Maximum entropy controller synthesis for colocated and noncolocated systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77185/1/AIAA-21277-539.pd

Robust Stability Analysis Using the Small Gain, Circle, Positivity, and Popov Theorems: A Comparative Study

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57852/1/SmallGainTCST1993.pd

Low-Temperature Physics

Contains reports on six research projects

AF-algebras and topology of mapping tori

A covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4.Comment: to appear Czechoslovak Math.

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Fate of Kaluza-Klein Bubble

We numerically study classical time evolutions of Kaluza-Klein bubble space-time which has negative energy after a decay of vacuum. As the zero energy Witten's bubble space-time, where the bubble expands infinitely, the subsequent evolutions of Brill and Horowitz's momentarily static initial data show that the bubble will expand in terms of the area. At first glance, this result may support Corley and Jacobson's conjecture that the bubble will expand forever as well as the Witten's bubble. The irregular signatures, however, can be seen in the behavior of the lapse function in the maximal slicing gauge and the divergence of the Kretchman invariant. Since there is no appearance of the apparent horizon, we suspect an appearance of a naked singularity as the final fate of this space-time.Comment: 13 pages including 10 figures, RevTeX, epsf.sty. CGPG-99/12-8, RESCEU-6/00 and DAMTP-2000-30. To appear in Phys. Rev.

Low Temperature Physics

Contains reports on six research projects

Loop corrections for Kaluza-Klein AdS amplitudes

Recently we conjectured the four-point amplitude of graviton multiplets in ${\rm AdS}_5 \times {\rm S}^5$ at one loop by exploiting the operator product expansion of $\mathcal{N}=4$ super Yang-Mills theory. Here we give the first extension of those results to include Kaluza-Klein modes, obtaining the amplitude for two graviton multiplets and two states of the first KK mode. Our method again relies on resolving the large N degeneracy among a family of long double-trace operators, for which we obtain explicit formulas for the leading anomalous dimensions. Having constructed the one-loop amplitude we are able to obtain a formula for the one-loop corrections to the anomalous dimensions of all twist five double-trace operators.Comment: 37 pages. One ancillary file containing data on the correlator

Change in hematologic indices over time in pediatric inflammatory bowel disease treated with azathioprine

Azathioprine leads to changes in mean corpuscular volume (MCV) and white blood cell (WBC) indices reflecting efficacy or toxicity. Understanding the interactions between bone marrow stem cells and azathioprine could highlight abnormal response patterns as forerunners for hematologic malig-nancies. This study gives a statistical description of factors influencing the relationship between MCV and WBC in children with inflammatory bowel disease treated with azathioprine. We found that leukopenia preceded macro¬cytosis. Macrocytosis is therefore not a good predictor of leukopenia. Further studies will be necessary to determine the subgroup of patients at increased risk of malignancies based on bone marrow response