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Joseph Liouville
Joseph Liouville ( ; ; 24 March 1809 – 8 September 1882) was a French mathematician and engineer. Life and work He was born in Saint-Omer in France on 24 March 1809. His parents were Claude-Joseph Liouville (an army officer) and Thérèse Liouville (née Balland). Liouville gained admission to the École Polytechnique in 1825 and graduated in 1827. Just like Augustin-Louis Cauchy before him, Liouville studied engineering at École des Ponts et Chaussées after graduating from the Polytechnique, but opted instead for a career in mathematics. After some years as an assistant at various institutions including the École Centrale Paris, he was appointed as professor at the École Polytechnique in 1838. He obtained a chair in mathematics at the Collège de France in 1850 and a chair in mechanics at the Faculté des Sciences in 1857. Besides his academic achievements, he was very talented in organisational matters. Liouville founded the ''Journal de Mathématiques Pures et A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Academy Of Sciences
The French Academy of Sciences (, ) is a learned society, founded in 1666 by 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 . __TOC__ 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 Nationale, 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, since no statutes had as yet been laid down for the ins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collège De France
The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most prestigious research establishment. It is an associate member of PSL University. Research and teaching are closely linked at the , whose ambition is to teach "the knowledge that is being built up in all fields of literature, science and the arts". Overview As of 2021, 21 Nobel Prize winners and 9 Fields Medalists have been affiliated with the Collège. It does not grant degrees. Each professor is required to give lectures where attendance is free and open to anyone. Professors, about 50 in number, are chosen by the professors themselves, from a variety of disciplines, in both science and the humanities. The motto of the Collège is ''Docet Omnia'', Latin for "It teaches everything"; its goal is to "teach science in the making" and ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles François Sturm
Charles is a masculine given name predominantly found in English and French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic name (in runic alphabet) or ''*karilaz'' (in Latin alphabet), whose meaning was "free man". The Old English descendant of this word was '' Ċearl'' or ''Ċeorl'', as the name of King Cearl of Mercia, that disappeared after the Norman conquest of England. The name was notably borne by Charlemagne (Charles the Great), and was at the time Latinized as ''Karolus'' (as in ''Vita Karoli Magni''), later also as '' Carolus''. Etymology The name's etymology is a Common Germanic noun ''*karilaz'' meaning "free man", which survives in English as churl (< Old English ''ċeorl''), which developed its deprecating sense in the period. Some Germanic languages, for example [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comptes Rendus De L'Académie Des Sciences
(, ''Proceedings of the Academy of Sciences''), or simply ''Comptes rendus'', is a French scientific journal published since 1835. It is the proceedings of the French Academy of Sciences. It is currently split into seven sections, published on behalf of the Academy until 2020 by Elsevier: ''Mathématique, Mécanique, Physique, Géoscience, Palévol, Chimie, ''and'' Biologies.'' As of 2020, the ''Comptes Rendus'' journals are published by the Academy with a diamond open access model. Naming history The journal has had several name changes and splits over the years. 1835–1965 ''Comptes rendus'' was initially established in 1835 as ''Comptes rendus hebdomadaires des séances de l'Académie des Sciences''. It began as an alternative publication pathway for more prompt publication than the ''Mémoires de l'Académie des Sciences,'' which had been published since 1666. The ''Mémoires,'' which continued to be published alongside the ''Comptes rendus'' throughout the ninetee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liouville Number
In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exists a pair of integers (p,q) with q>1 such that :0<\left, x-\frac\<\frac. The inequality implies that Liouville numbers possess an excellent sequence of approximations. In 1844, Joseph Liouville proved a bound showing that there is a limit to how well s can be approximated by rational numbers, and he defined Liouville numbers specifically so that they would have rational approximations better than the ones allowed by this bound. Liouville also exhibited examples of Liouville nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continued Fraction
A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, the continued fraction is finite or infinite. Different fields of mathematics have different terminology and notation for continued fraction. In number theory the standard unqualified use of the term continued fraction refers to the special case where all numerators are 1, and is treated in the article simple continued fraction. The present article treats the case where numerators and denominators are sequences \,\ of constants or functions. From the perspective of number theory, these are called generalized continued fraction. From the perspective of complex analysis or numerical analysis, however, they are just standard, and in the present article they will simply be called "continued fraction". Formulation A continued fraction is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendental Number
In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are and . The quality of a number being transcendental is called transcendence. Though only a few classes of transcendental numbers are known, partly because it can be extremely difficult to show that a given number is transcendental. Transcendental numbers are not rare: indeed, almost all real and complex numbers are transcendental, since the algebraic numbers form a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set. All transcendental real numbers (also known as real transcendental numbers or transcendental irrational numbers) are irrational numbers, since all rational numbers are algebraic. The converse is not true: Not all irrational numbers are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest include planets, natural satellite, moons, stars, nebulae, galaxy, galaxies, meteoroids, asteroids, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond atmosphere of Earth, Earth's atmosphere. Cosmology is a branch of astronomy that studies the universe as a whole. Astronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Egyptian astronomy, Egyptians, Babylonian astronomy, Babylonians, Greek astronomy, Greeks, Indian astronomy, Indians, Chinese astronomy, Chinese, Maya civilization, M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics. Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Classical mechanics Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints). Both formulations are embodied in analytical mechanics and lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry And Topology
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable, that is, '' holomorphic functions''. The concept can be extended to functions of several complex variables. Complex analysis is contrasted with real analysis, which dea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
