Points of Low Height on Elliptic Curves and Surfaces, I: Elliptic surfaces over P^1 with small d

For each of n=1,2,3 we find the minimal height h^(P) of a nontorsion point P of an elliptic curve E over C(T) of discriminant degree d=12n (equivalently, of arithmetic genus n), and exhibit all (E,P) attaining this minimum. The minimal h^(P) was known to equal 1/30 for n=1 (Oguiso-Shioda) and 11/420 for n=2 (Nishiyama), but the formulas for the general (E,P) were not known, nor was the fact that these are also the minima for an elliptic curve of discriminant degree 12n over a function field of any genus. For n=3 both the minimal height (23/840) and the explicit curves are new. These (E,P) also have the property that that mP is an integral point (a point of naive height zero) for each m=1,2,...,M, where M=6,8,9 for n=1,2,3; this, too, is maximal in each of the three cases.Comment: 15 pages; some lines in the TeX source are commented out with "%" to meet the 15-page limit for ANTS proceeding

Toxicity of cancer therapy: what the cardiologist needs to know about angiogenesis inhibitors

Clinical outcomes for patients with a wide range of malignancies have improved substantially over the last two decades. Tyrosine kinase inhibitors (TKIs) are potent signalling cascade inhibitors and have been responsible for significant advances in cancer therapy. By inhibiting vascular endothelial growth factor receptor (VEGFR)-mediated tumour blood vessel growth, VEGFR-TKIs have become a mainstay of treatment for a number of solid malignancies. However, the incidence of VEGFR-TKI-associated cardiovascular toxicity is substantial and previously under-recognised. Almost all patients have an acute rise in blood pressure, and the majority develop hypertension. They are associated with the development of left ventricular systolic dysfunction (LVSD), heart failure and myocardial ischaemia and can have effects on myocardial repolarisation. Attention should be given to rigorous baseline assessment of patients prior to commencing VEGFR-TKIs, with careful consideration of baseline cardiovascular risk factors. Baseline blood pressure measurement, ECG and cardiac imaging should be performed routinely. Hypertension management currently follows national guidelines, but there may be a future role forendothelin-1 antagonism in the prevention or treatment of VEGFR-TKI-associated hypertension. VEGFR-TKI-associated LVSD appears to be independent of dose and is reversible. Patients who develop LVSD and heart failure should be managed with conventional heart failure therapies, but the role of prophylactic therapy is yet to be defined. Serial monitoring of left ventricular function and QT interval require better standardisation and coordinated care. Management of these complex patients requires collaborative, cardio-oncology care to allow the true therapeutic potential from cancer treatment while minimising competing cardiovascular effects

Verified modeling of a low pressure hydrogen plasma generated by electron cyclotron resonance

A self-consistent fluid model has been successfully developed and employed to model an electron cyclotron resonance driven hydrogen plasma at low pressure. This model has enabled key insights to be made on the mutual interaction of microwave propagation, power density, plasma generation, and species transport at conditions where the critical plasma density is exceeded. The model has been verified by two experimental methods. Good agreement with the ion current density and floating potential—as measured by a retarding energy field analyzer—and excellent agreement with the atomic hydrogen density—as measured by two-photon absorption laser induced fluorescence—enables a high level of confidence in the validity of the simulation

On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine

We consider the relationship between the conjectured uniqueness of the Moonshine Module, ${\cal V}^\natural$, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possible $Z_n$ meromorphic orbifold constructions of ${\cal V}^\natural$ based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson series for all 51 non-Fricke classes of the Monster group $M$ together with a new relationship between the centralisers of these classes and 51 corresponding Conway group centralisers (generalising a well-known relationship for 5 such classes). Assuming that ${\cal V}^\natural$ is unique, we then consider meromorphic orbifoldings of ${\cal V}^\natural$ and show that Monstrous Moonshine holds if and only if the only meromorphic orbifoldings of ${\cal V}^\natural$ give ${\cal V}^\natural$ itself or the Leech theory. This constraint on the meromorphic orbifoldings of ${\cal V}^\natural$ therefore relates Monstrous Moonshine to the uniqueness of ${\cal V}^\natural$ in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0

Efficient pairing computation with theta functions

The original publication is available at www.springerlink.comInternational audienceIn this paper, we present a new approach based on theta functions to compute Weil and Tate pairings. A benefit of our method, which does not rely on the classical Miller's algorithm, is its generality since it extends to all abelian varieties the classical Weil and Tate pairing formulas. In the case of dimension $1$ and $2$ abelian varieties our algorithms lead to implementations which are efficient and naturally deterministic. We also introduce symmetric Weil and Tate pairings on Kummer varieties and explain how to compute them efficiently. We exhibit a nice algorithmic compatibility between some algebraic groups quotiented by the action of the automorphism $-1$, where the $\Z$-action can be computed efficiently with a Montgomery ladder type algorithm

Feasibility of Electrified Propulsion for Ultra-Efficient Commercial Aircraft Final Report

MIT, Aurora Flight Sciences, and USC have collaborated to assess the feasibility of electric, hybridelectric, and turbo-electric propulsion for ultra-efficient commercial transportation. The work has drawn on the team expertise in disciplines related to aircraft design, propulsion-airframe integration, electric machines and systems, engineering system design, and optimization. A parametric trade space analysis has been carried out to assess vehicle performance across a range of transport missions and propulsion architectures to establish how electrified propulsion systems scale. An optimization approach to vehicle conceptual design modeling was taken to enable rapid multidisciplinary design space exploration and sensitivity analysis. The results of the analysis indicate vehicle aero-propulsive integration benefits enabled by electrification are required to offset the increased weight and loss associated with the electric system and achieve enhanced performance; the report describes the conceptual configurations than can offer such enhancements. The main contribution of the present work is the definition of electric vehicle design attributes for potential efficiency improvements at different scales. Based on these results, key areas for future research are identified, and extensions to the trade space analysis suitable for higher fidelity electrified commercial aircraft design and analysis have been developed

Single gluino production in the R-parity lepton number violating MSSM at the LHC

We examine the $R_{p}$-violating signal of single gluino production associated with a charged lepton or neutrino at the large hadron collider (LHC), in the model of R-parity relaxed supersymmetric model. If the parameters in the ${\rlap/R}_p$ supersymmetric interactions are not too small, and the mass of gluino is considered in the range from several GeV (as the Lightest Supersymmetric Particle) to 800 GeV, the cross section of the single gluino production via Drell-Yan processes can be in the order of $10^2 \sim 10^3$ femto barn, and that via gluon fusion in the order of $10^{-1} \sim 10^3$ femto barn. If the gluino decay can be well detected in the CERN LHC, this process provides a prospective way to probe supersymmetry and $R_p$ violation.Comment: LaTex, 22 pages, 5 EPS file

Models for Enhanced Absorption in Inhomogeneous Superconductors

We discuss the low-frequency absorption arising from quenched inhomogeneity in the superfluid density rho_s of a model superconductor. Such inhomogeneities may arise in a high-T_c superconductor from a wide variety of sources, including quenched random disorder and static charge density waves such as stripes. Using standard classical methods for treating randomly inhomogeneous media, we show that both mechanisms produce additional absorption at finite frequencies. For a two-fluid model with weak mean-square fluctuations <(d rho_s)^2 > in rho_s and a frequency-independent quasiparticle conductivity, the extra absorption has oscillator strength proportional to the quantity <(d rho_s)^2>/rho_s, as observed in some experiments. Similar behavior is found in a two-fluid model with anticorrelated fluctuations in the superfluid and normal fluid densities. The extra absorption typically occurs as a Lorentzian centered at zero frequency. We present simple model calculations for this extra absorption under conditions of both weak and strong fluctuations. The relation between our results and other model calculations is briefly discussed