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Levi-Civita
Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significant contributions in other areas. He was a pupil of Gregorio Ricci-Curbastro, the inventor of tensor calculus. His work included foundational papers in both pure and applied mathematics, celestial mechanics (notably on the three-body problem), analytic mechanics (the Levi-Civita separability conditions in the Hamilton–Jacobi equation) and hydrodynamics. Biography Born into an Italian Jewish family in Padua, Levi-Civita was the son of Giacomo Levi-Civita, a lawyer and former senator. He graduated in 1892 from the University of Padua Faculty of Mathematics. In 1894 he earned a teaching diploma after which he was appointed to the Faculty of Science teacher's college in Pavia. In 1898 he was appointed to the Padua Chair of Rational Mechan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers; defined from the parity of a permutation, sign of a permutation of the natural numbers , for some positive integer . It is named after the Italian mathematician and physicist Tullio Levi-Civita. Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric tensor, antisymmetric property and definition in terms of permutations. The standard letters to denote the Levi-Civita symbol are the Greek lower case epsilon or , or less commonly the Latin lower case . Index notation allows one to display permutations in a way compatible with tensor analysis: \varepsilon_ where ''each'' index takes values . There are indexed values of , which can be arranged into an -dimensional array. The key defining property of the symbol is ''total antisymmetry'' in the ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Connection
In Riemannian or pseudo Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the ( pseudo-) Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection. The components (structure coefficients) of this connection with respect to a system of local coordinates are called Christoffel symbols. History The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel. Levi-Civita, along with Gregorio Ricci-Curbastro, used Christoffel's symbols to define the notion of parallel transport and explore the relationship of paral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Field
In mathematics, the Levi-Civita field, named after Tullio Levi-Civita, is a non-Archimedean ordered field; i.e., a system of numbers containing infinite and infinitesimal quantities. Each member a can be constructed as a formal series of the form : a = \sum_ a_q\varepsilon^q , where a_q are real numbers, \mathbb is the set of rational numbers, and \varepsilon is to be interpreted as a positive infinitesimal. The support of a, i.e., the set of indices of the nonvanishing coefficients \, must be a left-finite set: for any member of \mathbb, there are only finitely many members of the set less than it; this restriction is necessary in order to make multiplication and division well defined and unique. The ordering is defined according to the dictionary ordering of the list of coefficients, which is equivalent to the assumption that \varepsilon is an infinitesimal. The real numbers are embedded in this field as series in which all of the coefficients vanish except a_0. Examples * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gregorio Ricci-Curbastro
Gregorio Ricci-Curbastro (; 12January 1925) was an Italian mathematician. He is most famous as the discoverer of tensor calculus. With his former student Tullio Levi-Civita, he wrote his most famous single publication, a pioneering work on the calculus of tensors, signing it as Gregorio Ricci. This appears to be the only time that Ricci-Curbastro used the shortened form of his name in a publication, and continues to cause confusion. Ricci-Curbastro also published important works in other fields, including a book on higher algebra and infinitesimal analysis, and papers on the theory of real numbers, an area in which he extended the research begun by Richard Dedekind. Early life and education Completing privately his high school studies at only 16 years of age, he enrolled on the course of philosophy-mathematics at Rome University (1869). The following year the Papal State fell and so Gregorio was called by his father to the city of his birth, Lugo di Romagna. Subsequently he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Libera Trevisani
Libera Trevisani Levi-Civita (17 May 1890 – 11 December 1973) was an Italian mathematician born in Verona. Biography Libera Trevisani earned her classical lyceum A levels in 1908 at the "Bernardino Telesio" Lyceum in Cosenza. In the 1908–1909 academic year, she matriculated at the University of Padova. In 1912, she graduated at the University of Padova, under the guidance of the mathematician Tullio Levi-Civita, with a thesis titled ''Sul moto medio dei nodi nel problema dei tre corpi'' ("About the average motion within the three body problem"). This thesis extended Levi-Civita's researches on the average asymptotic motion existence, for a point represented by the generic solution of a linear system with periodic coefficients, to the problem of the three bodies, whenever this is referred to the moon theory. The results achieved by Trevisani were so satisfactory that her mentor decided to present them to 28 April 1912 meeting at the Istituto veneto di scienze, lettere ed art ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Differential Calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus), developed by Gregorio Ricci-Curbastro in 1887–1896, and subsequently popularized in a paper written with his pupil Tullio Levi-Civita in 1900. Jan Arnoldus Schouten developed the modern notation and formalism for this mathematical framework, and made contributions to the theory, during its applications to general relativity and differential geometry in the early twentieth century. A component of a tensor is a real number that is used as a coefficient of a basis element for the tensor space. The tensor is the sum of its components multiplied by their corresponding basis elements. Tensors and tensor fields can be expressed in terms of their components, and oper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Parallelogramoid
In the mathematical field of differential geometry, the Levi-Civita parallelogramoid is a quadrilateral in a curved space whose construction generalizes that of a parallelogram in the Euclidean plane. It is named for its discoverer, Tullio Levi-Civita. Like a parallelogram, two opposite sides ''AA''′ and ''BB''′ of a parallelogramoid are parallel (via parallel transport side ''AB'') and the same length as each other, but the fourth side ''A''′''B''′ will not in general be parallel to or the same length as the side ''AB,'' although it will be straight (a geodesic).In the article by Levi-Civita (1917, p. 199), the segments AB and A'B ′ are called (respectively) the '' base'' and ''suprabase'' of the parallelogramoid in question. Construction A parallelogram in Euclidean geometry can be constructed as follows: * Start with a straight line segment ''AB'' and another straight line segment ''AA''′. * Slide the segment ''AA''′ along ''AB'' to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antonio Signorini (physicist)
Antonio Signorini (2 April 1888 – 23 February 1963) was an influential Italian mathematical physicist and civil engineer of the 20th century.Signorini, Antonio — Treccani, Enciclopedie online He is known for his work in finite elasticity, thermoelasticity and for formulating the . Life Honors He was awarded the gold medal of the |
Tensor Calculus
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of relativity. Unlike the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold. Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning. Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern summarizes the role of tensor calculus:In our subject of differenti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry at the University of Oxford in the 1880s, and first awarded in 1901, having been suggested by a group of Sylvester's friends (primarily Raphael Meldola) after his death in 1897. Initially awarded every three years with a prize of around £900, the Royal Society have announced that starting in 2009 it will be awarded every two years instead, and is to be aimed at 'early to mid career stage scientist' rather than an established mathematician. The award winner is chosen by the Society's A-side awards committee, which handles physical rather than biological science awards. , 45 medals have been awarded, of which all but 10 have been awarded to citizens of the United Kingdom, two to citizens of France and United States, and one medal each has b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Calculus
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of relativity. Unlike the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold. Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning. Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern summarizes the role of tensor calculus:In our subject of differenti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italians
, flag = , flag_caption = The national flag of Italy , population = , regions = Italy 55,551,000 , region1 = Brazil , pop1 = 25–33 million , ref1 = , region2 = Argentina , pop2 = 20–25 million , ref2 = , region3 = United States , pop3 = 17-20 million , ref3 = , region4 = France , pop4 = 1-5 million , ref4 = , region5 = Venezuela , pop5 = 1-5 million , ref5 = , region6 = Paraguay , pop6 = 2.5 million , region7 = Colombia , pop7 = 2 million , ref7 = , region8 = Canada , pop8 = 1.5 million , ref8 = , region9 = Australia , pop9 = 1.0 million , ref9 = , region10 = Uruguay , pop10 = 1.0 million ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
