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Abstract algebra | Algèbre générale | In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term "abstract algebra" was coined in the early 20th century to distinguish this area of study from the other parts of algebra. | L'algèbre générale, ou algèbre abstraite, est la branche des mathématiques qui porte principalement sur l'étude des structures algébriques et de leurs relations. L'appellation "algèbre générale" s'oppose à celle d"'algèbre élémentaire" ; cette dernière enseigne le calcul algébrique, c'est-à-dire les règles de manipulation des formules et des expressions algébriques. | [
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] | null | null | null | null | null | null |
Linear algebra | Algèbre linéaire | Linear algebra is the branch of mathematics concerning linear equations such as linear maps such as and their representations in vector spaces and through matrices. | L’algèbre linéaire est la branche des mathématiques qui s'intéresse aux espaces vectoriels et aux transformations linéaires, formalisation générale des théories des systèmes d'équations linéaires. | [
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Algorithm | Algorithme | In mathematics and computer science, an algorithm () is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algorithms are always unambiguous and are used as specifications for performing calculations, data processing, automated reasoning, and other tasks. | Un algorithme est une suite finie et non ambiguë d’opérations ou d'instructions permettant de résoudre une classe de problèmes. Le mot "algorithme" vient du nom d'un mathématicien perse du, Al-Khwârizmî (en arabe : ). Une autre étymologie dit qu'un algorithme est un calcul (« arithmos » en grec), qui est tellement long et difficile à faire à la main qu'il en devient douloureux : « algos » signifie douleur en grec ; un algorithme est un calcul pénible à faire à la main. Étymologie elle aussi acceptable, puisqu'elle rend compte du "g ;" au, "algorithme" signifiait l'arithmétique avec les chiffres arabes. | [
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Politics of Argentina | Politique en Argentine | The politics of Argentina take place in the framework of what the Constitution defines as a federal presidential representative democratic republic, where the President of Argentina is both Head of State and Head of Government. Legislative power is vested in the two chambers of the Argentine National Congress. The Judiciary is independent of the Executive and the Legislature. Elections take place regularly on a multi-party system. | L'Argentine est une république présidentielle multipartite, où le président est à la fois chef de l'État et chef du gouvernement. Le pouvoir exécutif est détenu par le gouvernement et le pouvoir législatif est partagé entre le gouvernement et les deux chambres du parlement. Le pouvoir judiciaire est indépendant des deux premiers. | [
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Boolean algebra | Algèbre de Boole (logique) | In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values "true" and "false", usually denoted 1 and 0 respectively. Instead of elementary algebra where the values of the variables are numbers, and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction ("and)" denoted as ∧, the disjunction ("or)" denoted as ∨, and the negation ("not)" denoted as ¬. It is thus a formalism for describing logical operations in the same way that elementary algebra describes numerical operations. | L'algèbre de Boole, ou calcul booléen, est la partie des mathématiques qui s'intéresse à une approche algébrique de la logique, vue en termes de variables, d'opérateurs et de fonctions sur les variables logiques, ce qui permet d'utiliser des techniques algébriques pour traiter les expressions à deux valeurs du calcul des propositions. Elle fut lancée en 1854 par le mathématicien britannique George Boole. Aujourd'hui, l'algèbre de Boole trouve de nombreuses applications en informatique et dans la conception des circuits électroniques. Elle fut utilisée la première fois pour les circuits de commutation téléphoniques par Claude Shannon. | [
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Austria | Autriche | Austria (, ; ), officially the Republic of Austria (, ), is a landlocked East Alpine country in the southern part of Central Europe. It is composed of nine federated states ("Bundeslände"r), one of which is Vienna, Austria's capital and its largest city. It is bordered by Germany to the northwest, Czech Republic to the north, Slovakia to the northeast, Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the west. Austria occupies an area of and has a population of nearly 9 million people. While German is the country's official language, many Austrians communicate informally in a variety of Bavarian dialects. | L'Autriche ( ), en forme longue la république d'Autriche (), est un État fédéral d'Europe centrale sans accès à la mer. Pays montagneux, il est entouré, dans le sens des aiguilles d'une montre, par l'Allemagne et la Tchéquie au nord, la Slovaquie et la Hongrie à l'est, la Slovénie et l'Italie au sud, et par la Suisse et le Liechtenstein à l'ouest. L'Autriche est membre de l'Union européenne et de la zone euro respectivement depuis 1995 et 1999. Sa langue officielle est l'allemand, mais depuis la ratification de la Charte européenne des langues régionales ou minoritaires, six autres langues (hongrois, slovène, croate du Burgenland, tchèque, slovaque et romani) sont reconnues. Sa capitale et plus grande ville est Vienne. | [
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Aisne | Aisne (département) | Aisne (,, ) is a French department in the Hauts-de-France region of northern France. It is named after the river Aisne. | L'Aisne est un département français dont le nom vient de la rivière homonyme. Il appartient à la région Hauts-de-France. L'Insee et La Poste lui attribuent le code 02. Sa préfecture est Laon. | [
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Arc de Triomphe | Arc de triomphe de l'Étoile | The Arc de Triomphe de l'Étoile (,, ; ) is one of the most famous monuments in Paris, France, standing at the western end of the Champs-Élysées at the centre of Place Charles de Gaulle, formerly named Place de l'Étoile—the "étoile" or "star" of the juncture formed by its twelve radiating avenues. The location of the arc and the plaza is shared between three arrondissements, 16th (south and west), 17th (north) and 8th (east). The Arc de Triomphe honours those who fought and died for France in the French Revolutionary and Napoleonic Wars, with the names of all French victories and generals inscribed on its inner and outer surfaces. Beneath its vault lies the Tomb of the Unknown Soldier from World War I. | L’arc de triomphe de l’Étoile, souvent appelé simplement l’Arc de triomphe, dont la construction, décidée par l'empereur, débuta en 1806 et s'acheva en 1836 sous Louis-Philippe, est situé à Paris, dans les,, et arrondissements. | [
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Allier | Allier (département) | Allier (,, ; ) is a department in the Auvergne-Rhône-Alpes region in the centre of France. Named after the river Allier, it had a population of 339,384 in 2016. Moulins is the prefecture; Montluçon and Vichy are the subprefectures. Its INSEE and post code is 03. | L’Allier () est un département français situé dans la région Auvergne-Rhône-Alpes. L’Insee et La Poste lui attribuent le code 03. Sa préfecture est Moulins. | [
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Alpes-de-Haute-Provence | Alpes-de-Haute-Provence | Alpes-de-Haute-Provence (; ; ) is a department in the Provence-Alpes-Côte d'Azur region of Southeastern France. Formerly part of the province of Provence, it had a population of 161,588 in 2016. Its main cities are Digne-les-Bains (prefecture), Manosque, Sisteron, Barcelonnette, Castellane and Forcalquier. Inhabitants of Alpes-de-Haute-Provence are called the Bas-Alpins or Bas-Alpines referring to the department of Basses-Alpes which was the former name of the department until 1970. | Les Alpes-de-Haute-Provence ou AHP ( ), appelées Basses-Alpes jusqu'en 1970, sont un département français de la région Provence-Alpes-Côte d'Azur. L'Insee et la Poste lui attribuent le code 04. Sa préfecture est Digne-les-Bains. | [
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Aube | Aube (département) | Aube () is a French department in the Grand Est region of north-eastern France. As with sixty departments in France, this department is named after a river: the Aube. With 305,606 inhabitants (2012), Aube is 76th department in terms of population. The inhabitants of the department are known as "Aubois" or "Auboises" | LAube est un département français de la région Grand Est dont le nom vient de l'Aube, premier affluent notable de la Seine (rive droite). L'Insee et la Poste lui attribuent le code 10. Les habitants de ce département sont appelés les Aubois. Sa préfecture est Troyes. | [
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Arsène Lupin | Arsène Lupin | Arsène Lupin is a fictional gentleman thief and master of disguise created in 1905 by French writer Maurice Leblanc. He was originally called Arsène Lopin, until a local politician of the same name protested. The character was first introduced in a series of short stories serialized in the magazine "Je sais tout". The first story, "The Arrest of Arsène Lupin", was published on 15 July 1905. | Arsène Lupin est un personnage de fiction français créé par Maurice Leblanc. Ce gentleman cambrioleur est particulièrement connu pour son talent à user de déguisements et changer d'identité pour commettre ses délits. | [
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Aveyron | Aveyron (département) | Aveyron (; ; ) is a department located in Occitanie region of Southern France. Named after the Aveyron River, it had a population of 278,697 in 2016. Its inhabitants are known as "Aveyronnais" or "Aveyronnaises" in French. The inhabitants of Rodez are called "Ruthénois", based on the first Celtic settlers in the area, the "Ruteni". | L'Aveyron ( ) est un département français situé dans la région Occitanie, dans le sud-ouest de la France. Il prend le nom de la rivière Aveyron. Il est au centre d'un triangle formé par les villes de Toulouse, Clermont-Ferrand et Montpellier. Ce département reprend approximativement les contours de l'ancienne province du Rouergue. C'est l'un des plus grands départements de France métropolitaine par sa superficie (le cinquième avec, sixième si l'on tient compte de la Guyane). Les habitants de l’Aveyron sont les "Aveyronnais". | [
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Alpes-Maritimes | Alpes-Maritimes | Alpes-Maritimes (; ;, "Maritime Alps") is a department of France located in the extreme southeast corner of the country, on the border with Italy and on the Mediterranean coast. Part of the Provence-Alpes-Côte d'Azur region, it had a population of 1,083,310 in 2017. | Les Alpes-Maritimes ( ) sont un département français de la région Provence-Alpes-Côte d'Azur. Ses habitants sont appelés les "Maralpins". L'Insee et la Poste lui attribuent le. Sa préfecture est Nice. | [
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Ariège (department) | Ariège (département) | Ariège (; ) is a department in southwestern France, in the Occitanie region. It is named after the Ariège River and its capital is Foix. Ariège is known for its rural landscape, with a population of 153,067 as of 2016. Its INSEE and postal code is 09, hence the department's informal name of "le zéro neuf". The inhabitants of the department are known as "Ariègeois" or "Ariègeoises". | L’Ariège ( en français standard ; "Arièja" en occitan (en languedocien, en gascon...) est un département français de la région Occitanie, nommé d'après la rivière homonyme. L’Insee et la Poste lui attribuent le code 09. Sa préfecture est Foix. | [
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Auvergne | Auvergne | Auvergne (, ; or ) is a former administrative region in south-central France, comprising the four departments of Allier, Puy-de-Dôme, Cantal and Haute-Loire. Since 1 January 2016, it has been part of the new region Auvergne-Rhône-Alpes. | LAuvergne ( ou "Euvarnhà") est une région culturelle et historique de France située au cœur du Massif central. De 1941 à 1946 et de 1956 à 2015, la région Auvergne fut également une région administrative française composée des quatre départements de l'Allier, du Cantal, de la Haute-Loire et du Puy-de-Dôme. Sa plus grande ville, Clermont-Ferrand, en était le chef-lieu. Cette région a été supprimée le par la loi sur l'Acte de la décentralisation. Les départements qui la composaient font maintenant partie de la nouvelle région Auvergne-Rhône-Alpes. | [
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Alloy | Alliage | An alloy is a combination of metals or metals combined with one or more other elements. For example, combining the metallic elements gold and copper produces red gold, gold and silver becomes white gold, and silver combined with copper produces sterling silver. Elemental iron, combined with non-metallic carbon or silicon, produces alloys called steel or silicon steel. The resulting mixture forms a substance with properties that often differ from those of the pure metals, such as increased strength or hardness. Unlike other substances that may contain metallic bases but do not behave as metals, such as aluminium oxide (sapphire), beryllium aluminium silicate (emerald) or sodium chloride (salt), an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, opaqueness, and luster. Alloys are used in a wide variety of applications, from the steel alloys, used in everything from buildings to automobiles to surgical tools, to exotic titanium-alloys used in the aerospace industry, to beryllium-copper alloys for non-sparking tools. In some cases, a combination of metals may reduce the overall cost of the material while preserving important properties. In other cases, the combination of metals imparts synergistic properties to the constituent metal elements such as corrosion resistance or mechanical strength. Examples of alloys are steel, solder, brass, pewter, duralumin, bronze and amalgams. | Un alliage est la combinaison d'un élément métallique avec un ou plusieurs métaux par fusion. Les caractéristiques mécaniques des métaux purs sont la plupart du temps relativement faibles. Le fait d'ajouter d'autres éléments permet de « durcir » le métal en augmentant ses caractéristiques mécaniques. Outre les renforcements mécaniques engendrés par déformation, tel que l'écrouissage, il existe des durcissements chimiques par addition d'éléments en solution solide ou par précipitation de phases secondaires durcissantes telles que les carbures. Ces ajouts permettent également de modifier les caractéristiques chimiques, telle que la résistance à la corrosion, ou d'améliorer d'autres caractéristiques, par exemple la coulabilité. | [
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Ardèche | Ardèche (département) | Ardèche (; Occitan and Arpitan: "Ardecha") is a department in the Auvergne-Rhône-Alpes region of Southeastern France. It is named after the Ardèche River and had a population of 320,379 as of 2013. Its largest cities are Aubenas, Annonay, Guilherand-Granges, Tournon-sur-Rhône and Privas (prefecture). | Le département de l'Ardèche ( ) est un département français situé dans la région Auvergne-Rhône-Alpes. Sa préfecture est Privas. Il doit son nom à la rivière Ardèche qui le traverse d'ouest en est, ses habitants s'appellent les "Ardéchois(es)". Il est composé de 335 communes au. L'Insee et la Poste lui attribuent le code 07. | [
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Aude | Aude (département) | Aude (; ) is a department in Southern France, located in the Occitanie region and named after the Aude River. The departmental council also calls it "Cathar Country" (French: "Pays cathare") after a group of religious dissidents active in the 12th century. | L'Aude ( ) est un département français de la région Occitanie, qui se situe dans le Sud de la France. Sa préfecture est Carcassonne, avec sa ville médiévale fortifiée tandis que sa plus grande ville est Narbonne avec plus de. | [
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South Africa | Afrique du Sud | South Africa, officially the Republic of South Africa (RSA), is the southernmost country in Africa. With over 58 million people, it is the world's 24th-most populous nation and covers an area of. South Africa has three capital cities: executive Pretoria, judicial Bloemfontein and legislative Cape Town. The largest city is Johannesburg. About 80% of South Africans are of Black African ancestry, divided among a variety of ethnic groups speaking different African languages. The remaining population consists of Africa's largest communities of European, Asian, Indian, and multiracial ancestry. | LAfrique du Sud, en forme longue la république d'Afrique du Sud, est un pays situé à l'extrémité australe du continent africain. Sa capitale administrative est Pretoria. Il est frontalier à l'ouest-nord-ouest avec la Namibie, au nord et au nord-nord-est avec le Botswana, au nord-est avec le Zimbabwe, et à l'est-nord-est avec le Mozambique et l'Eswatini. Le Lesotho est pour sa part un État enclavé dans le territoire sud-africain. | [
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Aikido | Aïkido | Aikido's fundamental principles include: irimi (entering), atemi, kokyu-ho (breathing control), sankaku-ho (triangular principle) and tenkan (turning) movements that redirect the opponent's attack momentum. Its curriculum comprises various techniques, primarily throws and joint locks. It also includes a weapons system encompassing the "bokken", "tantō" and "jō". | L' est un art martial japonais (budo), fondé par Morihei Ueshiba "ōsensei" entre 1925 et 1969. L'aïkido a été officiellement reconnu par le gouvernement japonais en 1940 sous le nom d’"aikibudō" et sous le nom aikido en 1942 donné par la « Dai Nippon Butoku Kai », organisme gouvernemental visant à regrouper tous les arts martiaux japonais pendant la guerre. Il a été créé à partir de l'expérience que son fondateur avait de l'enseignement des koryu (écoles d'arts martiaux anciennes), essentiellement l"aikijutsu" de l'école "daitō ryū" et le kenjutsu (art du sabre japonais). L'aïkido est né de la rencontre entre ces techniques de combat et une réflexion métaphysique de Morihei Ueshiba sur le sens de la pratique martiale à l'ère moderne. | [
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Angola | Angola | Angola (; ), officially the Republic of Angola (), is a country on the west coast of Southern Africa. It is the seventh-largest country in Africa, bordered by Namibia to the south, the Democratic Republic of the Congo to the north, Zambia to the east, and the Atlantic Ocean to the west. Angola has an exclave province, the province of Cabinda that borders the Republic of the Congo and the Democratic Republic of the Congo. The capital and largest city of Angola is Luanda. | L’Angola, en forme longue la république d'Angola, en portugais, en kikongo, est un pays du Sud-Ouest de l'Afrique, limitrophe de la république démocratique du Congo au nord et au nord-est, de la république du Congo au nord-ouest (par l'enclave de Cabinda), de la Zambie à l'est-sud-est et de la Namibie au sud. | [
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Antigua and Barbuda | Antigua-et-Barbuda | Antigua and Barbuda (; ) is an island sovereign state in the West Indies in the Americas, lying between the Caribbean Sea and the Atlantic Ocean. It consists of two major islands, Antigua and Barbuda (separated by 39 miles), and a number of smaller islands (including Great Bird, Green, Guiana, Long, Maiden, Prickly Pear, York Islands and further south, the island of Redonda). The permanent population numbers about 95,900 (2018 est.), with 97% being resident on Antigua. The capital and largest port and city is St. John's on Antigua, with Codrington being the largest town on Barbuda. Lying near each other (the main Barbuda airport is less than 0.5° of latitude, or, north of the main Antigua airport), Antigua and Barbuda are in the middle of the Leeward Islands, part of the Lesser Antilles, roughly at 17°N of the equator. | Antigua-et-Barbuda ou Antigue-et-Barbude est un État des Antilles ayant pour capitale Saint John's, situé à une cinquantaine de kilomètres au nord de la Guadeloupe et au nord-est de l'île des Antilles britanniques de Montserrat, dans les Caraïbes. Cet État est composé de deux îles principales, Antigua, et Barbuda, ainsi que de quelques îles plus petites. | [
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Aten | Aton | Aten also Aton, Atonu, Itn (, "reconstructed" ) was the focus of Atenism, the religious system established in ancient Egypt by the Eighteenth Dynasty pharaoh Akhenaten. The Aten was the disc of the sun and originally an aspect of Ra, the sun god in traditional ancient Egyptian religion, but Akhenaten made it the sole focus of official worship during his reign. | Aton est un dieu solaire de l'Égypte antique. Il est surtout connu comme un dieu éphémère de la mythologie égyptienne du Nouvel Empire durant le règne d'Amenhotep qui prit le nom d'Akhenaton ("ȝḫ n Jtn", « Éclat d’Aton » ou, en l'absence du déterminatif : « Utile à Aton ») (v. -1353 à -1337). | [
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