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Gaston Floquet
Achille Marie Gaston Floquet (15 December 1847, Épinal – 7 October 1920, Nancy) was a French mathematician, best known for his work in mathematical analysis, especially in theory of differential equations. See also *Floquet theory Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form :\dot = A(t) x, with x\in and \displaystyle A(t) \in being a piecewise continu ... External links * * * 1847 births 1920 deaths People from Épinal École Normale Supérieure alumni 19th-century French mathematicians {{France-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Normale Supérieure (Paris)
The – PSL (; also known as ENS, , Ulm or ENS Paris) is a ''grande école'' in Paris, France. It is one of the constituent members of Paris Sciences et Lettres University (PSL). Due to its selectivity, historical role, and influence within French society, the ENS is generally considered the most prestigious of the ''grande école, grandes écoles,'' as well as one of the most prestigious higher education institutions in France. Its pupils are generally referred to as ''normaliens'', while its alumni are sometimes referred to as List of École normale supérieure people, ''archicubes''. The school was founded in 1794 during the French Revolution, to provide homogeneous training of high-school teachers in France, but it later closed. The school was subsequently reestablished by Napoleon I as ''pensionnat normal'' from 1808 to 1822, before being recreated in 1826 and taking the name École normale in 1830. When other institutes called ''écoles normales'' were created in 1845, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floquet Theory
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form :\dot = A(t) x, with x\in and \displaystyle A(t) \in being a piecewise continuous periodic function with period T and defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to , gives a canonical form for each fundamental matrix solution of this common linear system. It gives a coordinate change \displaystyle y=Q^(t)x with \displaystyle Q(t+2T)=Q(t) that transforms the periodic system to a traditional linear system with constant, real coefficients. When applied to physical systems with periodic potentials, such as crystals in condensed matter physics, the result is known as Bloch's theorem. Note that the solutions of the linear differential equation form a vector space. A matrix \phi\,(t) is called a '' fundamental matrix solution'' if the columns form a basi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Épinal
Épinal (; ; ) is a Communes of France, commune in northeastern France and the prefecture of the Vosges (department), Vosges Departments of France, department. Geography The commune has a land area of . It is situated on the river Moselle, south of Nancy, France, Nancy. Épinal station has rail connections to Paris, Remiremont, Strasbourg, Belfort and Nancy. History The mythical founding date of Épinal is said to be 983 since celebrations took place for the "Millennium" in June 1983. This date was chosen for political reasons to mark a "starting point" following the election of Philippe Séguin as mayor in March 1983. In 1444, the town of Épinal was still part of the domain of the Prince-Bishopric of Metz, bishops of Metz. In September, representatives of the town took advantage of King Charles VII of France, Charles VII's passage through Nancy to offer him the submission of the town and to ask for his protection in return. The act of submission of Épinal is dated Septem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nancy, France
Nancy is the Prefectures in France, prefecture of the northeastern Departments of France, French department of Meurthe-et-Moselle. It was the capital of the Duchy of Lorraine, which was Lorraine and Barrois, annexed by France under King Louis XV in 1766 and replaced by a Provinces of France, province, with Nancy maintained as capital. Following its rise to prominence in the Age of Enlightenment, it was nicknamed the "capital of Eastern France" in the late 19th century. The metropolitan area of Nancy had a population of 508,793 inhabitants as of 2021, making it the 16th-largest functional area (France), functional urban area in France and Lorraine's largest. The population of the city of Nancy proper is 104,387 (2022). The motto of the city is —a reference to the thistle, which is a symbol of Lorraine. Place Stanislas, a large square built between 1752 and 1756 by architect Emmanuel Héré under the direction of Stanislaus I of Poland to link the medieval old town of Nancy and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1847 Births
Events January–March * January 4 – Samuel Colt sells his first revolver pistol to the U.S. government. * January 13 – The Treaty of Cahuenga ends fighting in the Mexican–American War in California. * January 16 – John C. Frémont is appointed Governor of the new California Territory. * January 17 – St. Anthony Hall fraternity is founded at Columbia University, New York City. * January 30 – Yerba Buena, California, is renamed San Francisco. * February 5 – A rescue effort, called the First Relief, leaves Johnson's Ranch to save the ill-fated Donner Party of California-bound migrants who became snowbound in the Sierra Nevada earlier this winter. Some have resorted to survival by cannibalism. * February 22 – Mexican–American War: Battle of Buena Vista – 5,000 American troops under General Zachary Taylor use their superiority in artillery to drive off 15,000 Mexican troops under Antonio López de Santa Anna, defeating the Mexicans the next day. * Febr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1920 Deaths
Events January * January 1 ** Polish–Soviet War: The Russian Red Army increases its troops along the Polish border from 4 divisions to 20. ** Kauniainen in Finland, completely surrounded by the city of Espoo, secedes from Espoo as its own market town. * January 7 – Russian Civil War: The forces of White movement, Russian White Admiral Alexander Kolchak surrender in Krasnoyarsk; the Great Siberian Ice March ensues. * January 10 ** The Treaty of Versailles takes effect, officially ending World War I. ** The League of Nations Covenant enters into force. On January 16, the organization holds its first council meeting, in Paris. * January 11 – The Azerbaijan Democratic Republic is recognised de facto by European powers in Palace of Versailles, Versailles. * January 13 – ''The New York Times'' Robert H. Goddard#Publicity and criticism, ridicules American rocket scientist Robert H. Goddard, which it will rescind following the launch of Apollo 11 in 1969. * Janua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Épinal
The term "the people" refers to the public or common mass of people of a polity. As such it is a concept of human rights law, international law as well as constitutional law, particularly used for claims of popular sovereignty. In contrast, a people is any plurality of persons considered as a whole. Used in politics and law, the term "a people" refers to the collective or community of an ethnic group or nation. Concepts Legal Chapter One, Article One of the Charter of the United Nations states that "peoples" have the right to self-determination. Though the mere status as peoples and the right to self-determination, as for example in the case of Indigenous peoples (''peoples'', as in all groups of indigenous people, not merely all indigenous persons as in ''indigenous people''), does not automatically provide for independent sovereignty and therefore secession. Indeed, judge Ivor Jennings identified the inherent problems in the right of "peoples" to self-determination, as i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Normale Supérieure Alumni
École or Ecole 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 The École, formerly Ecole Internationale de New York, is an intimate and independent French-American school, which cultivates an internationally minded community of students from 2 to 14 years old in New York City’s vibrant Flatiron Distric ..., a French-American bilingual school in New York City * Ecole Software, a Japanese video-games developer/publisher {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
