Some Applications of the Bounded Convergence Theorem for an Introductory Course in Analysis

The Arzela bounded convergence theorem is the special case of the Lebesgue dominated convergence theorem in which the functions are assumed to be Riemann integrable

Head and Neck

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/145350/1/cpmia0700.pd

The hard quiescent spectrum of the neutron-star X-ray transient EXO 1745-248 in the globular cluster Terzan 5

We present a Chandra observation of the globular cluster Terzan 5 during times when the neutron-star X-ray transient EXO 1745-248 located in this cluster was in its quiescent state. We detected the quiescent system with a (0.5-10 keV) luminosity of ~2 x 10^{33} ergs/s. This is similar to several other neutron-star transients observed in their quiescent states. However, the quiescent X-ray spectrum of EXO 1745--48 was dominated by a hard power-law component instead of the soft component that usually dominates the quiescent emission of other neutron-star X-ray transients. This soft component could not conclusively be detected in EXO 1745-248 and we conclude that it contributed at most 10% of the quiescent flux in the energy range 0.5-10 keV. EXO 1745-248 is only the second neutron-star transient whose quiescent spectrum is dominated by the hard component (SAX J1808.4-3658 is the other one). We discuss possible explanations for this unusual behavior of EXO 1745-248, its relationship to other quiescent neutron-star systems, and the impact of our results on understanding quiescent X-ray binaries. We also discuss the implications of our results on the way the low-luminosity X-ray sources in globular clusters are classified.Comment: Accepted by ApJ Main Journal, September 22, 2004. Figure 2 is a color figur

XTE J2123-058: A New Neutron Star X-Ray Transient

We report on optical and RXTE observations of a new high-latitude bursting X-ray transient, XTE J2123-058. We identified the optical counterpart, measured the 5.9573 hr orbital period and constrained the binary inclination and the source distance. The distance lower limit indicates that the source is at least 2.6 kpc from the Galactic plane, which is unusual for an LMXB. RXTE observations were made between June and August 1998 during the first detected outburst from this source. We describe correlations between X-ray timing and spectral properties and discuss the possibility that the propeller mechanism turned on during the decay of the outburst. During one of the RXTE observations, we detect a pair of high frequency QPOs at 847.1 +/- 5.5 Hz and 1102 +/- 13 Hz simultaneously. According to the beat frequency model, the QPO separation implies a neutron star spin period near 3.9 ms. As the X-ray flux decreases at the end of the outburst, the amplitude of the optical modulation increases significantly. This behavior can be explained if the size of the accretion disk decreases during the decay of the outburst.Comment: 24 pages, 9 figures, accepted by Ap

Comparing the treatment of endometriosis‐related pain by excision of endometriosis or hysterectomy: A multicentre prospective cohort study

Objective: To compare the effectiveness of endometriosis excision alone to excision plus hysterectomy, with and without bilateral oophorectomy, for endometriosis‐related symptoms. Design: Multicentre prospective cohort. Setting: Eighty‐six specialist endometriosis centres. Population: Women undergoing rectovaginal endometriosis surgery between 2009 and 2021. Methods: We performed multivariable regression with random effects for patient and centre, controlling for age, BMI, smoking, laparoscopic versus open approach and type of bowel surgery performed, with sensitivity analysis for loss to follow‐up. Main Outcome Measures: Pain scores, bowel symptoms and quality‐of‐life measures. Results: Compared to endometriosis excision alone, women undergoing hysterectomy with conservation of ovaries had greater improvement in non‐cyclical pain (MD: 1.41/10, 95% CI: 1.03–1.78, p < 0.001), dyspareunia (MD: 1.12/10, 95% CI: 0.71–1.53, p < 0.001), back pain (MD: 1.29/10, 95% CI: 0.92–1.67, p < 0.001) and quality‐of‐life scores (MD: 8.77/100, 95% CI: 5.79–11.75, p < 0.001) at 24 months post‐operatively. Women undergoing hysterectomy with bilateral oophorectomy also had greater improvement in non‐cyclical pelvic pain (MD: 2.22/10, 95% CI: 1.80–2.63, p < 0.001), dyspareunia (MD: 1.05/10, 95% CI: 0.59–1.52, p < 0.001), back pain (MD: 1.18/10, 95% CI: 0.77–1.59, p < 0.001) and quality of life (MD: 12.41/100, 95% CI: 9.07–15.74, p < 0.001) at 24 months compared to endometriosis excision alone. Compared to hysterectomy with ovarian conservation, hysterectomy with bilateral oophorectomy was associated with greater improvement in non‐cyclical pelvic pain (MD: 0.81/10, 95% CI: 0.32–1.30, p = 0.001) at 24 months and quality of life (MD: 3.74/100, 95% CI: 0.56–6.92, p = 0.021) at 12 months, although this result was sensitive to loss to follow‐up. Conclusions: Patients who undergo endometriosis excision plus hysterectomy experience greater improvement in pain and quality of life compared to those who have endometriosis excision alone. There are additional benefits of bilateral oophorectomy with hysterectomy, although its value is less clear due to loss of follow‐up

Genomic organization and evolution of the ULBP genes in cattle

BACKGROUND: The cattle UL16-binding protein 1 (ULBP1) and ULBP2 genes encode members of the MHC Class I superfamily that have homology to the human ULBP genes. Human ULBP1 and ULBP2 interact with the NKG2D receptor to activate effector cells in the immune system. The human cytomegalovirus UL16 protein is known to disrupt the ULBP-NKG2D interaction, thereby subverting natural killer cell-mediated responses. Previous Southern blotting experiments identified evidence of increased ULBP copy number within the genomes of ruminant artiodactyls. On the basis of these observations we hypothesized that the cattle ULBPs evolved by duplication and sequence divergence to produce a sufficient number and diversity of ULBP molecules to deliver an immune activation signal in the presence of immunogenic peptides. Given the importance of the ULBPs in antiviral immunity in other species, our goal was to determine the copy number and genomic organization of the ULBP genes in the cattle genome. RESULTS: Sequencing of cattle bacterial artificial chromosome genomic inserts resulted in the identification of 30 cattle ULBP loci existing in two gene clusters. Evidence of extensive segmental duplication and approximately 14 Kbp of novel repetitive sequences were identified within the major cluster. Ten ULBPs are predicted to be expressed at the cell surface. Substitution analysis revealed 11 outwardly directed residues in the predicted extracellular domains that show evidence of positive Darwinian selection. These positively selected residues have only one residue that overlaps with those proposed to interact with NKG2D, thus suggesting the interaction with molecules other than NKG2D. CONCLUSION: The ULBP loci in the cattle genome apparently arose by gene duplication and subsequent sequence divergence. Substitution analysis of the ULBP proteins provided convincing evidence for positive selection on extracellular residues that may interact with peptide ligands. These results support our hypothesis that the cattle ULBPs evolved under adaptive diversifying selection to avoid interaction with a UL16-like molecule whilst preserving the NKG2D binding site. The large number of ULBPs in cattle, their extensive diversification, and the high prevalence of bovine herpesvirus infections make this gene family a compelling target for studies of antiviral immunity