Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes

We give a definition of weak n-categories based on the theory of operads. We work with operads having an arbitrary set S of types, or `S-operads', and given such an operad O, we denote its set of operations by elt(O). Then for any S-operad O there is an elt(O)-operad O+ whose algebras are S-operads over O. Letting I be the initial operad with a one-element set of types, and defining I(0) = I, I(i+1) = I(i)+, we call the operations of I(n-1) the `n-dimensional opetopes'. Opetopes form a category, and presheaves on this category are called `opetopic sets'. A weak n-category is defined as an opetopic set with certain properties, in a manner reminiscent of Street's simplicial approach to weak omega-categories. Similarly, starting from an arbitrary operad O instead of I, we define `n-coherent O-algebras', which are n times categorified analogs of algebras of O. Examples include `monoidal n-categories', `stable n-categories', `virtual n-functors' and `representable n-prestacks'. We also describe how n-coherent O-algebra objects may be defined in any (n+1)-coherent O-algebra.Comment: 59 pages LaTex, uses diagram.sty and auxdefs.sty macros, one encapsulated Postscript figure, also available as a compressed Postscript file at http://math.ucr.edu/home/baez/op.ps.Z or ftp://math.ucr.edu/pub/baez/op.ps.

Introduction to special section: Active Fault-Related Folding: Structural Evolution, Geomorphologic Expression, Paleoseismology, and Seismic Hazards

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Investigation of wrought steel railway car wheels : part I, tests of strength properties of wrought steel car wheels

Cover title.Prepared as part of an investigation conducted by the Engineering Experiment Station, University of Illinois at Urbana-Champaign

Stress concentration at fillets, holes, and keyways as found by the plaster-model method

Bibliography: p. 31-32

Changes in Small Mammal Community Attributes Associated with Increasing Pine Stand Age in Managed Pine Plantations in Southeastern Virginia

Loblolly pine plantations were examined at different ages to identify small mammal community attributes in relation to the succession of the plant community. Forest floor and understory plant communities were characterized. Small mammals were collected by Fitch (live) traps and pitfall traps in four age classes during five seasons of study. Fitch live traps and pitfall traps were used in conjunction with one another to obtain the most accurate depiction of the small mammal community. Fitch traps accounted for 65 % of small mammal captures and 7 of 9 species captured. Small mammal abundance and biomass declined with increasing stand age probably because of increasing plant community homogeneity. However, species diversity and evenness increased with increasing stand age. Although species diversity increased with increasing stand age, there were no significant differences among stands. Increasing evenness is probably the result of scarce and dispersed food supplies supporting low small mammal abundances, but having high evenness among small mammal species due to low abundances. Relative proportions of small mammal trophic groups changed after crown closure. Small mammals that prefer early successional habitats disappeared after crown closure. The golden mouse was the only consistently found rodent in stands after crown closure. However, after selective cutting and self thinning had occurred in late-age stands small mammals that prefer forested habitats and those preferring early successional habitats were found in the same stands. No significant trends of decreasing capture success was found in the trap data due to too few replicates. However, mean small mammal captures decreased from 41 to 14 over the five trapping periods

Extended leaves of absence for the professional improvement of public-school educators

Thesis (Ed.D.)--Boston University