Henri Dulac
Henri Claudius Rosarius Dulac (3 October 1870, Fayence – 2 September 1955, Fayence) was a French mathematician. Life Born in Fayence, France, Dulac graduated from École Polytechnique (Paris, class of 1892) and obtained a Doctorate in Mathematics. He started to teach a class of mathematic analysis at University, in Grenoble (France), Algiers (today Algeria) and Poitiers (France). Holder of a pulpit in pure mathematics in the Sciences University of Lyon (France) in 1911, his teaching was suspended during the first world war (1914 – 1918) and he had to serve as officer in the French army. After the war, he became holder of a pulpit of differential and integral calculus and also taught in École Centrale Lyon. He became examiner at École Polytechnique (Paris) and President of the admission jury. Awarded Officer of Legion d'honneur, the French order established by Napoleon and associate member of the French Academy of Sciences, he published part of Euler's works and contribu ...
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Henri Dulac
Henri Claudius Rosarius Dulac (3 October 1870, Fayence – 2 September 1955, Fayence) was a French mathematician. Life Born in Fayence, France, Dulac graduated from École Polytechnique (Paris, class of 1892) and obtained a Doctorate in Mathematics. He started to teach a class of mathematic analysis at University, in Grenoble (France), Algiers (today Algeria) and Poitiers (France). Holder of a pulpit in pure mathematics in the Sciences University of Lyon (France) in 1911, his teaching was suspended during the first world war (1914 – 1918) and he had to serve as officer in the French army. After the war, he became holder of a pulpit of differential and integral calculus and also taught in École Centrale Lyon. He became examiner at École Polytechnique (Paris) and President of the admission jury. Awarded Officer of Legion d'honneur, the French order established by Napoleon and associate member of the French Academy of Sciences, he published part of Euler's works and contribu ...
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Fayence
Fayence (; oc, Faiença) is a commune in the Var department in the Provence-Alpes-Côte d'Azur region in Southeastern France. In 2019, it had a population of 5,735. Fayence is one of a series of "perched villages" overlooking the plain between the southern Alps and the Esterel massif, which borders the Mediterranean Sea between Cannes and Saint-Raphaël. The village is located on the road to Mons, which later on joins the Route Napoléon linking Nice to Grenoble through the Alps. Some high-standing resorts have settled nearby the village in the recent years: the Domaine de Terre Blanche at Tourrettes and Domaine de Fayence attract a foreign clientele. The village contains a primary school (École de la Ferrage) and a junior high school (Collège Marie Mauron). The Aérodrome de Fayence-Tourettes is one of the most active in Europe for gliding; it hosts the Provence Côte d'Azur Aeronautical Association. History Before and during WWII, Fayence-Tourettes Airfield was an air fo ...
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France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pacific and Indian Oceans. Its Metropolitan France, metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean. Due to its several coastal territories, France has the largest exclusive economic zone in the world. France borders Belgium, Luxembourg, Germany, Switzerland, Monaco, Italy, Andorra, and Spain in continental Europe, as well as the Kingdom of the Netherlands, Netherlands, Suriname, and Brazil in the Americas via its overseas territories in French Guiana and Saint Martin (island), ...
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École Polytechnique
École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoie, a French commune * École-Valentin, a French commune in the Doubs département * Grandes écoles, higher education establishments in France * The École, a French-American bilingual school in New York City Ecole may refer to: * Ecole Software This is a list of Notability, notable video game companies that have made games for either computers (like PC or Mac), video game consoles, handheld or mobile devices, and includes companies that currently exist as well as now-defunct companies. ...

École Centrale Lyon
École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoie, a French commune * École-Valentin, a French commune in the Doubs département * Grandes écoles, higher education establishments in France * The École, a French-American bilingual school in New York City Ecole may refer to: * Ecole Software This is a list of Notability, notable video game companies that have made games for either computers (like PC or Mac), video game consoles, handheld or mobile devices, and includes companies that currently exist as well as now-defunct companies. ...

Legion D'honneur
The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleon Bonaparte, it has been retained (with occasional slight alterations) by all later French governments and regimes. The order's motto is ' ("Honour and Fatherland"); its seat is the Palais de la Légion d'Honneur next to the Musée d'Orsay, on the left bank of the Seine in Paris. The order is divided into five degrees of increasing distinction: ' (Knight), ' (Officer), ' (Commander), ' (Grand Officer) and ' (Grand Cross). History Consulate During the French Revolution, all of the French orders of chivalry were abolished and replaced with Weapons of Honour. It was the wish of Napoleon Bonaparte, the First Consul, to create a reward to commend civilians and soldiers. From this wish was instituted a , a body of men that was not an order of c ...
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Napoleon
Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader who rose to prominence during the French Revolution and led successful campaigns during the Revolutionary Wars. He was the ''de facto'' leader of the French Republic as First Consul from 1799 to 1804, then Emperor of the French from 1804 until 1814 and again in 1815. Napoleon's political and cultural legacy endures to this day, as a highly celebrated and controversial leader. He initiated many liberal reforms that have persisted in society, and is considered one of the greatest military commanders in history. His wars and campaigns are studied by militaries all over the world. Between three and six million civilians and soldiers perished in what became known as the Napoleonic Wars. Napoleon was born on the island of Corsica, not long af ...
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French Academy Of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefront of scientific developments in Europe in the 17th and 18th centuries, and is one of the earliest Academy of Sciences, Academies of Sciences. Currently headed by Patrick Flandrin (President of the Academy), it is one of the five Academies of the Institut de France. History The Academy of Sciences traces its origin to Colbert's plan to create a general academy. He chose a small group of scholars who met on 22 December 1666 in the King's library, near the present-day Bibliothèque nationale de France, Bibliothèque Nationals, and thereafter held twice-weekly working meetings there in the two rooms assigned to the group. The first 30 years of the Academy's existence were relatively informal ...
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Bendixson–Dulac Theorem
In mathematics, the Bendixson–Dulac theorem on dynamical systems states that if there exists a C^1 function \varphi(x, y) (called the Dulac function) such that the expression :\frac + \frac has the same sign (\neq 0) almost everywhere in a simply connected region of the plane, then the plane autonomous system : \frac = f(x,y), : \frac = g(x,y) has no nonconstant periodic solutions lying entirely within the region. "Almost everywhere" means everywhere except possibly in a set of measure 0, such as a point or line. The theorem was first established by Swedish mathematician Ivar Bendixson in 1901 and further refined by French mathematician Henri Dulac in 1923 using Green's theorem. Proof Without loss of generality, let there exist a function \varphi(x, y) such that :\frac +\frac >0 in simply connected region R. Let C be a closed trajectory of the plane autonomous system in R. Let D be the interior of C. Then by Green's theorem, : \begin & \iint_D \left( \frac +\ ...
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Hilbert's Sixteenth Problem
Hilbert's 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list of 23 problems in mathematics. The original problem was posed as the ''Problem of the topology of algebraic curves and surfaces'' (''Problem der Topologie algebraischer Kurven und Flächen''). Actually the problem consists of two similar problems in different branches of mathematics: * An investigation of the relative positions of the branches of real algebraic curves of degree ''n'' (and similarly for algebraic surfaces). * The determination of the upper bound for the number of limit cycles in two-dimensional polynomial vector fields of degree ''n'' and an investigation of their relative positions. The first problem is yet unsolved for ''n'' = 8. Therefore, this problem is what usually is meant when talking about Hilbert's sixteenth problem in real algebraic geometry. The second problem also remains unsolved: no up ...
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Transseries
In mathematics, the field \mathbb^ of logarithmic-exponential transseries is a non-Archimedean ordered differential field which extends comparability of asymptotic growth rates of elementary nontrigonometric functions to a much broader class of objects. Each log-exp transseries represents a formal asymptotic behavior, and it can be manipulated formally, and when it converges (or in every case if using special semantics such as through infinite surreal numbers), corresponds to actual behavior. Transseries can also be convenient for representing functions. Through their inclusion of exponentiation and logarithms, transseries are a strong generalization of the power series at infinity (\sum_^\infty \frac) and other similar asymptotic expansions. The field \mathbb^ was introduced independently by Dahn-Göring and Ecalle in the respective contexts of model theory or exponential fields and of the study of analytic singularity and proof by Ecalle of the Dulac conjectures. It constitutes ...
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1870 Births
Year 187 ( CLXXXVII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Quintius and Aelianus (or, less frequently, year 940 '' Ab urbe condita''). The denomination 187 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Septimius Severus marries Julia Domna (age 17), a Syrian princess, at Lugdunum (modern-day Lyon). She is the youngest daughter of high-priest Julius Bassianus – a descendant of the Royal House of Emesa. Her elder sister is Julia Maesa. * Clodius Albinus defeats the Chatti, a highly organized German tribe that controlled the area that includes the Black Forest. By topic Religion * Olympianus succeeds Pertinax as bishop of Byzantium (until 198). Births * Cao Pi, Chinese emperor of the Cao Wei state (d. 226) * ...
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