1.
Obernai
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Obernai commune in the Bas-Rhin department in Alsace in north-eastern France. It lies on the slopes of the Vosges mountains. Obernai is a growing city, its number of inhabitants having gone up from 6,304 in 1968 to 11,099 in 2006. The metropolitan area of Obernai had 12,369 inhabitants in 2006, from 7,293 in 1968. The Obernai region, which was the property of the dukes of Alsace in the 7th century, is the birthplace of St. Odile, daughter of the Duke, who would become the Patron Saint of Alsace. The Obernai name first appears in 1240, when the village acquires the status of town under the tutelage of the Hohenstaufen family and it became a member of the Décapole in 1354, an alliance of ten towns of the Holy Roman Empire in Alsace. Obernais status reaches its apex in the 15th and 16th century, in 1562, Emperor Ferdinand I visited the prosperous town of Obernai. The Thirty Years War damaged the town, which was occupied by the Imperial troops then by the Swedes, the town was ransomed and ceded to France in 1679, and started to recover some of its prosperity, without totally recapturing its former glory. The town was annexed by Germany in 1871 with the rest of Alsace then was returned to France after World War I in 1918, Obernai is an important center of wine and beer production as well as a touristic destination. The industrial activity features the following companies, Hager, Kronenbourg, Triumph, Sobovia, Supra, the historical wine of the city is called the Vin du Pistolet in reference to a local legend. During the mid-1800s, Obernai was home to a Marianist primary school, domain of the Léonardsau, current museum of the horse and the horse carriage. Truttenhausen abbey, old monastery of the canons of St-Augustin. Gail Castle, Currently the Freppel High School Oberkirch Castle, rebuilt between 1843 and 1846 with the characteristics of a fortified castle of the 16th or 17th century. El Biar Castle, Built between 1864 and 1865 on the site of an old mill, by General de Vives. Klevener de Heiligenstein, a wine produced in Obernai Communes of the Bas-Rhin department Official website

2.
Alsace
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Alsace is a cultural and historical region in eastern France now located in the administrative region of Grand Est. Alsace is located on Frances eastern border and on the west bank of the upper Rhine adjacent to Germany, from 1982 until January 2016, Alsace was the smallest of 22 administrative regions in metropolitan France, consisting of the Bas-Rhin and Haut-Rhin departments. Territorial reform passed by the French legislature in 2014 resulted in the merger of the Alsace administrative region with Champagne-Ardenne and Lorraine to form Grand Est. The predominant historical language of Alsace is Alsatian, a Germanic dialect also spoken across the Rhine, but today most Alsatians primarily speak French, the political status of Alsace has been heavily influenced by historical decisions, wars, and strategic politics. The economic and cultural capital as well as largest city of Alsace is Strasbourg, the city is the seat of several international organizations and bodies. The name Alsace can be traced to the Old High German Ali-saz or Elisaz, an alternative explanation is from a Germanic Ell-sass, meaning seated on the Ill, a river in Alsace. In prehistoric times, Alsace was inhabited by nomadic hunters, by 1500 BC, Celts began to settle in Alsace, clearing and cultivating the land. It should be noted that Alsace is a surrounded by the Vosges mountains. It creates Foehn winds which, along with irrigation, contributes to the fertility of the soil. In a world of agriculture, Alsace has always been a region which explains why it suffered so many invasions and annexations in its history. By 58 BC, the Romans had invaded and established Alsace as a center of viticulture, to protect this highly valued industry, the Romans built fortifications and military camps that evolved into various communities which have been inhabited continuously to the present day. While part of the Roman Empire, Alsace was part of Germania Superior, with the decline of the Roman Empire, Alsace became the territory of the Germanic Alemanni. The Alemanni were agricultural people, and their Germanic language formed the basis of modern-day dialects spoken along the Upper Rhine, Clovis and the Franks defeated the Alemanni during the 5th century AD, culminating with the Battle of Tolbiac, and Alsace became part of the Kingdom of Austrasia. Under Clovis Merovingian successors the inhabitants were Christianized, Alsace formed part of the Middle Francia, which was ruled by the eldest grandson Lothar I. Lothar died early in 855 and his realm was divided into three parts, the part known as Lotharingia, or Lorraine, was given to Lothars son. The rest was shared between Lothars brothers Charles the Bald and Louis the German, the Kingdom of Lotharingia was short-lived, however, becoming the stem duchy of Lorraine in Eastern Francia after the Treaty of Ribemont in 880. Alsace was united with the other Alemanni east of the Rhine into the duchy of Swabia. Alsace experienced great prosperity during the 12th and 13th centuries under Hohenstaufen emperors, Frederick I set up Alsace as a province to be ruled by ministeriales, a non-noble class of civil servants

3.
France
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France, officially the French Republic, is a country with territory in western Europe and several overseas regions and territories. The European, or metropolitan, area of France extends from the Mediterranean Sea to the English Channel and the North Sea, Overseas France include French Guiana on the South American continent and several island territories in the Atlantic, Pacific and Indian oceans. France spans 643,801 square kilometres and had a population of almost 67 million people as of January 2017. It is a unitary republic with the capital in Paris. Other major urban centres include Marseille, Lyon, Lille, Nice, Toulouse, during the Iron Age, what is now metropolitan France was inhabited by the Gauls, a Celtic people. The area was annexed in 51 BC by Rome, which held Gaul until 486, France emerged as a major European power in the Late Middle Ages, with its victory in the Hundred Years War strengthening state-building and political centralisation. During the Renaissance, French culture flourished and a colonial empire was established. The 16th century was dominated by civil wars between Catholics and Protestants. France became Europes dominant cultural, political, and military power under Louis XIV, in the 19th century Napoleon took power and established the First French Empire, whose subsequent Napoleonic Wars shaped the course of continental Europe. Following the collapse of the Empire, France endured a succession of governments culminating with the establishment of the French Third Republic in 1870. Following liberation in 1944, a Fourth Republic was established and later dissolved in the course of the Algerian War, the Fifth Republic, led by Charles de Gaulle, was formed in 1958 and remains to this day. Algeria and nearly all the colonies became independent in the 1960s with minimal controversy and typically retained close economic. France has long been a centre of art, science. It hosts Europes fourth-largest number of cultural UNESCO World Heritage Sites and receives around 83 million foreign tourists annually, France is a developed country with the worlds sixth-largest economy by nominal GDP and ninth-largest by purchasing power parity. In terms of household wealth, it ranks fourth in the world. France performs well in international rankings of education, health care, life expectancy, France remains a great power in the world, being one of the five permanent members of the United Nations Security Council with the power to veto and an official nuclear-weapon state. It is a member state of the European Union and the Eurozone. It is also a member of the Group of 7, North Atlantic Treaty Organization, Organisation for Economic Co-operation and Development, the World Trade Organization, originally applied to the whole Frankish Empire, the name France comes from the Latin Francia, or country of the Franks

4.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times

5.
University of Paris
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The University of Paris, metonymically known as the Sorbonne, was a university in Paris, France. Emerging around 1150 as an associated with the cathedral school of Notre Dame de Paris. Vast numbers of popes, royalties, scientists and intellectuals were educated at the University of Paris, following the turbulence of the French Revolution, education was suspended in 1793 whereafter its faculties were partly reorganised by Napoleon as the University of France. In 1896, it was renamed again to the University of Paris, in 1970, following the May 1968 events, the university was divided into 13 autonomous universities. Others, like Panthéon-Sorbonne University, chose to be multidisciplinary, in 1150, the future University of Paris was a student-teacher corporation operating as an annex of the Notre-Dame cathedral school. The university had four faculties, Arts, Medicine, Law, the Faculty of Arts was the lowest in rank, but also the largest, as students had to graduate there in order to be admitted to one of the higher faculties. The students were divided into four nationes according to language or regional origin, France, Normandy, Picardy, the last came to be known as the Alemannian nation. Recruitment to each nation was wider than the names might imply, the faculty and nation system of the University of Paris became the model for all later medieval universities. Under the governance of the Church, students wore robes and shaved the tops of their heads in tonsure, students followed the rules and laws of the Church and were not subject to the kings laws or courts. This presented problems for the city of Paris, as students ran wild, students were often very young, entering the school at age 13 or 14 and staying for 6 to 12 years. Three schools were especially famous in Paris, the palatine or palace school, the school of Notre-Dame, the decline of royalty brought about the decline of the first. The other two were ancient but did not have much visibility in the early centuries, the glory of the palatine school doubtless eclipsed theirs, until it completely gave way to them. These two centres were much frequented and many of their masters were esteemed for their learning, the first renowned professor at the school of Ste-Geneviève was Hubold, who lived in the tenth century. Not content with the courses at Liège, he continued his studies at Paris, entered or allied himself with the chapter of Ste-Geneviève, and attracted many pupils via his teaching. Distinguished professors from the school of Notre-Dame in the century include Lambert, disciple of Fulbert of Chartres, Drogo of Paris, Manegold of Germany. Three other men who added prestige to the schools of Notre-Dame and Ste-Geneviève were William of Champeaux, Abélard, humanistic instruction comprised grammar, rhetoric, dialectics, arithmetic, geometry, music, and astronomy. To the higher instruction belonged dogmatic and moral theology, whose source was the Scriptures and it was completed by the study of Canon law. The School of Saint-Victor arose to rival those of Notre-Dame and Ste-Geneviève and it was founded by William of Champeaux when he withdrew to the Abbey of Saint-Victor

6.
Jean-Marc Deshouillers
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Jean-Marc Deshouillers is a French mathematician, specializing in analytic number theory. He is a professor at the University of Bordeaux, Deshouillers attended the Paris École Polytechnique, graduating with an engineer diploma in 1968. He received his PhD in 1972 at the University Paris VI Pierre et Marie Curie, in the seventies, he was assistant professor in mathematics at the École Polytechnique, which moved from Paris to Palaiseau. Deshouillers is a professor at the University of Bordeaux, in 2009 he was at the Institute for Advanced Study. With Henryk Iwaniec, he improved the Kuznetsov trace formula, in 1997, with Effinger and Herman te Riele, he proved the ternary Goldbach conjecture under the Generalized Riemann Hypothesis. Among his students was Gérald Tenenbaum, problème de Waring pour les bicarrés. Séminaire de théorie des nombres de Bordeaux, 1984/85, Online

7.
French people
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The French are an ethnic group and nation who are identified with the country of France. This connection may be legal, historical, or cultural, modern French society can be considered a melting pot. To be French, according to the first article of the French Constitution, is to be a citizen of France, regardless of origin, race. The debate concerning the integration of this view with the underlying the European Community remains open. A large number of foreigners have traditionally been permitted to live in France, indeed, the country has long valued its openness, tolerance and the quality of services available. Application for French citizenship is often interpreted as a renunciation of previous state allegiance unless a dual citizenship agreement exists between the two countries, the European treaties have formally permitted movement and European citizens enjoy formal rights to employment in the state sector. Seeing itself as a nation with universal values, France has always valued. However, the success of such assimilation has recently called into question. There is increasing dissatisfaction with, and within, growing ethno-cultural enclaves, the 2005 French riots in some troubled and impoverished suburbs were an example of such tensions. However they should not be interpreted as ethnic conflicts but as social conflicts born out of socioeconomic problems endangering proper integration, the name France etymologically derives from the word Francia, the territory of the Franks. The Franks were a Germanic tribe that overran Roman Gaul at the end of the Roman Empire, in the pre-Roman era, all of Gaul was inhabited by a variety of peoples who were known collectively as the Gaulish tribes. Gaul was militarily conquered in 58-51 BCE by the Roman legions under the command of General Julius Caesar, the area then became part of the Roman Empire. Over the next five centuries the two cultures intermingled, creating a hybridized Gallo-Roman culture, the Gaulish vernacular language disappeared step by step to be replaced everywhere by Vulgar Latin, which would later develop under Frankish influence into the French language in the North of France. With the decline of the Roman Empire in Western Europe, a federation of Germanic peoples entered the picture, the Franks were Germanic pagans who began to settle in northern Gaul as laeti, already during the Roman era. They continued to filter across the Rhine River from present-day Netherlands, at the beginning, they served in the Roman army and reached high commands. Their language is spoken as a kind of Dutch in northern France. Another Germanic people immigrated massively to Alsace, the Alamans, which explains the Alemannic German spoken there and they were competitors of the Franks, thats why it became at the Renaissance time the word for German in French, Allemand. By the early 6th century the Franks, led by the Merovingian king Clovis I and his sons, had consolidated their hold on much of modern-day France, the Vikings eventually intermarried with the local people, converting to Christianity in the process

8.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems

9.
Nicolas Bourbaki
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With the goal of grounding all of mathematics on set theory, the group strove for rigour and generality. Their work led to the discovery of several concepts and terminologies still used, in 1934, young French mathematicians from various French universities felt the need to form a group to jointly produce textbooks that they could all use for teaching. André Weil organized the first meeting on 10 December 1934 in the basement of a Parisian grill room, Bourbakis main work is the Elements of Mathematics series. This series aims to be a completely self-contained treatment of the areas of modern mathematics. Assuming no special knowledge of mathematics, it takes up mathematics from the beginning, proceeds axiomatically. The volume on spectral theory from 1967 was for almost four decades the last new book to be added to the series, after that several new chapters to existing books as well as revised editions of existing chapters appeared until the publication of chapters 8-9 of Commutative Algebra in 1983. Then a long break in publishing activity occurred, leading many to suspect the end of the publishing project, however, chapter 10 of Commutative Algebra appeared in 1998, and after another long break a completely re-written and expanded chapter 8 of Algèbre was published in 2012. More importantly, the first four chapters of a new book on algebraic topology were published in 2016. Besides the Éléments de mathématique series, lectures from the Séminaire Bourbaki also have been published in monograph form since 1948. Notations introduced by Bourbaki include the symbol ∅ for the empty set and a dangerous bend symbol ☡, and the terms injective, surjective, and bijective. The emphasis on rigour may be seen as a reaction to the work of Henri Poincaré, the impact of Bourbakis work initially was great on many active research mathematicians world-wide. For example, Our time is witnessing the creation of a monumental work and it provoked some hostility, too, mostly on the side of classical analysts, they approved of rigour but not of high abstraction. This led to a gulf with the way theoretical physics was practiced, Bourbakis direct influence has decreased over time. This is partly because certain concepts which are now important, such as the machinery of category theory, are not covered in the treatise. It also mattered that, while especially algebraic structures can be defined in Bourbakis terms. On the other hand, the approach and rigour advocated by Bourbaki have permeated the current mathematical practices to such extent that the task undertaken was completed and this is particularly true for the less applied parts of mathematics. The Bourbaki seminar series founded in post-WWII Paris continues, it has going on since 1948. It is an important source of survey articles, with sketches of proofs, the topics range through all branches of mathematics, including sometimes theoretical physics

10.
Rational function
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In mathematics, a rational function is any function which can be defined by a rational fraction, i. e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be numbers, they may be taken in any field K. In this case, one speaks of a function and a rational fraction over K. The values of the variables may be taken in any field L containing K, then the domain of the function is the set of the values of the variables for which the denominator is not zero and the codomain is L. The set of functions over a field K is a field. A function f is called a function if and only if it can be written in the form f = P Q where P and Q are polynomials in x and Q is not the zero polynomial. The domain of f is the set of all points x for which the denominator Q is not zero and it is a common usage to identify f and f 1, that is to extend by continuity the domain of f to that of f 1. Indeed, one can define a rational fraction as a class of fractions of polynomials. In this case P Q is equivalent to P1 Q1, a proper rational function is a rational function in which the degree of P is no greater than the degree of Q and both are real polynomials. The rational function f = x 3 −2 x 2 is not defined at x 2 =5 ⇔ x = ±5 and it is asymptotic to x 2 as x approaches infinity. A constant function such as f = π is a function since constants are polynomials. Note that the function itself is rational, even though the value of f is irrational for all x, every polynomial function f = P is a rational function with Q =1. A function that cannot be written in form, such as f = sin , is not a rational function. The adjective irrational is not generally used for functions, the rational function f = x x is equal to 1 for all x except 0, where there is a removable singularity. The sum, product, or quotient of two functions is itself a rational function. However, the process of reduction to standard form may result in the removal of such singularities unless care is taken. Using the definition of functions as equivalence classes gets around this. For example,1 x 2 − x +2 = ∑ k =0 ∞ a k x k, combining like terms gives 1 =2 a 0 + x + ∑ k =2 ∞ x k

11.
JSTOR
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JSTOR is a digital library founded in 1995. Originally containing digitized back issues of journals, it now also includes books and primary sources. It provides full-text searches of almost 2,000 journals, more than 8,000 institutions in more than 160 countries have access to JSTOR, most access is by subscription, but some older public domain content is freely available to anyone. William G. Bowen, president of Princeton University from 1972 to 1988, JSTOR originally was conceived as a solution to one of the problems faced by libraries, especially research and university libraries, due to the increasing number of academic journals in existence. Most libraries found it prohibitively expensive in terms of cost and space to maintain a collection of journals. By digitizing many journal titles, JSTOR allowed libraries to outsource the storage of journals with the confidence that they would remain available long-term, online access and full-text search ability improved access dramatically. Bowen initially considered using CD-ROMs for distribution, JSTOR was initiated in 1995 at seven different library sites, and originally encompassed ten economics and history journals. JSTOR access improved based on feedback from its sites. Special software was put in place to make pictures and graphs clear, with the success of this limited project, Bowen and Kevin Guthrie, then-president of JSTOR, wanted to expand the number of participating journals. They met with representatives of the Royal Society of London and an agreement was made to digitize the Philosophical Transactions of the Royal Society dating from its beginning in 1665, the work of adding these volumes to JSTOR was completed by December 2000. The Andrew W. Mellon Foundation funded JSTOR initially, until January 2009 JSTOR operated as an independent, self-sustaining nonprofit organization with offices in New York City and in Ann Arbor, Michigan. JSTOR content is provided by more than 900 publishers, the database contains more than 1,900 journal titles, in more than 50 disciplines. Each object is identified by an integer value, starting at 1. In addition to the site, the JSTOR labs group operates an open service that allows access to the contents of the archives for the purposes of corpus analysis at its Data for Research service. This site offers a facility with graphical indication of the article coverage. Users may create focused sets of articles and then request a dataset containing word and n-gram frequencies and they are notified when the dataset is ready and may download it in either XML or CSV formats. The service does not offer full-text, although academics may request that from JSTOR, JSTOR Plant Science is available in addition to the main site. The materials on JSTOR Plant Science are contributed through the Global Plants Initiative and are only to JSTOR

12.
Virtual International Authority File
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The Virtual International Authority File is an international authority file. It is a joint project of national libraries and operated by the Online Computer Library Center. The project was initiated by the US Library of Congress, the German National Library, the National Library of France joined the project on October 5,2007. The project transitions to a service of the OCLC on April 4,2012, the aim is to link the national authority files to a single virtual authority file. In this file, identical records from the different data sets are linked together, a VIAF record receives a standard data number, contains the primary see and see also records from the original records, and refers to the original authority records. The data are available online and are available for research and data exchange. Reciprocal updating uses the Open Archives Initiative Protocol for Metadata Harvesting protocol, the file numbers are also being added to Wikipedia biographical articles and are incorporated into Wikidata. VIAFs clustering algorithm is run every month, as more data are added from participating libraries, clusters of authority records may coalesce or split, leading to some fluctuation in the VIAF identifier of certain authority records

13.
Integrated Authority File
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The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly for documentation in libraries and increasingly also by archives, the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license, the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, and an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format