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Jacques Feldbau
Jacques Feldbau was a French mathematician, born on 22 October 1914 in Strasbourg, of an Alsatian Jewish traditionalist family. He died on 22 April 1945 at the ''Ganacker'' Camp, annex of the concentration camp of Flossenbürg in Germany. As a mathematician he worked on differential geometry and topology. He was the first student of Charles Ehresmann. He is known as one of the founders of the theory of fiber bundles. He is the one who first proved that a fiber bundle over a simplex is trivializable and who used this to classify bundles over spheres. In a paper, written together with Ehresmann, he introduced the notion of an associated bundle and proved results known today as the exact homotopy sequence of a fibration. Biography Childhood and education Described by Michèle Audin as "a handsome young man with a very friendly and likeable personality" he demonstrated an early interest in mathematics, whilst also being enthusiastic about music and sport. He studied at the Lyc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Straßburg
Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Alsatian, Strossburi , gsw, label=Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the European Parliament. Located at the border with Germany in the historic region of Alsace, it is the prefecture of the Bas-Rhin department. In 2019, the city proper had 287,228 inhabitants and both the Eurométropole de Strasbourg (Greater Strasbourg) and the Arrondissement of Strasbourg had 505,272 inhabitants. Strasbourg's metropolitan area had a population of 846,450 in 2018, making it the eighth-largest metro area in France and home to 14% of the Grand Est region's inhabitants. The transnational Eurodistrict Strasbourg-Ortenau had a population of 958,421 inhabitants. Strasbourg is one of the ''de facto'' four main capitals of the European Union (alongside Brussels, Luxembourg and Frankfurt), as it is the seat of several European insti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''infi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exact Sequence
An exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category) such that the image of one morphism equals the kernel of the next. Definition In the context of group theory, a sequence :G_0\;\xrightarrow\; G_1 \;\xrightarrow\; G_2 \;\xrightarrow\; \cdots \;\xrightarrow\; G_n of groups and group homomorphisms is said to be exact at G_i if \operatorname(f_i)=\ker(f_). The sequence is called exact if it is exact at each G_i for all 1\leq i |
André Weil
André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was a founding member and the ''de facto'' early leader of the mathematical Bourbaki group. The philosopher Simone Weil was his sister. The writer Sylvie Weil is his daughter. Life André Weil was born in Paris to agnostic Alsatian Jewish parents who fled the annexation of Alsace-Lorraine by the German Empire after the Franco-Prussian War in 1870–71. Simone Weil, who would later become a famous philosopher, was Weil's younger sister and only sibling. He studied in Paris, Rome and Göttingen and received his doctorate in 1928. While in Germany, Weil befriended Carl Ludwig Siegel. Starting in 1930, he spent two academic years at Aligarh Muslim University in India. Aside from mathematics, Weil held lifelong interests in classical Greek and Latin literature, in Hinduism and Sanskrit literature: he had taught himself Sanskrit in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up to homeomorphism, though usually most classify up to Homotopy#Homotopy equivalence and null-homotopy, homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Main branches of algebraic topology Below are some of the main areas studied in algebraic topology: Homotopy groups In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bavaria
Bavaria ( ; ), officially the Free State of Bavaria (german: Freistaat Bayern, link=no ), is a state in the south-east of Germany. With an area of , Bavaria is the largest German state by land area, comprising roughly a fifth of the total land area of Germany. With over 13 million inhabitants, it is second in population only to North Rhine-Westphalia, but due to its large size its population density is below the German average. Bavaria's main cities are Munich (its capital and largest city and also the third largest city in Germany), Nuremberg, and Augsburg. The history of Bavaria includes its earliest settlement by Iron Age Celtic tribes, followed by the conquests of the Roman Empire in the 1st century BC, when the territory was incorporated into the provinces of Raetia and Noricum. It became the Duchy of Bavaria (a stem duchy) in the 6th century AD following the collapse of the Western Roman Empire. It was later incorporated into the Holy Roman Empire, became an ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fatigue (medical)
Fatigue describes a state of tiredness that does not resolve with rest or sleep. In general usage, fatigue is synonymous with extreme tiredness or exhaustion that normally follows prolonged physical or mental activity. When it does not resolve after rest or sleep, or occurs independently of physical or mental exertion, it may be a symptom of a medical condition that may become severe or progressive. Fatigue can be a feature of a mental disorder such as depression; may be associated with conditions of chronic pain such as fibromyalgia; it may also feature in conditions of chronic low-level inflammation, and be a disease-related symptom in many other conditions. Fatigue often has no known cause, and is recognised as being very complex in nature. Fatigability describes a susceptibility to fatigue. Physical fatigue results from muscle fatigue brought about by intense physical activity. Mental fatigue results from prolonged periods of cognitive activity which impairs cognitive abil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Auschwitz
Auschwitz concentration camp ( (); also or ) was a complex of over 40 concentration and extermination camps operated by Nazi Germany in occupied Poland (in a portion annexed into Germany in 1939) during World War II and the Holocaust. It consisted of Auschwitz I, the main camp (''Stammlager'') in Oświęcim; Auschwitz II-Birkenau, a concentration and extermination camp with gas chambers; Auschwitz III-Monowitz, a labor camp for the chemical conglomerate IG Farben; and dozens of subcamps. The camps became a major site of the Nazis' final solution to the Jewish question. After Germany sparked World War II by invading Poland in September 1939, the ''Schutzstaffel'' (SS) converted Auschwitz I, an army barracks, into a prisoner-of-war camp. The initial transport of political detainees to Auschwitz consisted almost solely of Poles for whom the camp was initially established. The bulk of inmates were Polish for the first two years. In May 1940, German criminals brought to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Drancy Internment Camp
Drancy internment camp was an assembly and detention camp for confining Jews who were later deported to the extermination camps during the German occupation of France during World War II. Originally conceived and built as a modernist urban community under the name ''La Cité de la Muette'', it was located in Drancy, a northeastern suburb of Paris, France. Between 22 June 1942 and 31 July 1944, during its use as an internment camp, 67,400 French, Polish, and German Jews were deported from the camp in 64 rail transports, The 61,000 deported to Auschwitz and remaining number to Sobibor were murdered. which included 6,000 children. Only 1,542 prisoners remained alive at the camp when the German authorities in Drancy fled as Allied forces advanced and the Swedish Consul-General Raoul Nordling took control of the camp on 17 August 1944, before handing it over to the French Red Cross to care for the survivors. Drancy was under the control of the French police until 1943 when admini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PhD Thesis
A thesis ( : theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144: DocumentationâPresentation of theses and similar documents International Organization for Standardization, Geneva, 1986. In some contexts, the word "thesis" or a cognate is used for part of a bachelor's or master's course, while "dissertation" is normally applied to a doctorate. This is the typical arrangement in American English. In other contexts, such as within most institutions of the United Kingdom and Republic of Ireland, the reverse is true. The term graduate thesis is sometimes used to refer to both master's theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, and the required minimum study period may thus vary significantly in dur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gestapo
The (), abbreviated Gestapo (; ), was the official secret police of Nazi Germany and in German-occupied Europe. The force was created by Hermann Göring in 1933 by combining the various political police agencies of Prussia into one organisation. On 20 April 1934, oversight of the Gestapo passed to the head of the ''Schutzstaffel'' (SS), Heinrich Himmler, who was also appointed Chief of German Police by Hitler in 1936. Instead of being exclusively a Prussian state agency, the Gestapo became a national one as a sub-office of the (SiPo; Security Police). From 27 September 1939, it was administered by the Reich Security Main Office (RSHA). It became known as (Dept) 4 of the RSHA and was considered a sister organisation to the (SD; Security Service). During World War II, the Gestapo played a key role in the Holocaust. After the war ended, the Gestapo was declared a criminal organisation by the International Military Tribunal (IMT) at the Nuremberg trials. History After Adol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vichy Regime
Vichy France (french: Régime de Vichy; 10 July 1940 – 9 August 1944), officially the French State ('), was the fascist French state headed by Marshal Philippe Pétain during World War II. Officially independent, but with half of its territory occupied under harsh terms of the armistice, it adopted a policy of collaboration with Nazi Germany, which occupied the northern and western portions before occupying the remainder of Metropolitan France in November 1942. Though Paris was ostensibly its capital, the collaborationist Vichy government established itself in the resort town of Vichy in the unoccupied "Free Zone" (), where it remained responsible for the civil administration of France as well as its colonies. The Third French Republic had begun the war in September 1939 on the side of the Allies. On 10 May 1940, it was invaded by Nazi Germany. The German Army rapidly broke through the Allied lines by bypassing the highly fortified Maginot Line and invading through Be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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