The Loop Theorem using hierarchies

textThis report will build up the machinery of special hierarchies by discussing normal surfaces and boundary patterns. Then the report will use this construction to prove the Loop Theorem, following closely the proof presented by Marc Lackenby.Mathematic

John LueckeThe Loop Theorem using Hierarchies

This report will build up the machinery of special hierarchies by discussing normal surfaces and boundary patterns. Then the report will use this construction to prove the Loop Theorem, following closely the proof presented by Marc Lackenby. iii Table of Content

Structural Studies Of Amorphous Si-Ni-H

It is well know that the transition from an insulator to a metallic conductor may be induced in amorphous semiconductor : metal alloys by increasing the metal concentration above a certain critical limit. However, without a detailed understanding of the changes taking place in the atomic scale structure, it is difficult to ascribe a mechanism to the process. We have investigated the microstructure of one such alloy system, a-Si1-yNiyH, using EXAFS as the principal technique. Thin film samples, prepared by rf co-sputtering, were studied over the composition range 0<y<0.3. Both silicon and nickel K-edge EXAFS results are presented, together with complimentary data from Raman scattering, neutron diffraction and scanning calorimetry experiments. The results indicate that the samples contain two separate amorphous phases: a Ni:Si alloy which is embedded in the surviving, modified a-Si host network. The measured electrical conductivity is discussed in the light of this structural model

Thermal Expansion and Glass Transition Temperatures of Y-Mg-Si-Al-O-N Glasses

.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65315/1/j.1151-2916.1995.tb08922.x.pd