Arithmetik, Algebra und Zahlentheorie von 1759 bis 1799

Inhaltsverzeichnis - S. 37 [3]: Arithmetik - S. 72 [36]: Algebra - S. 153 [117]: Zahlentheorie Die Zahlen in eckigen Klammern geben die Seitennr. der PDF-Datei an. Originaltitel des Aufsatzes: Abschnitt XX. Arithmetik - Gleichungslehre - Zahlentheori

Slide Rules with 'Runners'

We have seen that the use of the runner was suggested by Newton, Stone and Nicholson, also that Robertson actually had constructed slide rules with runner. Nevertheless this ingenious invention failed to meet with appreciation

The Mass of a Spin Vortex in a Bose-Einstein Condensate

In contrast to charge vortices in a superfluid, spin vortices in a ferromagnetic condensate move inertially (if the condensate has zero magnetization along an axis). The mass of spin vortices depends on the spin-dependent interactions, and can be measured as a part of experiments on how spin vortices orbit one another. For Rb87 in a 1 micron thick trap m_v is about 10^-21 kg.Comment: 5 pages, 3 figures; 2nd version has added referenc

Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.Comment: 10 pages, 4 figure

How Ordinary Elimination Became Gaussian Elimination

Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre called "ordinary," and that Gauss called "common" - is now named after Gauss: "Gaussian" elimination. Gauss's name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices.Comment: 56 pages, 21 figures, 1 tabl

Limits of the energy-momentum tensor in general relativity

A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justifies part of the procedure for classification of a given spacetime using Cartan scalars.Comment: LaTeX, 21 page

Broad-Spectrum Antimicrobial Epiphytic and Endophytic Fungi from Marine Organisms: Isolation, Bioassay and Taxonomy

In the search for new marine derived antibiotics, 43 epi- and endophytic fungal strains were isolated from the surface or the inner tissue of different marine plants and invertebrates. Through preliminary and secondary screening, 10 of them were found to be able to produce broad-spectrum antimicrobial metabolites. By morphological and molecular biological methods, three active strains were characterized to be Penicillium glabrum, Fusarium oxysporum, and Alternaria alternata