Coherent System of Models for a Family of Modular Curves

Modular curves of the form X0(N) are intrinsically interesting curves to investigate. They contain a wealth of information and cross over the boundaries of geometric, algebraic, and analytic mathematics. We set out to compute all of the information for a specific family of related modular curves, namely X0(N) for those integers N dividing 36. In this paper, we work out the parameters for the curves, the coordinates of the important points in relation to those parameters, and then we find equations for the important maps between the curves. Also, since X0(36) has genus one, and therefore has a natural group structure, we include a brief section on the subgroup generated by its cusps

Verlinde K-theory.

This thesis concerns computations of twisted equivariant K-theory functors evaluated on certain spaces. In the second chapter, for simple, ompact, simply-connected Lie groups G, I determine K^{tau+h}_(LBG) ^X= R^{tau}(LG)^_I as an abelian group, where R^{tau}(LG) is the representation ring of projective, positive energy representations of LG, and (PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86341/1/kneedan_1.pd

Seeing Community for the Trees: The Links among Contact with Natural Environments, Community Cohesion, and Crime

Individuals may be losing touch with nature as their contact with it decreases worldwide. Although the consequences for people's personal well-being outcomes are becoming well documented, there is almost no research examining the social correlates of contact with nature. This article used a large nationally representative sample to link objective (percent greenspace) and subjective measurements of contact with nature, community cohesion, and local crime incidence. The perceived quality, views, and amount of time spent in nature were linked to more community cohesion, and in turn, the perception of cohesive communities enhanced individual well-being outcomes and contributions back to society through higher workplace productivity and environmentally responsible behaviors. Our findings also indicated that local nature was linked to lower crime both directly and indirectly through its effects on community cohesion

ULTRASONIC ATTENUATION AND VELOCITY CHANGES DURING THE FCC-HCP MARTENSITIC TRANSFORMATION IN COBALT-NICKEL

Measurements were made to search for evidence of widening of extended dislocations as the transformation temperature is approached in a single crystal Co68Ni32 alloy. Specimens were prestressed plastically in shear to introduce dislocations primarily on one slip system. During transformation, measurements were made of longitudinal and shear strain as well as velocity and attenuation at 10 MHz. The sound waves were polarized to excite the "optical" mode of vibration of the two partial dislocations using a (111) [11[MATH]] polarization shear wave. Pre-transformation changes were found which are consistent with a simple model for the effect

COMPLETING VERLINDE ALGEBRAS

Abstract. We compute the completion of the Verlinde algebra of a simply connected simple compact Lie group G at the augmentation ideal of the representation ring. By results of Freed, Hopkins, Teleman and C.Dwyer and Lahtinen, this gives a computation of (non-equivariant) twisted K-theory of the free loop space of BG. 1

The attenuation of lattice vibrations by oscillations of independent and coupled dislocations

U of I OnlyThesi

PHONON-DISLOCATION DIPOLE INTERACTION IN LiF AT LOW TEMPERATURE

We compare the effects of isolated dislocations and a somewhat larger density of edge dislocation dipoles on thermal conductivity, specific heat, and ultrasonic velocity and attenuation in alkali halides such as LiF. The motivation for this study is to check the implications of earlier work where it was demonstrated that the effect of deformation on thermal conductivity in LiF could not be accounted for by dynamic scattering by a dislocation density equal to the etch pit density, but could be fit assuming scattering was due to the "optical" mode of vibration of a much larger density of dislocation dipoles

A MODEL FOR ULTRASONIC EFFECTS DURING AN FCC-HCP MARTENSITIC TRANSFORMATION

It is proposed that the FCC-HCP martensitic phase transformation may be studied ultrasonically by measuring the effect of "optical" vibrations of extended dislocations on the [111] shear sound velocity and attenuation. A simple model for the behavior of such dislocations predicts a dip in velocity and a rise in attenuation as the transformation is approached