The complex AGM, periods of elliptic curves over C and complex elliptic logarithms

We give an account of the complex Arithmetic-Geometric Mean (AGM), as first studied by Gauss, together with details of its relationship with the theory of elliptic curves over \C, their period lattices and complex parametrisation. As an application, we present efficient methods for computing bases for the period lattices and elliptic logarithms of points, for arbitrary elliptic curves defined over \C. Earlier authors have only treated the case of elliptic curves defined over the real numbers; here, the multi-valued nature of the complex AGM plays an important role. Our method, which we have implemented in both \Magma\ and \Sage, is illustrated with several examples using elliptic curves defined over number fields with real and complex embeddings.Comment: The addional file elog_ex.sage contains a Sage script for the examples in the last section of the paper, and the file elog_ex.out contains the result of running that script with Sage version 5.

Recovery of Water from Boiler Flue Gas Using Condensing Heat Exchangers

Most of the water used in a thermoelectric power plant is used for cooling, and DOE has been focusing on possible techniques to reduce the amount of fresh water needed for cooling. DOE has also been placing emphasis on recovery of usable water from sources not generally considered, such as mine water, water produced from oil and gas extraction, and water contained in boiler flue gas. This report deals with development of condensing heat exchanger technology for recovering moisture from flue gas from coal-fired power plants. The report describes: • An expanded data base on water and acid condensation characteristics of condensing heat exchangers in coal-fired units. This data base was generated by performing slip stream tests at a power plant with high sulfur bituminous coal and a wet FGD scrubber and at a power plant firing highmoisture, low rank coals. • Data on typical concentrations of HCl, HNO{sub 3} and H{sub 2}SO{sub 4} in low temperature condensed flue gas moisture, and mercury capture efficiencies as functions of process conditions in power plant field tests. • Theoretical predictions for sulfuric acid concentrations on tube surfaces at temperatures above the water vapor dewpoint temperature and below the sulfuric acid dew point temperature. • Data on corrosion rates of candidate heat exchanger tube materials for the different regions of the heat exchanger system as functions of acid concentration and temperature. • Data on effectiveness of acid traps in reducing sulfuric acid concentrations in a heat exchanger tube bundle. • Condensed flue gas water treatment needs and costs. • Condensing heat exchanger designs and installed capital costs for full-scale applications, both for installation immediately downstream of an ESP or baghouse and for installation downstream of a wet SO{sub 2} scrubber. • Results of cost-benefit studies of condensing heat exchangers

Recurrent Endometrial Stromal Sarcoma: Treatment with a Progestin and Gonadotropin Releasing Hormone Agonist

Endometrial stromal sarcoma (ESS) formerly classified as low-grade endometrial stromal sarcoma is a rare uterine malignancy with a good prognosis despite a tendency to recur. Primary surgical management for ESS includes total abdominal hysterectomy and bilateral salpingo-oophorectomy. Patients with ESS have long disease-free survival rates when treated with primary surgical therapy, but nearly fifty percent of these patients will recur. We present the case of a patient with recurrent ESS who had an excellent response to combined therapy with megestrol and leuprolide

Public Thinking About Coping With the Cost of Health Care: How Do We Pay for What We Need

Summarizes discussions from the 2008 National Issues Forums held nationwide on the public's views on the U.S. healthcare system, the factors behind rising costs, and proposed solutions. Outlines areas of consensus as well as reservations about reforms

Thermographic Inspection of Metallic Honeycomb Sandwich Structures

The X-33/VentureStar has a Thermal Protection System (TPS) consisting mainly of brazed metallic honeycomb sandwich structures. Inspection of these structures is changing as a result of the extremely thin (less than 200 microns) skins, the small critical defect size (less than 2 mm long by 100 microns wide) and the large number (more than 1000) of parts to be inspected. Pulsed Infrared Thermography has been determined to be the most appropriate inspection method for manufacturing inspection based on performance comparison with other methods, cost, schedule and other factors. The results of the assessment of the different methods will be summarized and data on the performance of the final production inspection system will be given. Finite difference thermal methods have been used to model the whole inspection process. Details of correlation between the models and experimental data will be given and data on the use of pulsed infrared thermography on other metallic honeycomb sandwich structures will be given

Szemer\'edi's theorem in the primes

Green and Tao famously proved in 2005 that any subset of the primes of fixed positive density contains arbitrarily long arithmetic progressions. Green had previously shown that in fact any subset of the primes of relative density tending to zero sufficiently slowly contains a 3-term term progression. This was followed by work of Helfgott and de Roton, and Naslund, who improved the bounds on the relative density in the case of 3-term progressions. The aim of this note is to present an analogous result for longer progressions by combining a quantified version of the relative Szemer\'edi theorem given by Conlon, Fox and Zhao with Henriot's estimates of the enveloping sieve weights.Comment: 11 page

Do quantum dots allow one access to pseudogap Kondo physics?

For the last decade, tunable quantum dot systems have allowed the investigation of Kondo physics wherein the quenching of a single spin on an artificial atom affects the conductance. The pseudogap Kondo model featuring a density of states $\rho(\epsilon)$ = C$|\epsilon|^{r}$, introduced by Withoff and Fradkin in 1990 was predicted to exhibit Kondo-like physics above a critical value of the Kondo coupling, J$_c$, which several groups have shown by numerical renormalization group (RG) is finite for r$< {1/2}$. Gonzalez-Buxton {\it{et al}} showed that the strong coupling limit of the particle-hole symmetric model leads to a non-trivial $\frac{\pi (1-r)}{2}$ phase shift at low temperatures indicating incomplete screening of the local moment, while away from particle-hole symmetry one generically flows towards a ground state with $\delta \sim \pi$. We examine the implications of this model for quantum dots whose leads are Fermi-liquid-like, yet possess a tunneling density of states which is suppressed at the Fermi energy as a power law.Comment: 2 pages, 1 figure, poster to be presented at SCES'04 Karlsruhe July 26-3