In this Wednesday night section for Algebraic Number Theory, we will go through basic facts about one dimensional formal groups and hopefully get to see how they might be useful and interesting. All rings are commutative with identity. The sources of this material are my notes from Elliptic Curves, a course taught by Tom Fisher at Cambridge last year, J. Silverman’s Elliptic Curves Book. A few ...

We discuss restrictions of two-dimensional translation-invariant Gibbs measures to a one-dimensional layer. We prove that there exists a translation invariant a.s. absolutely convergent potential making these restrictions into weakly Gibbsian measures. We discuss the existence of the thermodynamic functions for this potential and the variational principle for the weakly Gibbsian measures.

A new NMR experiment for correlating diffusion coefficients and chemical shifts is presented. This experiment provides the same information as the conventional DOSY experiment, but only requires a single dimension because a nonuniform magnetic field gradient is used to encode the diffusion information into the lineshapes of the peaks in the chemical shift dimension. By fitting the resulting lin...

For a long time, lower bounds on the difficulty of estimation have been constructed by showing that estimation was difficult even in certain 1-dimensional subproblems. The logical extension of this is to identify hardest one dimensional subproblems and to ask whether these are, either exactly or approximately, as difficult as the full problem. We do this in three settings: estimating linear fun...

Based on reasonable assumptions and mathematical approximations a one dimensional, analytical model for solar quiescent prominences is constructed, which is in both magnetohydrostatic and thermal equilibrium. Thermal equilibrium here is a balance among thermal conduction, radiation and wave heating. The wave heating (H) is assumed to be equal to a constant (EH ) times the product of pressure (p...

an internal ballistics model has been developed for performance prediction of a solid propellant rocket motor. inthis model a 1-d unsteady euler equation with source terms is considered. the flow is assumed as a non-reacting mixture of perfect gases with space and time varying thermo physical properties. the governing equations in the combustion chamber are solved numerically by using the stege...

This paper describes our work in-progress on a new automatic indexing technique for large one-dimensional (1D) or time-series data. The principal idea of the proposed time-series data indexing method is to encode the shape of time-series into an alphabet of characters and then to treat them as text. As far as we know this is a novel approach to 1D data indexing. In this paper we report our prel...

Methods A measuring ophthalmoscope based on the Zeiss retina camera RC 310 is coupled with a CCD device. A frame grabber digitizes the picture section with the interesting vessel segments. An adaptive algorithm recognizes the position and direction of the vessels automatically and calculates the vessel diameters. Other measuring data are recorded additionally, for example the R spike of the ele...