Euler characteristics and elliptic curves

Let E be a modular elliptic curve over ℚ, without complex multiplication; let p be a prime number where E has good ordinary reduction; and let F∞ be the field obtained by adjoining to ℚ all p-power division points on E. Write G∞ for the Galois group of F∞ over ℚ. Assume that the complex L-series of E over ℚ does not vanish at s = 1. If p ⩾ 5, we make a precise conjecture about the value of the G∞-Euler characteristic of the Selmer group of E over F∞. If one makes a standard conjecture about the behavior of this Selmer group as a module over the Iwasawa algebra, we are able to prove our conjecture. The crucial local calculations in the proof depend on recent joint work of the first author with R. Greenberg.

A joint hazard and time scaling model to compare survival curves.

To provide a more general method for comparing survival experience, we propose a model that independently scales both hazard and time dimensions. To test the curve shape similarity of two time-dependent hazards, h1(t) and h2(t), we apply the proposed hazard relationship, h12(tKt)/ h1(t) = Kh, to h1. This relationship doubly scales h1 by the constant hazard and time scale factors, Kh and Kt, producing a transformed hazard, h12, with the same underlying curve shape as h1. We optimize the match of h12 to h2 by adjusting Kh and Kt. The corresponding survival relationship S12(tKt) = [S1(t)]KtKh transforms S1 into a new curve S12 of the same underlying shape that can be matched to the original S2. We apply this model to the curves for regional and local breast cancer contained in the National Cancer Institute's End Results Registry (1950-1973). Scaling the original regional curves, h1 and S1 with Kt = 1.769 and Kh = 0.263 produces transformed curves h12 and S12 that display congruence with the respective local curves, h2 and S2. This similarity of curve shapes suggests the application of the more complete curve shapes for regional disease as templates to predict the long-term survival pattern for local disease. By extension, this similarity raises the possibility of scaling early data for clinical trial curves according to templates of registry or previous trial curves, projecting long-term outcomes and reducing costs. The proposed model includes as special cases the widely used proportional hazards (Kt = 1) and accelerated life (KtKh = 1) models.

Determination of absorption curves, dissolution profiles and establishment of in vitro-in vivo correlation by in silico methods using GastroPlusTM and DDDPlusTM

The use of computer programs to predict drug absorption in humans and to simulate dissolution profiles has become a valuable tool in the pharmaceutical area. The objective of this study was to use in silico methods through software GastroPlusTM and DDDPlusTM to simulate drug absorption curves and dissolution profiles, and to establish in vitro-in vivo correlations (IVIVCs). The work presented herein is divided into five chapters and includes the drugs ketoprofen, pyrimethamine, metronidazole, fluconazole, carvedilol and doxazosin. In Chapter 1, simulated plasma curves for ketoprofen matrix tablets are presented and IVIVC was established. The use of simulated intrinsic dissolution tests for pyrimethamine and metronidazole as a tool for biopharmaceutics classification is detailed in Chapter 2. In Chapter 3, simulation of plasma curves for fluconazole capsules with different dissolution profiles is demonstrated as a tool for biowaiver. IVIVC studies were also conducted for carvedilol immediate-release tablets from dissolution profiles in Chapter 4. Chapter 5 covers the application of simulated dissolution tests for development of doxazosin extended-release formulations. Simulation of plasma curves and IVIVC using the software GastroPlusTM as well as intrinsic dissolution tests and dissolution profiles using the software DDDPlusTM proved to be a tool of wide application in predicting biopharmaceutical characteristics of drugs and formulations, allowing the reduction of time and costs of experimental laboratory work.

Graphical User Interface (GUI) for the representation of GM surfaces (using the NRTL model) and curves, including tie-lines and Hessian matrix

A single and very easy to use Graphical User Interface (GUI- MATLAB) based on the topological information contained in the Gibbs energy of mixing function has been developed as a friendly tool to check the coherence of NRTL parameters obtained in a correlation data procedure. Thus, the analysis of the GM/RT surface, the GM/RT for the binaries and the GM/RT in planes containing the tie lines should be necessary to validate the obtained parameters for the different models for correlating phase equlibrium data.

Labour Supply Curves for EU Member and Candidate States: An applied general equilibrium analysis. Factor Markets Working Paper No. 26, June 2012

This paper introduces a more sophisticated modelling of the labour market functioning of the European member and candidate states through the introduction of labour supply curves in an applied general equilibrium model. A labour supply curve offers a middle way in labour supply modelling, sitting between the two commonly adopted extremes of spare capacity and full employment. The first part of the paper outlines the theoretical foundation of the labour supply curve. Real world data is then used to derive labour supply curves for each member state, along with Croatia and Turkey. Finally, the impact of the newly specified labour markets on the results of an illustrative scenario involving reform of the common agricultural policy is explored. The results of computable general equilibrium analysis with the labour supply curve confirm the theoretical expectation that modelling the labour supply through an upwards-sloping curve produces results that lie between the extremes of spare capacity of the labour factor and fully employed labour. This specification captures a greater degree of heterogeneity in the labour markets of the member and candidate states, allowing for a more nuanced modelling of the effects of policy reform, including welfare effects.

HVOSM studies of cross-slope breaks on highway curves. Final report.

Federal Highway Administration, Office of Research and Development, Washington, D.C.

Optimal application and placement of roadside reflective devices for curves on two-lane rural highways. Final report.

Ohio Department of Transportation, Columbus

Plane curves of the third order /

Includes bibliographical references and index.

Executive summary and abstract for the report entitled "An evaluation of warning and regulatory signs for curves on rural roads."".

Federal Highway Administration, Office of Research, Washington, D.C.

Analysis of truck safety on crest vertical curves. Final report.

Federal Highway Administration, Washington, D.C.

An evaluation of warning and regulatory signs for curves on rural roads. Final report.

Federal Highway Administration, Office of Research and Development, Washington, D.C.

Accidents on spiral transition curves in California. Final report.

Federal Highway Administration, Washington, D.C.

Simultaneous fitting of exponential decay curves /

Includes bibliographies (p. 23).

Revised wave runup curves for smooth slopes /

"July 1978."

Departure curves and electrode factors for the determination of true formation resistivity from electric logs obtained with roller type electrodes in air drilled bore holes not containing fluid /

"Contract No. AT(05-1)-725."