Discrete logarithms in curves over finite fields

A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields

The complexity of class polynomial computation via floating point approximations

We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of modular functions in several arguments. The fastest one of the presented approaches uses a technique devised by Dupont to evaluate modular functions by Newton iterations on an expression involving the arithmetic-geometric mean. It runs in time $O (|D| \log^5 |D| \log \log |D|) = O (|D|^{1 + \epsilon}) = O (h^{2 + \epsilon})$ for any $\epsilon > 0$, where $D$ is the CM discriminant and $h$ is the degree of the class polynomial. Another fast algorithm uses multipoint evaluation techniques known from symbolic computation; its asymptotic complexity is worse by a factor of $\log |D|$. Up to logarithmic factors, this running time matches the size of the constructed polynomials. The estimate also relies on a new result concerning the complexity of enumerating the class group of an imaginary-quadratic order and on a rigorously proven upper bound for the height of class polynomials

Generalised Weber Functions

A generalised Weber function is given by \w_N(z) = \eta(z/N)/\eta(z), where $\eta(z)$ is the Dedekind function and $N$ is any integer; the original function corresponds to $N=2$. We classify the cases where some power \w_N^e evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating \w_N(z) and $j(z)$. Our ultimate goal is the use of these invariants in constructing reductions of elliptic curves over finite fields suitable for cryptographic use

Digital analysis of wind tunnel imagery to measure fluid thickness

Documented here are the procedure and results obtained from the application of digital image processing techniques to the problem of measuring the thickness of a deicing fluid on a model airfoil during simulated takeoffs. The fluid contained a fluorescent dye and the images were recorded under flash illumination on photographic film. The films were digitized and analyzed on a personal computer to obtain maps of the fluid thickness

Measurement of low energy cosmic rays aboard Spacelab-1

In December 1983 the first Spacelab mission was launched for a duration of 10 days. Aboard was the Kiel experiment Isotopic Stack designed for measurement of heavy cosmic ray nuclei with nuclear charge equal to or greater than 3 and energies up to some 100MeV/nuc. One part of the stack was rotated in well defined steps registered by an angle encoder to receive information on impact times of the nuclei. Using this time resolving system geomagnetically forbidden particles can be detected. The chemical composition and energy spectra of mainly CNO particles are examined using a rotated 300 microns m thick CR-39 foil beneath a fixed 100 microns m thick Kodak-Cellulose Nitrate foil. About 600 sq cm have been scanned yielding nearly 100 nuclear tracks within an energy range of approximately 8 to 30 MeV/nuc. The calibration is done by means of a postflight irradiation with 410 MeV/nuc Fe-56 at Berkeley Laboratory, California, USA. Relative abundances and energy spectra are presented

Heavy ion measurement on LDEF

A stack of CR-39 and Kodak CN track detectors was exposed on the NASA satellite LDEF and recovered after almost six years in space. The quick look analysis yielded heavy ion tracks on a background of low energy secondaries from proton interaction. The detected heavy ions show a steep energy spectrum which indicates a radiation belt origin

Power generation assets

Wir betrachten die Einsatzplanung (Unit Commitment Problem) für ein thermisches Kraftwerk mit zusätzlicher Energienebenbedingung. Dazu definieren wir ein stochastisches dynamisches Programm (SDP)mit stetigem Zustandsraum und integriertem gemischt-ganzzahligem Programm (MIP). Wir stellen einen effizienten Algorithmus vor zur Lösung des MIP über eine Matrixmultiplikation und verwenden eine Hauptkomponentenanalyse zur Reduzierung der Dimension des Preisvektors. Außerdem liefern wir zum Vergleich des SDP eine vereinfachte Regel zur Energieallokation. Zur Beurteilung der Güte der Ergbnisse betrachten wir als nächstes obere Grenzen. Für eine vereinfachte Modellierung des Kraftwerks als Swing Option mit Mehrfachausübung auf derselben Stufe bestimmen wir formal eine solche obere Grenze. Abschließend untersuchen wir Strategien zur Vermeidung des Spotpreisrisikos, dem das Kraftwerk aufgrund der Nichtspeicherbarkeit von Strom besonders ausgesetzt ist. Zunächst konzentrieren wir uns auf die Messung des Spotpreisrisikos und stellen drei neue Maße vor (Forward Delta, Synthetisches Spot Delta und Earnings-at-Risk). Danach präsentieren wir Strategien zur Risikoreduzierung vor und während der Lieferperiode. Im zweiten Fall wird versucht, durch einen neuen Produktionsplan das Risiko mehr als den Gewinn zu senken. Wir schlagen dazu einen Referenzwert vor, den wir EaR-effizienten Optionswert nennen und in eine neue Erzeugungspolitik basierend auf Quantil-Regression einfließt. Die Politik beschreibt ein Preisband innerhalb dessen ein beobachteter Preis zur Ausübung eines Swing-Rechts führt. Für den Fall der amerikanischen Option können wir EaR-Effizienz mit dieser Strategie nachweisen. Abschließend betrachten wir die Absicherung des Kraftwerks vor der Lieferung durch gezielten Verkauf einer Swing Option. Wir stellen eine Heuristik basierend auf unserem synthetischen Spot Delta vor, um Swinghöhe und –anzahl effizient zu finden.We define a new not yet investigated unit commitment problem that introduces an energy constraint to a thermal power plant. We define a stochastic dynamic program with continuous state space and nested mixed integer program (MIP). We introduce a fast implementation approach by replacing the MIP with an efficient matrix calculation and use principal component analysis to reduce the dimension of the price vector. We also provide a fast heuristic valuation approach for comparison. We investigate the theory of upper bounds for a proper validation of our power plant results. In particular we provide an extension for swing options with multiple exercises at the same stage. Finally we provide a risk analysis for our thermal power plant. In particular we investigate strategies to reduce the spot price risk to which power plants are significantly exposed. First, we focus on the measurement of spot price risk and propose three appropriate risk figures (Forward delta, synthetic spot delta and Earnings-at-Risk ). Second we suggest risk mitigation strategies for both periods, before and in delivery. The latter tries to alter the dispatch policy i.e. pick less risky hours and accept a (desirably only slightly) smaller return. We introduce a benchmark that we will call EaR-efficient option value. We propose a mitigation strategy for this benchmark that is based on quantile regression. It defines a price interval for executing an individual swing right and is therefore very well suited for real world applications. In case of an American option we are able to show EaR-efficiency of our strategy. Finally, we investigate hedging strategies before delivery. In particular, we look at a hedge for the spot price risk of the power plant using a swing option. We propose a heuristic based on our synthetic spot deltas to find the swing number and size of the swing option for a given upper generation amount

The Doctrine of Resurrection unto Life Eternal as Presented by St. Paul in His First Espistle to the Corinthians

First a brief word in regard to the word resurrection. Whenever we shall speak of the resurrection, we shall always mean the resurrection of the body. Moreover we shall limit ourselves in this discussion to the resurrection unto life eternal, because this is the resurrection that is of such vital concern to us and to all Christians. This resurrection, not that of the wicked, was the one concerning which Paul desired to instruct the Corinthians. Therefore he speaks of the resurrection unto life eternal almost exclusively when treating the doctrine of the resurrection in his First Epistle to the Corinthians. -- All Biblical references in the following paragraphs are to the fifteenth chapter of First Corinthians, unless the contrary is clearly indicated

Effects of Coach Turnovers on Intensity for Training and Matches in a Norwegian Football Club

The aim of this study was to examine physical variables between four weeks before and eight weeks after two coach turnovers in a second division Norwegian football club for both training and matches. Individual physical data (n=1174 observations) was derived from the players using GPS-data in combination with the subjects employing wearable instruments from Catapult. The means for variables were divided into four study periods (training 2019, matches 2019, training 2021, and matches 2021) to analyze each variable for each of the four periods. The training period in 2019 revealed four variables having a significant negative effect, including total distance covered, sprint running distance, total player load, and total player load 2D, with all parameters representing a small effect size. Only repeat high-intensity efforts had a statistically significant negative effect for matches in 2019, with the effect size being small. For the training period in 2021, sprint running distance had a small positive effect size but a statistically significant positive outcome. On the other hand, decelerations in band 3 had a statistically significant and small negative influence after the switch. High-speed running distance revealed a statistically significant negative effect, with the effect size being moderate for matches in 2021