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Franz Rellich
Franz Rellich (September 14, 1906 – September 25, 1955) was an Austrians, Austrian-Germans, German mathematician. He made important contributions in mathematical physics, in particular for the foundations of quantum mechanics and for the theory of partial differential equations. The Rellich–Kondrachov theorem is named after him. Biography Rellich was born in Tramin, then in the County of Tyrol. He studied from 1924 to 1929 at the universities of Graz and Göttingen and received his doctor's degree in 1929 under Richard Courant at Georg August University of Göttingen with the thesis about ''"Verallgemeinerung der Riemannschen Integrationsmethode auf Differentialgleichungen n-ter Ordnung in zwei Veränderlichen" ("Generalization of Riemann's integration method on differential equations of ''n''-th order in two variables"). When in 1933 the great mathematical-physical tradition in Göttingen terminated with the ''Machtergreifung'' of the Nazism, Nazis, Rellich, having taken an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marburg
Marburg ( or ) is a university town in the German federal state (''Bundesland'') of Hesse, capital of the Marburg-Biedenkopf district (''Landkreis''). The town area spreads along the valley of the river Lahn and has a population of approximately 76,000. Having been awarded town privileges in 1222, Marburg served as capital of the landgraviate of Hessen-Marburg during periods of the fifteenth to seventeenth centuries. The University of Marburg was founded in 1527 and dominates the public life in the town to this day. Marburg is a historic centre of the pharmaceutical industry in Germany, and there is a plant in the town (by BioNTech) to produce vaccines to tackle Covid-19. History Founding and early history Like many settlements, Marburg developed at the crossroads of two important early medieval highways: the trade route linking Cologne and Prague and the trade route from the North Sea to the Alps and on to Italy, the former crossing the river Lahn here. A first mention o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1906 Births
Events January–February * January 12 – Persian Constitutional Revolution: A nationalistic coalition of merchants, religious leaders and intellectuals in Persia forces the shah Mozaffar ad-Din Shah Qajar to grant a constitution, and establish a national assembly, the Majlis. * January 16–April 7 – The Algeciras Conference convenes, to resolve the First Moroccan Crisis between France and Germany. * January 22 – The strikes a reef off Vancouver Island, Canada, killing over 100 (officially 136) in the ensuing disaster. * January 31 – The Ecuador–Colombia earthquake (8.8 on the Moment magnitude scale), and associated tsunami, cause at least 500 deaths. * February 7 – is launched, sparking a naval race between Britain and Germany. * February 11 ** Pope Pius X publishes the encyclical ''Vehementer Nos'', denouncing the 1905 French law on the Separation of the Churches and the State. ** Two British members of a poll tax collecting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical physics. He served as doctoral supervisor for many Nobel Prize winners in physics and chemistry (only J. J. Thomson's record of mentorship is comparable to his). He introduced the second quantum number (azimuthal quantum number) and the third quantum number (magnetic quantum number). He also introduced the fine-structure constant and pioneered X-ray wave theory. Early life and education Sommerfeld was born in 1868 to a family with deep ancestral roots in Prussia. His mother Cäcilie Matthias (1839–1902) was the daughter of a Potsdam builder. His father Franz Sommerfeld (1820–1906) was a physician from a leading family in Königsberg, where Arnold's grandfather had resettled from the hinterland in 1822 for a career as Court Postal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Degeneracy
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class, and the term degeneracy is the condition of being a degenerate case. The definitions of many classes of composite or structured objects often implicitly include inequalities. For example, the angles and the side lengths of a triangle are supposed to be positive. The limiting cases, where one or several of these inequalities become equalities, are degeneracies. In the case of triangles, one has a ''degenerate triangle'' if at least one side length or angle is zero. Equivalently, it becomes a "line segment". Often, the degenerate cases are the exceptional cases where changes to the usual dimension or the cardinality of the object (or of some part of it) occur. For example, a triangle is an object of dimension two, and a degenerate triangle is contained in a line, which makes its dimension one. This is similar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-adjoint Operator
In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space ''V'' with inner product \langle\cdot,\cdot\rangle (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map ''A'' (from ''V'' to itself) that is its own adjoint. If ''V'' is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of ''A'' is a Hermitian matrix, i.e., equal to its conjugate transpose ''A''. By the finite-dimensional spectral theorem, ''V'' has an orthonormal basis such that the matrix of ''A'' relative to this basis is a diagonal matrix with entries in the real numbers. In this article, we consider generalizations of this concept to operators on Hilbert spaces of arbitrary dimension. Self-adjoint operators are used in functional analysis and quantum mechanics. In quantum mechanics their importance lies in the Dirac–von Neumann formulation of quantum mechanics, in which physical observables such as positi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert Space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that defines a distance function for which the space is a complete metric space. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer), and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the term ''Hilbert space'' for the abstract concept that under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Operator
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a . In the case where V = W, a linear map is called a (linear) ''endomorphism''. Sometimes the term refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily with V = W), or it can be used to emphasize that V is a function space, which is a common convention in functional analysis. Sometimes the term ''linear function'' has the same meaning as ''linear map' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bartel Leendert Van Der Waerden
Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amsterdam and the University of Göttingen, from 1919 until 1926. He was much influenced by Emmy Noether at Göttingen, Germany. Amsterdam awarded him a Ph.D. for a thesis on algebraic geometry, supervised by Hendrick de Vries. Göttingen awarded him the habilitation in 1928. In that year, at the age of 25, he accepted a professorship at the University of Groningen. In his 27th year, Van der Waerden published his ''Moderne Algebra'', an influential two-volume treatise on abstract algebra, still cited, and perhaps the first treatise to treat the subject as a comprehensive whole. This work systematized an ample body of research by Emmy Noether, David Hilbert, Richard Dedekind, and Emil Artin. In the following year, 1931, he was appointed professor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jürgen Moser
Jürgen Kurt Moser (July 4, 1928 – December 17, 1999) was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations. Life Moser's mother Ilse Strehlke was a niece of the violinist and composer Louis Spohr. His father was the neurologist Kurt E. Moser (July 21, 1895 – June 25, 1982), who was born to the merchant Max Maync (1870–1911) and Clara Moser (1860–1934). The latter descended from 17th century French Huguenot immigrants to Prussia. Jürgen Moser's parents lived in Königsberg, German empire and resettled in Stralsund, East Germany as a result of the second world war. Moser attended the Wilhelmsgymnasium (Königsberg) in his hometown, a high school specializing in mathematics and natural sciences education, from which David Hilbert had graduated in 1880. His older brother Friedrich Robert Ernst (Friedel) Moser (August 31, 1925 – January 14, 1945) served in the German Army ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
