## Conclusion

This summer I worked on a mathematical proof. I, working with Professor Johnson, proved that a partial TP (TN) matrix with a border pattern is TP (TN) completable. Though TP and TN are very similar properties, to show their completability require two different proofs. In TN case, we developed a Northwest principle and a (m,n) entry argument to show competability. In TP case, penultimate line insertion was used to show TP competability. The insertion is only possible with a previous theorem proved in S.M. Fallat et al. (2000).

## Hillslope asymmetry update (4)

The last couple of weeks of research was pretty busy. My advisor and I spent some time moving the gamma detection lab from Millington to ISC 3. We have started to set up the detectors that we will use to count the Cesium-137 in the samples in order to help get the erosion rates if you recall. We have 2 detectors currently working, and one waiting to be fixed. These are gamma ray detectors. In order to be able to effectively count, these detectors need to be shielded from natural radiation. That is, there are many common radioactive elements that are decaying in the earth. Unless these are shielded from the detector, the detector would include these rays coming from the ground and the walls in the count, which we don’t want. In order to avoid this we used lead bricks and copper to build an effective shield. We surrounded the detector with a layer of copper first before extending the shield at least 4 inches in every direction with the lead bricks (We did more than 4 inches though for certainty). These lead bricks were generally about 8 by 2 inches and were very heavy. They proved annoying to work with, especially when I had to carry a few across campus to the metal shop (to get cut) in 95-degree weather and 90% humidity. Needless to say I may have temporarily developed back problems. In the end we built a pretty good shield (see picture below). Thankfully for the other detector there was a premade shield and a majority of what we had to do was put the detector in the premade shield. Once in the shield some smaller lead bricks were used to make a shield within the shield. Some copper was also placed over the lead, blocking the lead from the detector directly. It seemed as though the detectors were ready to go and start counting the samples. For these detectors to work they have to be chilled. They are connected to liquid nitrogen tanks that are refilled every couple days. In order to find out if the shields we made were effective, we started out by running a blank for a background count. We put in an empty petri dish, taped and wax sealed, just like the samples. After running background counts on the detectors it seemed as though the shield we built worked pretty well. In the last week I began counting the first of my samples. Unfortunately to get a good count it needs to run for about 24hours. Throughout the Fall semester the samples will be counted and hopefully give us the Cesium data needed to calculate erosion rates on the hill slopes being studied.