothesized that practices that increased vegetational diversity would positively affect beneficial arthropods. Only modest differences were observed in the composition and abundance of beneficial arthropods with the addition of a rye cover crop and none were detected among crop rotations with different lengths. Two on-farm studies were conducted to quantify the effects rye cover crop and the use of extended crop rotations on insect pests of corn. Farming practices, corn root injury and abundance of Diabrotica spp. were compared among cornfields that differed in the frequency of crop rotation and previous pest injury. Root injury and abundance of Diabrotica spp. were similar among cornfields, however, fields that had a history of crop rotation required significantly fewer pest management inputs. In the second study, the abundance of early season insect pests and injury to corn were compared between fields with and without a rye cover crop. Although adult moths were captured around all cornfields, significantly greater abundance of Mythimna unipuncta and greater proportion of defoliated corn were found in fields where corn followed a rye cover crop

Cables and connectors for Large Space System Technology (LSST)

The effect of the environment and extravehicular activity/remote assembly operations on the cables and connectors for spacecraft with metallic and/or nonmetallic structures was examined. Cable and connector philosophy was outlined for the electrical systems and electronic compartments which contain high-voltage, high-power electrical and electronic equipment. The influence of plasma and particulates on the system is analyzed and the effect of static buildup on the spacecraft electrical system discussed. Conceptual cable and connector designs are assessed for capability to withstand high current and high voltage without danger of arcs and electromagnetic interference. The extravehicular activites required of the space station and/or supply spacecraft crew members to join and inspect the electrical system, using manual or remote assembly construction are also considered

Ground/bonding for Large Space System Technology (LSST)

The influence of the environment and extravehicular activity remote assembly operations on the grounding and bonding of metallic and nonmetallic structures is discussed. Grounding and bonding philosophy is outlined for the electrical systems and electronic compartments which contain high voltage, high power electrical and electronic equipment. The influence of plasma and particulate on the system was analyzed and the effects of static buildup on the spacecraft electrical system discussed. Conceptual grounding bonding designs are assessed for capability to withstand high current arcs to ground from a high voltage conductor and electromagnetic interference. Also shown were the extravehicular activities required of the space station and or supply spacecraft crew members to join and inspect the ground system using manual on remote assembly construction

Admission mixing duct assembly

A variable cycle jet engine is provided with a mixing duct assembly which mixes core engine exhaust gas with bypass air when the engine is operating in a turbofan mode and which blocks flow from the core engine and isolates the core engine from the bypass flow when the engine is operating as a ramjet

Scenes and Adventures, as a Soldier and Settler During Half a Century

https://commons.und.edu/settler-literature/1148/thumbnail.jp