Framed vertex operator algebras, codes and the moonshine module

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1/2 are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras.Comment: Latex, 54 page

WHEN PRICES MISS THE MARK: METHODS FOR VALUING ENVIRONMENTAL CHANGE

Environmental Economics and Policy,

Low-Temperature Deformation of Mixed Siliciclastic & Carbonate Fault Rocks of the Copper Creek, Hunter Valley, and McConnell Thrusts

This study analyzes the low-temperature deformation of fault rocks associated thrust faults. Each fault has dominantly carbonate rocks in one wall and dominantly siliciclastic rocks in the other. The rocks from the Hunter Valley and Copper Creek thrusts of the Southern Appalachians, and McConnell thrust of the Canadian Rockies, were analyzed using data extracted at the thin section and SEM scale. The rocks, all of which featured a fine-grained carbonate matrix surrounding larger carbonate and siliciclastic carbonates, all experienced general shearing, but deformed by different deformation mechanisms. The Hunter Valley and McConnell samples showed evidence of cataclasis, diffusive mass transfer, diffusion accommodated grain boundary sliding and, in the case of the Hunter Valley fault rocks dislocation creep. The Copper Creek samples, by contrast, deformed primarily via plastic processes such as diffusion mass transfer and dislocation creep, and showed no evidence of cataclasis. Within the Hunter Valley and McConnell fault rocks, brittle processes such as cataclasis seemed to dominate at the thin section scale but SEM data supported ductile deformation of the fine matrix material. In each case, analysis of fabrics defined by grain orientations found that the rocks were deformed under general shear conditions and moderate convergence angles, although the Hunter Valley rocks showed evidence for a strong simple shear component of strain and relatively low (37° to 48°) while rocks from the Copper Creek and McConnell thrusts experienced roughly equal pure and shear strain components and showed evidence for higher convergence angles (51° to 59° and 61° to 68°, respectively). The findings of this study highlight the complicated nature of fault rock deformation as well as the difficulty of situating fault rocks within schemes of fault rock nomenclature, which are largely genetic in nature

The solar dynamic radiator with a historical perspective

A historical perspective on pumped-fluid loop space radiators provides a basis for the design of the Space Station Solar Dynamic (SD) power module radiator. SD power modules, capable of generating 25 kW (electrical) each, are planned for growth in Station power requirements. The Brayton cycle SD module configuration incorporates a pumped-fluid loop radiator that must reject up to 99 kW (thermal). The thermal/hydraulic design conditions in combination with required radiator orientation and packaging envelope form a unique set of constraints as compared to previous pumped-fluid loop radiator systems. Nevertheless, past program successes have demonstrated a technology base that can be applied to the SD radiator development program to ensure a low risk, low cost system

Modelling a New Product Model on the Basis of an Existing STEP Application Protocol

During the last years a great range of computer aided tools has been generated to support the development process of various products. The goal of a continuous data flow, needed for high efficiency, requires powerful standards for the data exchange. At the FZG (Gear Research Centre) of the Technical University of Munich there was a need for a common gear data format for data exchange between gear calculation programs. The STEP standard ISO 10303 was developed for this type of purpose, but a suitable definition of gear data was still missing, even in the Application Protocol AP 214, developed for the design process in the automotive industry. The creation of a new STEP Application Protocol or the extension of existing protocol would be a very time consumpting normative process. So a new method was introduced by FZG. Some very general definitions of an Application Protocol (here AP 214) were used to determine rules for an exact specification of the required kind of data. In this case a product model for gear units was defined based on elements of the AP 214. Therefore no change of the Application Protocol is necessary. Meanwhile the product model for gear units has been published as a VDMA paper and successfully introduced for data exchange within the German gear industry associated with FVA (German Research Organisation for Gears and Transmissions). This method can also be adopted for other applications not yet sufficiently defined by STEP.