The life of Gotthold Ferdinand Eisenstein

Gotthold Ferdinand Eisenstein (1823-1852) was one of the brilliant mathematicians of the nineteenth century. The main goal of this article is to give a translation – from German into English – of a Curriculum Vita that he wrote at age twenty, as part of his application for the Examination of General Maturity for University Entrance (Abitur). This has often been referred to as his autobiography. Some additional biographical information is also given, with the aim of providing some further insights into his life and character in general

Pricing exotic options using strong convergence properties?

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multi-level Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O($\epsilon^{−2}$) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all 1−dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the 2−Dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the Multi-level Monte Carlo give a substantial reduction in the computation cost

Time evolution of intrinsic alignments of galaxies

Intrinsic alignments (IA), correlations between the intrinsic shapes and orientations of galaxies on the sky, are both a significant systematic in weak lensing and a probe of the effect of large-scale structure on galactic structure and angular momentum. In the era of precision cosmology, it is thus especially important to model IA with high accuracy. Efforts to use cosmological perturbation theory to model the dependence of IA on the large-scale structure have thus far been relatively successful; however, extant models do not consistently account for time evolution. In particular, advection of galaxies due to peculiar velocities alters the impact of IA, because galaxy positions when observed are generally different from their positions at the epoch when IA is believed to be set. In this work, we evolve the galaxy IA from the time of galaxy formation to the time at which they are observed, including the effects of this advection, and show how this process naturally leads to a dependence of IA on the velocity shear. We calculate the galaxy-galaxy-IA bispectrum to tree level (in the linear matter density) in terms of the evolved IA coefficients. We then discuss the implications for weak lensing systematics as well as for studies of galaxy formation and evolution. We find that considering advection introduces nonlocality into the bispectrum, and that the degree of nonlocality represents the memory of a galaxy's path from the time of its formation to the time of observation. We discuss how this result can be used to constrain the redshift at which IA is determined and provide Fisher estimation for the relevant measurements using the example of SDSS-BOSS.Comment: 30 pages, 5 figures, 2 table

Far infrared supplement: Catalog of infrared observations

The development of a new generation of orbital, airborne and ground-based infrared astronomical observatory facilities, including the infrared astronomical satellite (IRAS), the cosmic background explorer (COBE), the NASA Kuiper airborne observatory, and the NASA infrared telescope facility, intensified the need for a comprehensive, machine-readable data base and catalog of current infrared astronomical observations. The Infrared Astronomical Data Base and its principal data product, this catalog, comprise a machine-readable library of infrared (1 micrometer to 1000 micrometers) astronomical observations published in the scientific literature since 1965

Far infrared supplement: Catalog of infrared observations

The Far Infrared Supplement: catalog of infrared observations summarizes all infrared astronomical observations at far infrared wavelengths published in the scientific literature between 1965 and 1982. The Supplement list contains 25% of the observations in the full catalog of infrared observations (C10), and essentially eliminates most visible stars from the listings. The Supplement is more compact than the main Catalog (it does not contain the bibliography and position index of the C10), and is intended for easy reference during astronomical observations

Catalog of infrared observations including: Bibliography of infrared astronomy and index of infrared source positions

The Catalog of Infrared Observations and its Far Infrared Supplement summarize all infrared astronomical observations at infrared wavelengths published in the scientific literature between 1965 and 1982. The Catalog includes as appendices the Bibliography of infrared astronomy which keys observations in the Catalog with the original journal references, and the index of infrared source positions which gives source positions for alphabetically listed sources in the Catalog. The Catalog data base contains over 85,000 observations of about 10,000 infrared sources, of which about 2,000 have no known visible counterpart

FOOD NUTRITIONAL QUALITY: A PILOT STUDY ON CONSUMER AWARENESS

Retail food demand studies are becoming increasingly concerned with the role of nutrition and health, yet consumer perceptions and attitudes are often ignored. The purpose of this pilot study is to determine consumer perceptions involving nutrition levels for selected foods. The influence of demographics and information about nutrition and health on perceptions toward meat items are determined. Results generally indicate that consumer perceptions toward fat and cholesterol levels in meats are based on the comparison of animal sources, not the comparison of individual cuts or preparation techniques. Recent efforts in the study of retail food demand have moved toward the role of nutrition and health. Several attempts have been made to measure the role that nutrition plays in food value or purchase habits (LaFrance (1983), Huffman (1988), Brown and Shrader (1990)). These studies use actual nutritional content of foods consumed to estimate demand impacts. However, it is possible that consumers perceive the nutritional elements of certain foods to be significantly different than actual levels. Differences between actual and perceived levels represent measurement error in these variables. Such errors may adversely affect the results of our demand studies. Consumer misperceptions may be an especially important issue when a utility maximization model such as Lancaster's Consumer Goods Characteristics Model (CGCM) is used. In such a model, the utility function arguments are the characteristics of the goods not the goods themselves. If consumers misperceive the nutritional value of food products, such models should include the perceived levels of nutrition, not the actual levels. The CGCM has been used extensively in recent years. In particular, CGCM was used by Ladd and Suvannant (1976) to test if food prices were a sum of the values of certain nutrients; by Adrian and Daniels (1976) to estimate nutrient demand based in part on demographic variables; by Morgan, Metzen, and Johnson (1979) to estimate hedonic prices for breakfast cereal characteristics; and by Terry, Brooker, and Eastwood (1986) to estimate the demand for nutrients. Each of these studies used actual nutrition levels. If, however, perceived nutrition levels are different than the actual levels, the results and conclusions may be affected. Results from these models vary widely. In the case of some nutrients, the implicit values can switch from significantly positive to significantly negative across models. Some of the variability may be associated with specification and differences in time periods. However, some variation may result from differences in perceptions which also change over time. Models which do not directly specify nutrient levels may fall prey to another problem. Work by Brown and Schrader (1990) and later by Capps and Schmitz (1990) utilize an index of nutritional awareness. Models of this nature allow for consumer perceptions to be included. However, when results of these models are reviewed, the results are compared to actual data, not perceptions. These results may be compared to the wrong benchmarks. Thus perceptions need to be considered, regardless of the approach used.Food Consumption/Nutrition/Food Safety,

Cosmic-ray exposure ages of fossil micrometeorites from mid-Ordovician sediments at Lynna River, Russia

We measured the He and Ne concentrations of 50 individual extraterrestrial chromite grains recovered from mid-Ordovician (lower Darriwilian) sediments from the Lynna River section near St. Petersburg, Russia. High concentrations of solar wind-like He and Ne found in most grains indicate that they were delivered to Earth as micrometeoritic dust, while their abundance, stratigraphic position and major element composition indicate an origin related to the L chondrite parent body (LCPB) break-up event, 470 Ma ago. Compared to sediment-dispersed extraterrestrial chromite (SEC) grains extracted from coeval sediments at other localities, the grains from Lynna River are both highly concentrated and well preserved. As in previous work, in most grains from Lynna River, high concentrations of solar wind-derived He and Ne impede a clear quantification of cosmic-ray produced He and Ne. However, we have found several SEC grains poor in solar wind Ne, showing a resolvable contribution of cosmogenic 21Ne. This makes it possible, for the first time, to determine robust cosmic-ray exposure (CRE) ages in these fossil micrometeorites, on the order of a few hundred-thousand years. These ages are similar to the CRE ages measured in chromite grains from cm-sized fossil meteorites recovered from coeval sediments in Sweden. As the CRE ages are shorter than the orbital decay time of grains of this size by Poynting-Robertson drag, this suggests that the grains were delivered to Earth through direct injection into an orbital resonance. We demonstrate how CRE ages of fossil micrometeorites can be used, in principle, to determine sedimentation rates, and to correlate the sediments at Lynna River with the fossil meteorite-bearing sediment layers in Sweden.Comment: 25 pages, 4 figures, 2 table

The role of use cases in development of a reference framework for interoperability of data exchange in agriculture

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