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Tonelli
Tonelli may refer to: * Tonelli (surname) Arts * ''Tonelli'' (film), a 1943 German film Science * Tonelli's theorem (functional analysis) * Tonelli's theorem * Tonelli–Shanks algorithm The Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for ''r'' in a congruence of the form ''r''2 ≡ ''n'' (mod ''p''), where ''p'' is a prime: that is, to find a square root of ''n'' ... * Tonelli–Hobson test See also {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fubini's Theorem
In mathematical analysis Fubini's theorem is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral, introduced by Guido Fubini in 1907. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value. \, \iint\limits_ f(x,y)\,\text(x,y) = \int_X\left(\int_Y f(x,y)\,\texty\right)\textx=\int_Y\left(\int_X f(x,y) \, \textx \right) \texty \qquad \text \qquad \iint\limits_ , f(x,y), \,\text(x,y) <+\infty. Fubini's theorem implies that two iterated integrals are equal to the corresponding double integral across its integrands. Tonelli's theorem, introduced by in 1909, is similar, but applies to a non-negative measurable function rather than one integrable over their domains. A related theorem is oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonelli (surname)
Tonelli is an Italian surname. Notable people with this name include the following: * Alessandro Tonelli (born 1992), Italian cyclist * Anna Tonelli (c.1763–1846), Italian portrait painter in the late 17th century and early 18th century. * Annalena Tonelli (1943–2003), Italian lawyer and social activist * Bobby Tonelli (born 1975), American actor * Gilles Tonelli (born 1957), Monegasque politician * Giuseppe Tonelli (1668–1732), Italian painter * Guido Tonelli (born 1950), Italian physicist * Ideler Tonelli (1924–2016), Argentine lawyer and politician * John Tonelli (born 1957), Canadian ice hockey player * Leonida Tonelli (1885–1946), Italian mathematician * Lorenzo Tonelli (born 1990), Italian footballer * Maria Valentina Tonelli (1939–2016), Italian writer * Mario Tonelli (1916–2003), American gridiron football player and survivor of the Bataan Death March * Mark Tonelli (born 1957), Australian swimmer * Pablo Tonelli (born 1954), Argentine politician * Simone To ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonelli–Shanks Algorithm
The Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for ''r'' in a congruence of the form ''r''2 ≡ ''n'' (mod ''p''), where ''p'' is a prime: that is, to find a square root of ''n'' modulo ''p''. Tonelli–Shanks cannot be used for composite moduli: finding square roots modulo composite numbers is a computational problem equivalent to integer factorization. An equivalent, but slightly more redundant version of this algorithm was developed by Alberto Tonelli in 1891. The version discussed here was developed independently by Daniel Shanks in 1973, who explained: My tardiness in learning of these historical references was because I had lent Volume 1 of Dickson's History to a friend and it was never returned. According to Dickson, Tonelli's algorithm can take square roots of ''x'' modulo prime powers ''pλ'' apart from primes. Core ideas Given a non-zero n and an odd prime p, Euler's criterion tells us that n h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonelli (film)
''Tonelli'' is a 1943 German drama film directed by Victor Tourjansky and starring Ferdinand Marian, Winnie Markus and Mady Rahl.Bock& Bergfelder p. 346 The film's sets were designed by the art director Ludwig Reiber. It was shot at the Bavaria Studios in Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ... and at the Deutsches Theater in the city. Cast References Bibliography * Hans-Michael Bock and Tim Bergfelder. ''The Concise Cinegraph: An Encyclopedia of German Cinema''. Berghahn Books, 2009. External links * 1943 films 1943 comedy-drama films German comedy-drama films Films of Nazi Germany 1940s German-language films Films directed by Victor Tourjansky Circus films Bavaria Film films Films shot at Bavaria Studios German black-and-white films 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonelli's Theorem (functional Analysis)
In mathematics, Tonelli's theorem in functional analysis is a fundamental result on the weak lower semicontinuity of nonlinear functionals on ''L''''p'' spaces. As such, it has major implications for functional analysis and the calculus of variations. Roughly, it shows that weak lower semicontinuity for integral functionals is equivalent to convexity of the integral kernel. The result is attributed to the Italian mathematician Leonida Tonelli. Statement of the theorem Let \Omega be a bounded domain in n-dimensional Euclidean space \Reals^n and let f : \Reals^m \to \Reals \cup \ be a continuous extended real-valued function. Define a nonlinear functional F on functions u : \Omega \to \Reals^mby F = \int_ f(u(x)) \, \mathrm x. Then F is sequentially weakly lower semicontinuous on the L^p space L^p(\Omega, \Reals^m) for 1 < p < +\infty and weakly-∗ lower semicontinuous on |