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Lanczos
__NOTOC__ Cornelius (Cornel) Lanczos ( hu, Lánczos Kornél, ; born as Kornél Lőwy, until 1906: ''Löwy (Lőwy) Kornél''; February 2, 1893 – June 25, 1974) was a Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians. Biography He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary to Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory. He sent his thesis copy to Albert Einstein, and Einstein wrote back, saying: "I studied your paper as far as my present overload allowed. I believe I may say this much: this does involve competent and original brainwork, on the basis of which a doctorate should be obtainable ... I gladly accept the honorable dedication."Barbara Gellai (2010) ''The Intrinsic Nature of Things: the life and science of Cornelius Lanczos'', American Mathematical Society In 1924 he discovered an exact solution of the Einstein field equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanczos Algorithm
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power iteration, power methods to find the m "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an n \times n Hermitian matrix, where m is often but not necessarily much smaller than n . Although computationally efficient in principle, the method as initially formulated was not useful, due to its Numerical stability, numerical instability. In 1970, Ojalvo and Newman showed how to make the method numerically stable and applied it to the solution of very large engineering structures subjected to dynamic loading. This was achieved using a method for purifying the Lanczos vectors (i.e. by repeatedly reorthogonalizing each newly generated vector with all previously generated ones) to any degree of accuracy, which when not performed, produced a series of vectors that were highly contaminated by those associated with the lowest natural frequencies. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanczos Resampling
filtering and Lanczos resampling are two applications of a mathematical formula. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its samples. In the latter case it maps each sample of the given signal to a translated and scaled copy of the Lanczos kernel, which is a sinc function windowed by the central lobe of a second, longer, sinc function. The sum of these translated and scaled kernels is then evaluated at the desired points. Lanczos resampling is typically used to increase the sampling rate of a digital signal, or to shift it by a fraction of the sampling interval. It is often used also for multivariate interpolation, for example to resize or rotate a digital image. It has been considered the "best compromise" among several simple filters for this purpose. The filter is named after its inventor, Cornelius Lanczos (). Definition Lanczos kernel The effect of each input sample on the interpolated values ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanczos Tensor
The Lanczos tensor or Lanczos potential is a rank 3 tensor in general relativity that generates the Weyl tensor.Hyôitirô Takeno, "On the spintensor of Lanczos", ''Tensor'', 15 (1964) pp. 103–119. It was first introduced by Cornelius Lanczos in 1949. The theoretical importance of the Lanczos tensor is that it serves as the gauge field for the gravitational field in the same way that, by analogy, the electromagnetic four-potential generates the electromagnetic field.P. O’Donnell and H. Pye, "A Brief Historical Review of the Important Developments in Lanczos Potential Theory", ''EJTP'', 7 (2010) pp. 327–350. Definition The Lanczos tensor can be defined in a few different ways. The most common modern definition is through the Weyl–Lanczos equations, which demonstrate the generation of the Weyl tensor from the Lanczos tensor. These equations, presented below, were given by Takeno in 1964. The way that Lanczos introduced the tensor originally was as a Lagrange multiplie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanczos Differentiator
__NOTOC__ Cornelius (Cornel) Lanczos ( hu, Lánczos Kornél, ; born as Kornél Lőwy, until 1906: ''Löwy (Lőwy) Kornél''; February 2, 1893 – June 25, 1974) was a Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians. Biography He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary to Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory. He sent his thesis copy to Albert Einstein, and Einstein wrote back, saying: "I studied your paper as far as my present overload allowed. I believe I may say this much: this does involve competent and original brainwork, on the basis of which a doctorate should be obtainable ... I gladly accept the honorable dedication."Barbara Gellai (2010) ''The Intrinsic Nature of Things: the life and science of Cornelius Lanczos'', American Mathematical Society In 1924 he discovered an exact solution of the Einstein field equatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanczos Approximation
In mathematics, the Lanczos approximation is a method for computing the gamma function numerically, published by Cornelius Lanczos in 1964. It is a practical alternative to the more popular Stirling's approximation for calculating the gamma function with fixed precision. Introduction The Lanczos approximation consists of the formula :\Gamma(z+1) = \sqrt ^ e^ A_g(z) for the gamma function, with :A_g(z) = \frac12p_0(g) + p_1(g) \frac + p_2(g) \frac + \cdots. Here ''g'' is a real constant that may be chosen arbitrarily subject to the restriction that Re(''z''+''g''+) > 0. The coefficients ''p'', which depend on ''g'', are slightly more difficult to calculate (see below). Although the formula as stated here is only valid for arguments in the right complex half-plane, it can be extended to the entire complex plane by the reflection formula, :\Gamma(1-z) \; \Gamma(z) = . The series ''A'' is convergent, and may be truncated to obtain an approximation with the desired pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Stockum Dust
In general relativity, the van Stockum dust is an exact solution of the Einstein field equations in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Since the density of the dust is ''increasing'' with distance from this axis, the solution is rather artificial, but as one of the simplest known solutions in general relativity, it stands as a pedagogically important example. This solution is named after Willem Jacob van Stockum, who rediscovered it in 1937 independently of a much earlier discovery by Cornelius Lanczos in 1924. It is currently recommended that the solution be referred to as the Lanczos–van Stockum dust. Derivation One way of obtaining this solution is to look for a cylindrically symmetric perfect fluid solution in which the fluid exhibits ''rigid rotation''. That is, we demand that the world lines of the fluid particles form a timelike congruence having nonzero vorticity but vanishing expansion and shear. (In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hungarian Americans
Hungarian Americans ( Hungarian: ''amerikai magyarok'') are Americans of Hungarian descent. The U.S. Census Bureau has estimated that there are approximately 1.396 million Americans of Hungarian descent as of 2018. The total number of people with ethnic Hungarian background is estimated to be around 4 million. The largest concentration is in the Greater Cleveland Metropolitan Area in Northeast Ohio. At one time, the presence of Hungarians within Cleveland proper was so great that the city was known as the "American Debrecen," with one of the highest concentrations of Hungarians in the world. History In 1583, a Hungarian poet Stephanus Parmenius joined Humphrey Gilbert's expedition to North America with the intention of writing a chronicle of the voyage and its discoveries. Parmenius reached Newfoundland, likely becoming the first Hungarian in the New World. Hungarians have long settled in the New World, such as Michael de Kovats, the founder of United States Cavalry, activ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanczos Sigma Factor
In mathematics, σ-approximation adjusts a Fourier summation to greatly reduce the Gibbs phenomenon, which would otherwise occur at discontinuities. A σ-approximated summation for a series of period ''T'' can be written as follows: s(\theta) = \frac a_0 + \sum_^ \operatorname \frac \cdot \left _ \cos \left( \frac \theta \right) + b_k \sin \left( \frac \theta \right) \right in terms of the normalized sinc function \operatorname x = \frac. The term \operatorname \frac is the Lanczos σ factor, which is responsible for eliminating most of the Gibbs phenomenon. It does not do so entirely, however, but one can square or even cube the expression to serially attenuate Gibbs phenomenon in the most extreme cases. See also * Lanczos resampling filtering and Lanczos resampling are two applications of a mathematical formula. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its samples. In the latter case it maps each sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lipót Fejér
Lipót Fejér (or Leopold Fejér, ; 9 February 1880 – 15 October 1959) was a Hungarian mathematician of Jewish heritage. Fejér was born Leopold Weisz, and changed to the Hungarian name Fejér around 1900. Biography Fejér studied mathematics and physics at the University of Budapest and at the University of Berlin, where he was taught by Hermann Schwarz. In 1902 he earned his doctorate from University of Budapest (today Eötvös Loránd University). From 1902 to 1905 Fejér taught there and from 1905 until 1911 he taught at Franz Joseph University in Kolozsvár in Austria-Hungary (now Cluj-Napoca in Romania). In 1911 Fejér was appointed to the chair of mathematics at the University of Budapest and he held that post until his death. He was elected corresponding member (1908), member (1930) of the Hungarian Academy of Sciences. During his period in the chair at Budapest Fejér led a highly successful Hungarian school of analysis. He was the thesis advisor of mathematicians s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chauvenet Prize
The Chauvenet Prize is the highest award for mathematical expository writing. It consists of a prize of $1,000 and a certificate, and is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. The prize is named in honor of William Chauvenet and was established through a gift from J. L. Coolidge in 1925. The Chauvenet Prize was the first award established by the Mathematical Association of America. A gift from MAA president Walter B. Ford in 1928 allowed the award to be given every 3 years instead of the originally planned 5 years. Winners *1925 G. A. Bliss *1929 T. H. Hildebrandt *1932 G. H. Hardy *1935 Dunham Jackson *1938 G. T. Whyburn *1941 Saunders Mac Lane *1944 R. H. Cameron *1947 Paul Halmos *1950 Mark Kac *1953 E. J. McShane *1956 Richard H. Bruck *1960 Cornelius Lanczos *1963 Philip J. Davis *1964 Leon Henkin *1965 Jack K. Hale & Joseph P. LaSalle *1967 Guido Weiss *1968 Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dublin Institute For Advanced Studies
The Dublin Institute for Advanced Studies (DIAS) ( ga, Institiúid Ard-Léinn Bhaile Átha Cliath) is a statutory independent research institute in Ireland. It was established in 1940 on the initiative of the Taoiseach, Éamon de Valera, in Dublin. The institute consists of three schools: the School of Theoretical Physics, the School of Cosmic Physics and the School of Celtic Studies. The directors of these schools are, as of 2022, Professor Denjoe O'Connor, Professor Chris Bean and Professor Ruairí Ó hUiginn. The institute, under its governing act, is empowered to "train students in methods of advanced research" but does not itself award degrees; graduate students working under the supervision of Institute researchers can, with the agreement of the governing board of the appropriate school, be registered for a higher degree in any university worldwide. Following a comprehensive review of the higher education sector and its institutions, conducted by the Higher Education Auth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Judaism
Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the Middle East during the Bronze Age. Modern Judaism evolved from Yahwism, the religion of ancient Israel and Judah, by the late 6th century BCE, and is thus considered to be one of the oldest monotheistic religions. Judaism is considered by religious Jews to be the expression of the covenant that God established with the Israelites, their ancestors. It encompasses a wide body of texts, practices, theological positions, and forms of organization. The Torah, as it is commonly understood by Jews, is part of the larger text known as the ''Tanakh''. The ''Tanakh'' is also known to secular scholars of religion as the Hebrew Bible, and to Christians as the " Old Testament". The Torah's supplemental oral tradition is represented by later texts s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
