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Herbert Grötzsch
Camillo Herbert Grötzsch (21 May 1902 – 15 May 1993) was a German mathematician known primarily for his work on complex analysis, specifically univalent functions and conformal mappings, and graph theory. He was the first to introduce the concept of a quasiconformal mapping. He was the discoverer and eponym of the Grötzsch graph, a triangle-free graph that requires four colors in any graph coloring, and Grötzsch's theorem, the result that every triangle-free planar graph requires at most three colors. Biography Camillo Herbert Grötzsch was born in Döbeln in 1902. His father, Emil Camillo Grötzsch, received his doctorate under Sophus Lie and was a mathematics teacher. Grötzsch studied mathematics at the University of Jena from 1922 to 1926 under Paul Koebe. He followed Koebe to the University of Leipzig and received his doctorate there in 1929. In 1931 Grötzsch obtained his habilitation at the University of Giessen, where he taught until his termination for refusing to j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Döbeln
Döbeln (; , ) is a town in Saxony, Germany, part of the Mittelsachsen district. It sits on the banks of the Freiberger Mulde, Freiberger Mulde river. Location and geography Döbeln is situated in the Central Saxon Hills, Central Saxon Hill country in the wide basin of the Freiberger Mulde, roughly in the middle of the triangle between Chemnitz (40 km away), Dresden (50 km away) and Leipzig (70 km away). The surrounding area is characterized by the Mulde valley, the lower Zschopau (river), Zschopau valley and the surrounding hilly landscape. The Zschopau flows into the Mulde near the village of Schweta. Döbeln has a traditional old town, whose central part is located on the Mulde Island and is surrounded by two branches of the Freiberger Mulde river. Districts of the town are Döbeln-Ost, Döbeln-Nord, Gärtitz, Großbauchlitz, Keuern, Kleinbauchlitz, Masten, Pommlitz, Sörmitz, and Zschackwitz. Döbeln has two highway exits on the Bundesautobahn 14, Döbeln Nord and Döbeln ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Mapping
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\in U if it preserves angles between directed curves through u_0, as well as preserving orientation. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. The transformation is conformal whenever the Jacobian at each point is a positive scalar times a rotation matrix (orthogonal with determinant one). Some authors define conformality to include orientation-reversing mappings whose Jacobians can be written as any scalar times any orthogonal matrix. For mappings in two dimensions, the (orientation-preserving) conformal mappings are precisely the locally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aerodynamics Research Institute
The ''Aerodynamische Versuchsanstalt'' (AVA) in Göttingen was one of the four predecessor organizations of the 1969 founded "German Research and Experimental Institute for Aerospace", which in 1997 was renamed German Aerospace Center (DLR). History The AVA was created in 1919 from the 1907 Göttingen by Ludwig Prandtl founded "Modellversuchsanstalt für Aerodynamik der Motorluftschiff-Studiengesellschaft". In its founding years, it was still concerned with the development of the "best" form of airship. In 1908, the first wind tunnel was built in Göttingen for tests on models for aviation. In 1915, founded in 1911 Kaiser Wilhelm Society (KWG) and under the direction of Ludwig Prandtl the "Modellversuchsanstalt aerodynamics" was founded in 1919 as the "Aerodynamic Research Institute of the Kaiser Wilhelm Society" (AVA) was transferred to the KWG and converted in 1925 into the " Kaiser Wilhelm Institute for Flow Research linked to the Aerodynamic Research Institute". Ludwig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jet Engine
A jet engine is a type of reaction engine, discharging a fast-moving jet (fluid), jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition may include Rocket engine, rocket, Pump-jet, water jet, and hybrid propulsion, the term typically refers to an internal combustion airbreathing jet engine, air-breathing jet engine such as a turbojet, turbofan, ramjet, pulse jet engine, pulse jet, or scramjet. In general, jet engines are internal combustion engines. Air-breathing jet engines typically feature a Axial compressor, rotating air compressor powered by a turbine, with the leftover power providing thrust through the propelling nozzle—this process is known as the Brayton cycle, Brayton thermodynamic cycle. Jet aircraft use such engines for long-distance travel. Early jet aircraft used turbojet engines that were relatively inefficient for subsonic flight. Most modern subsonic jet aircraft use more complex High-bypass turbofan, high-bypas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second World War
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the world's countries participated, with many nations mobilising all resources in pursuit of total war. Tanks in World War II, Tanks and Air warfare of World War II, aircraft played major roles, enabling the strategic bombing of cities and delivery of the Atomic bombings of Hiroshima and Nagasaki, first and only nuclear weapons ever used in war. World War II is the List of wars by death toll, deadliest conflict in history, causing World War II casualties, the death of 70 to 85 million people, more than half of whom were civilians. Millions died in genocides, including the Holocaust, and by massacres, starvation, and disease. After the Allied victory, Allied-occupied Germany, Germany, Allied-occupied Austria, Austria, Occupation of Japan, Japan, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johann Christian Poggendorf
Johann Christian Poggendorff (29 December 1796 – 24 January 1877) was a German physicist born in Hamburg. By far the greater and more important part of his work related to electricity and magnetism. Poggendorff is known for his electrostatic motor which is analogous to Wilhelm Holtz's electrostatic machine. In 1841 he described the use of the potentiometer for measurement of electrical potentials without current draw. Biography Poggendorf had apprenticed himself to an apothecary in Hamburg, and when twenty-two began to earn his living as an apothecary's assistant at Itzehoe. Ambition and a strong inclination towards a scientific career led him to throw up his business and move to Berlin, where he entered Humboldt University in 1820. Here his abilities were speedily recognized, and in 1823 he was appointed meteorological observer to the Academy of Sciences. Even at this early period he had conceived the idea of founding a physical and chemical scientific journal, and the realiza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leipzig
Leipzig (, ; ; Upper Saxon: ; ) is the most populous city in the States of Germany, German state of Saxony. The city has a population of 628,718 inhabitants as of 2023. It is the List of cities in Germany by population, eighth-largest city in Germany and is part of the Central German Metropolitan Region. The name of the city is usually interpreted as a Slavic term meaning ''place of linden trees'', in line with many other Slavic placenames in the region. Leipzig is located about southwest of Berlin, in the southernmost part of the North German Plain (the Leipzig Bay), at the confluence of the White Elster and its tributaries Pleiße and Parthe. The Leipzig Riverside Forest, Europe's largest intra-city riparian forest, has developed along these rivers. Leipzig is at the centre of Neuseenland (''new lake district''). This district has Bodies of water in Leipzig, several artificial lakes created from former lignite Open-pit_mining, open-pit mines. Leipzig has been a trade city s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sturmabteilung
The (; SA; or 'Storm Troopers') was the original paramilitary organisation under Adolf Hitler and the Nazi Party of Germany. It played a significant role in Adolf Hitler's rise to power, Hitler's rise to power in the 1920s and early 1930s. Its primary purposes were providing protection for Nazi rallies and assemblies, disrupting the meetings of opposing parties, fighting against the paramilitary units of the opposing parties, especially the ''Roter Frontkämpferbund'' of the Communist Party of Germany (KPD) and the ''Reichsbanner Schwarz-Rot-Gold'' of the Social Democratic Party of Germany (SPD), and intimidating Romani people, Romani, trade unionists, and especially Jews. The SA were colloquially called Brownshirts () because of the colour of their Uniforms and insignia of the Sturmabteilung, uniform's shirts, similar to Benito Mussolini's Blackshirts. The official uniform of the SA was a brown shirt with a brown tie. The color came about because a large shipment of Paul von ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Giessen
University of Giessen, official name Justus Liebig University Giessen (), is a large public research university in Giessen, Hesse, Germany. It is one of the oldest institutions of higher education in the German-speaking world. It is named after its most famous faculty member, Justus von Liebig, the founder of modern agricultural chemistry and inventor of artificial fertiliser. It covers the areas of arts/humanities, business, dentistry, economics, law, medicine, science, social sciences and veterinary medicine. Its university hospital, which has two sites, Giessen and Marburg (the latter of which is the teaching hospital of the University of Marburg), is the only private university hospital in Germany. History The University of Giessen is among the oldest institutions of higher educations in the German-speaking world. It was founded in 1607 as a Lutheran university in the city of Giessen in Hesse-Darmstadt because the all-Hessian ''Landesuniversität'' (the nearby University o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excellence in research, teaching, and further education, which usually includes a dissertation. The degree, sometimes abbreviated ''Dr. habil''. (), ''dr hab.'' (), or ''D.Sc.'' ('' Doctor of Sciences'' in Russia and some CIS countries), is often a qualification for full professorship in those countries. In German-speaking countries it allows the degree holder to bear the title ''PD'' (for ). In a number of countries there exists an academic post of docent, appointment to which often requires such a qualification. The degree conferral is usually accompanied by a public oral defence event (a lecture or a colloquium) with one or more opponents. Habilitation is usually awarded 5–15 years after a PhD degree or its equivalent. Achieving this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sophus Lie
Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial contributions to the development of algebra. Life and career Marius Sophus Lie was born on 17 December 1842 in the small town of Nordfjordeid. He was the youngest of six children born to Lutheran pastor Johann Herman Lie and his wife, who came from a well-known Trondheim family. He had his primary education in the south-eastern coast of Moss, before attending high school in Oslo (known then as Christiania). After graduating from high school, his ambition towards a military career was dashed when the army rejected him due to poor eyesight. He then enrolled at the University of Christiania. Sophus Lie's first mathematical work, ''Repräsentation der Imaginären der Plangeometrie'', was published in 1869 by the Academy of Sciences in Chris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Graph
In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph, or a planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs can be encoded by combinatorial maps or rotation systems. An equivalence class of topologically equivalent drawings on the sphere, usually with addit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
