Multiple discoveryThe concept of multiple discovery (also known as simultaneous invention) is the hypothesis that most scientific discoveries and inventions are made independently and more or less simultaneously by multiple scientists and inventors. The concept of multiple discovery opposes a traditional view—the "heroic theory" of invention and discovery. Multiple discovery is analogous to convergent evolution in biological evolution.
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
German languageGerman (Standard High German: Deutsch, dɔʏtʃ) is a West Germanic language mainly spoken in Western Europe and Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, Liechtenstein, and the Italian province of South Tyrol. It is also an official language of Luxembourg and Belgium, as well as a recognized national language in Namibia. Outside Germany, it is also spoken by German communities in France (Alsace), Czech Republic (North Bohemia), Poland (Upper Silesia), Slovakia (Košice Region, Spiš, and Hauerland), and Hungary (Sopron).
German diasporaThe German diaspora consists of German people and their descendants who live outside of Germany. The term is used in particular to refer to the aspects of migration of German speakers from Central Europe to different countries around the world. This definition describes the "German" term as a sociolinguistic group as opposed to the national one since the emigrant groups came from different regions with diverse cultural practices and different varieties of German.
Standard GermanStandard High German (SHG), less precisely Standard German, or High German (Standardhochdeutsch, Standarddeutsch, Hochdeutsch or, in Switzerland, Schriftdeutsch) while referring to its regional origins and not to be confused with High German dialects, is the standardized variety of the German language used in formal contexts and for communication between different dialect areas. It is a pluricentric Dachsprache with three codified (or standardised) specific regional variants: German Standard German, Austrian Standard German and Swiss Standard German.
