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Fritz John
Fritz John (14 June 1910 – 10 February 1994) was a German-born mathematician specialising in partial differential equations and ill-posed problems. His early work was on the Radon transform and he is remembered for John's equation. He was a 1984 MacArthur Fellow. Life and career John was born in Berlin, Imperial Germany, the son of Hedwig (née Bürgel) and Hermann Jacobson-John. He studied mathematics from 1929 to 1933 in Göttingen where he was influenced by Richard Courant, among others. Following Hitler's rise to power in 1933 "non-aryans" were being expelled from teaching posts, and John, being half Jewish, emigrated from Germany to England. John published his first paper in 1934 on Morse theory. He was awarded his doctorate in 1934 with a thesis entitled ''Determining a function from its integrals over certain manifolds'' from Göttingen. With Richard Courant's assistance he spent a year at St John's College, Cambridge. During this time he published papers on the Rado ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and List of cities in Germany by population, largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's List of cities in the European Union by population within city limits, most populous city, according to population within city limits. One of Germany's States of Germany, sixteen constituent states, Berlin is surrounded by the Brandenburg, State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin/Brandenburg Metropolitan Region, Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Metropolitan regions in Germany, Germany's third-largest metropolitan region after the Rhine-Ruhr and Frankfurt Rhine-Main, Rhine-Main regions. Berlin straddles the banks of the Spree (river), Spree, which flows into the Havel (a tributary of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
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] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Water Waves
In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of the wind is known as the '' fetch''. Waves in the oceans can travel thousands of kilometers before reaching land. Wind waves on Earth range in size from small ripples, to waves over high, being limited by wind speed, duration, fetch, and water depth. When directly generated and affected by local wind, a wind wave system is called a wind sea. Wind waves will travel in a great circle route after being generated – curving slightly left in the southern hemisphere and slightly right in the northern hemisphere. After moving out of the area of fetch, wind waves are called '' swells'' and can travel thousands of kilometers. A noteworthy example of this is waves generated south of Tasmania during heavy winds that will travel across the Pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Geometry
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming, probability theory, game theory, etc. Classification According to the Mathematics Subject Classification MSC2010, the mathematical discipline ''Convex and Discrete Geometry'' includes three major branches: * general convexity * polytopes and polyhedra * discrete geometry (though only portions of the latter two are included in convex geometry). General convexity is further subdivided as follows: *axiomatic and generalized convexity *convex sets without dimension restrictions *convex sets in topological vector spaces *convex sets in 2 dimensions (including convex curves) *convex sets in 3 dimensions (including convex surfaces) *convex sets in ''n'' dimensions (including conv ... [...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 ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aberdeen Proving Ground, Maryland
Aberdeen Proving Ground (APG) (sometimes erroneously called Aberdeen Proving ''Grounds'') is a U.S. Army facility located adjacent to Aberdeen, Harford County, Maryland, United States. More than 7,500 civilians and 5,000 military personnel work at APG.There are 11 major commands among the tenant units, including: * United States Army Communications-Electronics Command (CECOM) * United States Army Combat Capabilities Development Command (CCDC) * United States Army Test and Evaluation Command (ATEC) * Edgewood Arsenal * Adelphi Laboratory Center **The Army Reserve Information Operations Command **Unified Cross Domain Services Management Office **HQ, U.S. Army Contracting Command (Army Contracting Command –APG, Adelphi Contracting Division) **U.S Army 93rd Signal Network - Network Enterprise Center **Logistics Readiness Center **U.S. Army Cyber Operation Group – 335th Signal Command **Blossom Point Research Facility History APG is the U.S. Army's oldest active proving ground, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge founded by the Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corporation established by a charter dated 9 April 1511. The full, formal name of the college is the College of St John the Evangelist in the University of Cambridge. The aims of the college, as specified by its statutes, are the promotion of education, religion, learning and research. It is one of the larger Oxbridge colleges in terms of student numbers. For 2022, St John's was ranked 6th of 29 colleges in the Tompkins Table (the annual league table of Cambridge colleges) with over 35 per cent of its students earning first-class honours. College alumni include the winners of twelve Nobel Prizes, seven prime ministers and twelve archbishops of various countries, at least two princes and three saints."Johnian Nobel Laureates". St John's College, Cambridge. 2016. Retrieved 5 May 2016. http://www.j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morse Theory
In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite directly. Morse theory allows one to find CW structures and handle decompositions on manifolds and to obtain substantial information about their homology. Before Morse, Arthur Cayley and James Clerk Maxwell had developed some of the ideas of Morse theory in the context of topography. Morse originally applied his theory to geodesics ( critical points of the energy functional on the space of paths). These techniques were used in Raoul Bott's proof of his periodicity theorem. The analogue of Morse theory for complex manifolds is Picard–Lefschetz theory. Basic concepts To illustrate, consider a mountainous landscape surface M (more generally, a manifold). If f is the functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aryan Race
The Aryan race is an obsolete historical race concept that emerged in the late-19th century to describe people of Proto-Indo-European heritage as a racial grouping. The terminology derives from the historical usage of Aryan, used by modern Indo-Iranians as an epithet of "noble". Anthropological, historical, and archaeological evidence does not support the validity of this concept.Arvidsson 2006:298 Arvidsson, Stefan (2006), Aryan Idols: Indo-European Mythology as Ideology and Science, translated by Sonia Wichmann, Chicago and London: The University of Chicago Press. The concept derives from the notion that the original speakers of the Proto-Indo-European language were distinct progenitors of a superior specimen of humankind, and that their descendants up to the present day constitute either a distinctive race or a sub-race of the Caucasian race, alongside the Semitic race and the Hamitic race. This taxonomic approach to categorizing human population groups is now conside ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Hitler
Adolf Hitler (; 20 April 188930 April 1945) was an Austrian-born German politician who was dictator of Nazi Germany, Germany from 1933 until Death of Adolf Hitler, his death in 1945. Adolf Hitler's rise to power, He rose to power as the leader of the Nazi Party, becoming the Chancellor of Germany, chancellor in 1933 and then taking the title of in 1934. During his dictatorship, he initiated European theatre of World War II, World War II in Europe by invasion of Poland, invading Poland on 1 September 1939. He was closely involved in military operations throughout the war and was central to the perpetration of the Holocaust: the genocide of Holocaust victims, about six million Jews and millions of other victims. Hitler was born in Braunau am Inn in Austria-Hungary and was raised near Linz. He lived in Vienna later in the first decade of the 1900s and moved to Germany in 1913. He was decorated during his Military career of Adolf Hitler, service in the German Army in Worl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Courant
Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real analysis, mathematical physics, the calculus of variations and partial differential equations. He wrote textbooks widely used by generations of students of physics and mathematics. He is also known for founding the institute now bearing his name. Life and career Courant was born in Lublinitz, in the Prussian Province of Silesia. His parents were Siegmund Courant and Martha Courant ''née'' Freund of Oels. Edith Stein was Richard's cousin on the paternal side. During his youth his parents moved often, including to Glatz, then to Breslau and in 1905 to Berlin. He stayed in Breslau and entered the university there, then continued his studies at the University of Zürich and the University of Göttingen. He became David Hilbert's a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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