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Jean Leray
Jean Leray (; 7 November 1906 – 10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology. Life and career He was born in Chantenay-sur-Loire (today part of Nantes). He studied at École Normale Supérieure from 1926 to 1929. He received his Ph.D. in 1933. In 1934 Leray published an important paper that founded the study of weak solutions of the Navier–Stokes equations. In the same year, he and Juliusz Schauder discovered a topological invariant, now called the Leray–Schauder degree, which they applied to prove the existence of solutions for partial differential equations lacking uniqueness. From 1938 to 1939 he was professor at the University of Nancy. He did not join the Bourbaki group, although he was close with its founders. His main work in topology was carried out while he was in a prisoner of war camp in Edelbach, Austria from 1940 to 1945. He concealed his expertise on differential equations, fearing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Research Institute Of Oberwolfach
The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazis in order to further the German war effort, which at that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leray Projection
The Leray projection, named after Jean Leray, is a linear operator used in the theory of partial differential equations, specifically in the fields of fluid dynamics. Informally, it can be seen as the projection on the divergence-free vector fields. It is used in particular to eliminate both the pressure term and the divergence-free term in the Stokes equations and Navier–Stokes equations. Definition By pseudo-differential approach For vector fields \mathbf u (in any dimension n \geq 2), the Leray projection \mathbb P is defined by : \mathbb P(\mathbf u) = \mathbf u - \nabla \Delta^ (\nabla \cdot \mathbf u). This definition must be understood in the sense of pseudo-differential operators: its matrix valued Fourier multiplier m(\xi) is given by : m(\xi)_ = \delta_-\frac,\quad 1 \leq k,j \leq n. Here, \delta is the Kronecker delta. Formally, it means that for all \mathbf u \in \mathcal S(\R^n)^n, one has : \mathbb P(\mathbf u)_k(x) = \frac \int_ \left( \delta_-\frac\right) \wideh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Main branches of algebraic topology Below are some of the main areas studied in algebraic topology: Homotopy groups In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space. Homolog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, 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 mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biographical Memoirs Of Fellows Of The Royal Society
The ''Biographical Memoirs of Fellows of the Royal Society'' is an academic journal on the history of science published annually by the Royal Society. It publishes obituaries of Fellows of the Royal Society. It was established in 1932 as ''Obituary Notices of Fellows of the Royal Society'' and obtained its current title in 1955, with volume numbering restarting at 1. Prior to 1932, obituaries were published in the '' Proceedings of the Royal Society''. The memoirs are a significant historical record and most include a full bibliography of works by the subjects. The memoirs are often written by a scientist of the next generation, often one of the subject's own former students, or a close colleague. In many cases the author is also a Fellow. Notable biographies published in this journal include Albert Einstein, Alan Turing, Bertrand Russell, Claude Shannon, Clement Attlee, Ernst Mayr, and Erwin Schrödinger. Each year around 40 to 50 memoirs of deceased Fellows of the Royal Soc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lomonosov Gold Medal
The Lomonosov Gold Medal (russian: Большая золотая медаль имени М. В. Ломоносова ''Bol'shaya zolotaya medal' imeni M. V. Lomonosova''), named after Russian scientist and polymath Mikhail Lomonosov, is awarded each year since 1959 for outstanding achievements in the natural sciences and the humanities by the USSR Academy of Sciences and later the Russian Academy of Sciences (RAS). Since 1967, two medals are awarded annually: one to a Russian and one to a foreign scientist. It is the Academy's highest accolade. Recipients of Lomonosov Gold Medal __NOTOC__ 1959 * Pyotr Leonidovich Kapitsa: cumulatively, for works in physics of low temperatures. 1961 * Aleksandr Nikolaevich Nesmeyanov: accumulatively for works in chemistry. 1963 * Sin-Itiro Tomonaga (member of the Japanese academy of Sciences, president of the Scientific Council of Japan): for substantial scientific contributions to the development of physics. * Hideki Yukawa (member of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf Prize In Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. According to a reputation survey conducted in 2013 and 2014, the Wolf Prize in Mathematics is the third most prestigious international academic award in mathematics, after the Abel Prize and the Fields Medal. Until the establishment of the Abel Prize, it was probably the closest equivalent of a "Nobel Prize in Mathematics", since the Fields Medal is awarded every four years only to mathematicians under the age of 40. Laureates Laureates per country Below is a chart of all laureates per country (updated to 2022 laureates). Some laureates are counted more than once if have multiple citizenship. Notes See also * List of mathematics awards This list of mathematics awards is an index to articles about notable awards for mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann Prize
The John von Neumann Prize (until 2019 named John von Neumann Lecture Prize) was established in 1959 with funds from IBM and other industry corporations, and is awarded for "outstanding and distinguished contributions to the field of applied mathematical sciences and for the effective communication of these ideas to the community". It is considered the highest honor bestowed by the Society for Industrial and Applied Mathematics (SIAM). The recipient receives a monetary award and presents a survey lecture at the SIAM Annual Meeting. Selection process Anybody is able to nominate a mathematician for the prize. Nominations are reviewed by a selection committee, consisting of members of SIAM who serve two-year appointments. The committee selects one recipient for the prize nine months before the SIAM Annual Meeting and forwards their nomination to SIAM's Executive Committee and Vice President for Programs. Past lecturers *1960: Lars Valerian Ahlfors *1961: Mark Kac *1962: Jean L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feltrinelli Prize
The Feltrinelli Prize (from the Italian "Premio Feltrinelli", also known as "International Feltrinelli Prize" or "Antonio Feltrinelli Prize") is an award for achievement in the arts, music, literature, history, philosophy, medicine, and physical and mathematical sciences. Administered by the Antonio Feltrinelli Fund, the award comes with a monetary grant ranging between €50,000 and €250,000, a certificate, and a gold medal. The prize is awarded, both nationally and internationally, once every five years in each field by Italy's Accademia Nazionale dei Lincei. A further prize is awarded periodically for an exceptional enterprise in moral and humanitarian value. Considered to be Italy's most distinguished scientific society, the organization was founded in 1603 and included Galileo Galilei among its first members. Award winners Source: * 1956 (Mathematics) ** ''Prize reserved for Italian citizens'' (L. 1.500.000) *** Beppo Levi * 1957 (Literature) ** ''Prize reserved for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prix Francoeur
The Prix Francoeur, or Francoeur Prize, was an award granted by the Institut de France, Academie des Sciences, Fondation Francoeur to authors of works useful to the progress of pure and applied mathematics. Preference was given to young scholars or to geometricians not yet established. It was established in 1882 and has been discontinued. Prize winners * 1882–1888 — Emile Barbier * 1889–1890 — Maximilien Marie * 1891–1892 — Augustin Mouchot * 1893 — Guy Robin * 1894 — J. Collet * 1895 — Jules Andrade * 1896 — Alphonse Valson * 1897 — Guy Robin * 1898 — Aimé Vaschy * 1899 — Le Cordier * 1900 — Edmond Maillet * 1901 — Léonce Laugel * 1902–1904 — Emile Lemoine * 1905 — Xavier Stouff * 1906–1912 — Emile Lemoine * 1913–1914 — A. Claude * 1915 — Joseph Marty * 1916 — René Gateaux * 1917 — Henri Villat * 1918 — Paul Montel * 1919 — Georges Giraud * 1920–1921 — René Baire * 1922 — Louis Antoine * 1923 — Gaston Bertran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leray–Schauder Degree
In mathematics, the Leray–Schauder degree is an extension of the degree of a base point preserving continuous map between spheres (S^n, *) \to (S^n , *) or equivalently to a boundary sphere preserving continuous maps between balls (B^n, S^) \to (B^n, S^) to boundary sphere preserving maps between balls in a Banach space f: (B(V), S(V)) \to (B(V), S(V)), assuming that the map is of the form f = id - C where id is the identity map and C is some compact map (i.e. mapping bounded sets to sets whose closure is compact). The degree was invented by Jean Leray and Juliusz Schauder Juliusz Paweł Schauder (; 21 September 1899, Lwów, Austria-Hungary – September 1943, Lwów, Occupied Poland) was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equations and m ... to prove existence results for partial differential equations.Mawhin, J. (2018). A tribute to Juliusz Schauder. '' Antiquitates Mathematicae'', ''12''. Refere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
