Asymptotics of polynomials orthogonal over circular multiply connected domains

Let $D$ be a domain obtained by removing, out of the unit disk $\{z:|z|<1\}$, finitely many mutually disjoint closed disks, and for each integer $n\geq 0$, let $P_n(z)=z^n+\cdots$ be the monic $n$th-degree polynomial satisfying the planar orthogonality condition $\int_D P_n(z)\overline{z^m}dxdy=0$, $0\leq m<n$. Under a certain assumption on the domain $D$, we establish asymptotic expansions and formulae that describe the behavior of $P_n(z)$ as $n\to\infty$ at every point $z$ of the complex plane. We also give an asymptotic expansion for the squared norm $\int_D|P_n|^2dxdy$

Letter from James Erwin to James B. Finley

Erwin responds to Finley\u27s letter concerning the whereabouts of Dr. Early. It seems that Early was at the Conference but left with a certain Dr. Taylor the day the Conference broke up. It has been rumored that he went to Mississippi but no one is certain. Where is he? Erwin had thought Early a pious and zealous man and was sorry to learn otherwise. Abstract Number - 106https://digitalcommons.owu.edu/finley-letters/1104/thumbnail.jp

Fuel-rich catalytic combustion: A fuel processor for high-speed propulsion

Fuel-rich catalytic combustion of Jet-A fuel was studied over the equivalence ratio range 4.7 to 7.8, which yielded combustion temperatures of 1250 to 1060 K. The process was soot-free and the gaseous products were similar to those obtained in the iso-octane study. A carbon atom balance across the catalyst bed calculated for the gaseous products accounted for about 70 to 90 percent of the fuel carbon; the balance was condensed as a liquid in the cold trap. It was shown that 52 to 77 percent of the fuel carbon was C1, C2, and C3 molecules. The viability of using fuel-rich catalytic combustion as a technique for preheating a practical fuel to very high temperatures was demonstrated. Preliminary results from the scaled up version of the catalytic combustor produced a high-temperature fuel containing large amounts of hydrogen and carbon monoxide. The balance of the fuel was completely vaporized and in various stages of pyrolysis and oxidation. Visual observations indicate that there was no soot present

A study of participation in the Eastern Massachusetts Chapter of National Association of Social Workers

Thesis (M.S.)--Boston Universit

Epithelial cell specific Raptor is required for initiation of type 2 mucosal immunity in small intestine

AbstractIntestinal tuft cells are one of 4 secretory cell linages in the small intestine and the source of IL-25, a critical initiator of the type 2 immune response to parasite infection. When Raptor, a critical scaffold protein for mammalian target of rapamycin complex 1 (mTORC1), was acutely deleted in intestinal epithelium via Tamoxifen injection in Tritrichomonas muris (Tm) infected mice, tuft cells, IL-25 in epithelium and IL-13 in the mesenchyme were significantly reduced, but Tm burden was not affected. When Tm infected mice were treated with rapamycin, DCLK1 and IL-25 expression in enterocytes and IL-13 expression in mesenchyme were diminished. After massive small bowel resection, tuft cells and Tm were diminished due to the diet used postoperatively. The elimination of Tm and subsequent re-infection of mice with Tm led to type 2 immune response only in WT, but Tm colonization in both WT and Raptor deficient mice. When intestinal organoids were stimulated with IL-4, tuft cells and IL-25 were induced in both WT and Raptor deficient organoids. In summary, our study reveals that enterocyte specific Raptor is required for initiating a type 2 immune response which appears to function through the regulation of mTORC1 activity.</jats:p