Literatura académica sobre el tema "Multiple integrals. Numerical integration. Lattice theory"

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Artículos de revistas sobre el tema "Multiple integrals. Numerical integration. Lattice theory"

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Sloan, Ian H., and Philip J. Kachoyan. "Lattice Methods for Multiple Integration: Theory, Error Analysis and Examples." SIAM Journal on Numerical Analysis 24, no. 1 (1987): 116–28. http://dx.doi.org/10.1137/0724010.

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Kazashi, Y., F. Y. Kuo, and I. H. Sloan. "Derandomised lattice rules for high dimensional integration." ANZIAM Journal 60 (November 16, 2019): C247—C260. http://dx.doi.org/10.21914/anziamj.v60i0.14110.

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We seek shifted lattice rules that are good for high dimensional integration over the unit cube in the setting of an unanchored weighted Sobolev space of functions with square-integrable mixed first derivatives. Many existing studies rely on random shifting of the lattice, whereas here we work with lattice rules with a deterministic shift. Specifically, we consider 'half-shifted' rules in which each component of the shift is an odd multiple of \(1/(2N)\) where \(N\) is the number of points in the lattice. By applying the principle that there is always at least one choice as good as the average
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LAPORTA, S. "ANALYTICAL EXPRESSIONS OF THREE- AND FOUR-LOOP SUNRISE FEYNMAN INTEGRALS AND FOUR-DIMENSIONAL LATTICE INTEGRALS." International Journal of Modern Physics A 23, no. 31 (2008): 5007–20. http://dx.doi.org/10.1142/s0217751x08042869.

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In this paper we continue the work began in 2002 on the identification of the analytical expressions of Feynman integrals which require the evaluation of multiple elliptic integrals. We rewrite and simplify the analytical expression of the three-loop self-mass integral with three equal masses and on-shell external momentum. We collect and analyze a number of results on double and triple elliptic integrals. By using very high-precision numerical fits, for the first time we are able to identify a very compact analytical expression for the four-loop on-shell self-mass integral with four equal mas
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Parkin, Blaine R., and Brian B. Baker. "Bubble Dynamics and Cavitation Inception Theory." Journal of Ship Research 32, no. 03 (1988): 155–67. http://dx.doi.org/10.5957/jsr.1988.32.3.155.

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In order to provide some theoretical background and to motivate the more refined theory introduced herein, some encouraging known theoretical results on bubble-ring cavitation inception are reviewed. This review is followed by the development of the theory of bubble-ring cavitation cutoff. Its outcome, when compared with experiment, shows the need for a more refined inception theory. The above comparison and the basic ideas behind the cutoff theory's formulation suggest a possible approach for a refinement based on a multiple scales expansion. This seems reasonable because the forcing function
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Anastasiou, Charalampos, Rayan Haindl, George Sterman, Zhou Yang, and Mao Zeng. "Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation." Journal of High Energy Physics 2021, no. 4 (2021). http://dx.doi.org/10.1007/jhep04(2021)222.

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Abstract We study the singularity structure of two-loop QED amplitudes for the production of multiple off-shell photons in massless electron-positron annihilation and develop counterterms that remove their infrared and ultraviolet divergences point by point in the loop integrand. The remainders of the subtraction are integrable in four dimensions and can be computed in the future with numerical integration. The counterterms capture the divergences of the amplitudes and factorize in terms of the Born amplitude and the finite remainder of the one-loop amplitude. They consist of simple one- and t
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Tesis sobre el tema "Multiple integrals. Numerical integration. Lattice theory"

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Sinescu, Vasile. "Construction of lattice rules for multiple integration based on a weighted discrepancy." The University of Waikato, 2008. http://hdl.handle.net/10289/2542.

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High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and chemistry of molecules, statistical mechanics and more recently, in financial applications. In order to approximate multidimensional integrals, one may use Monte Carlo methods in which the quadrature points are generated randomly or quasi-Monte Carlo methods, in which points are generated deterministically. One particular class of quasi-Monte Carlo methods for multivariate integration is represented by lattice rules. Lattice rules constructed throughout this thesis allow good approximations to in
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Waterhouse, Benjamin James School of Mathematics UNSW. "New developments in the construction of lattice rules: applications of lattice rules to high-dimensional integration problems from mathematical finance." 2007. http://handle.unsw.edu.au/1959.4/40711.

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There are many problems in mathematical finance which require the evaluation of a multivariate integral. Since these problems typically involve the discretisation of a continuous random variable, the dimension of the integrand can be in the thousands, tens of thousands or even more. For such problems the Monte Carlo method has been a powerful and popular technique. This is largely related to the fact that the performance of the method is independent of the number of dimensions. Traditional quasi-Monte Carlo techniques are typically not independent of the dimension and as such have not been su
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Libros sobre el tema "Multiple integrals. Numerical integration. Lattice theory"

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Sloan, I. H. Lattice methods for multiple integration. Clarendon Press, 1994.

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Actas de conferencias sobre el tema "Multiple integrals. Numerical integration. Lattice theory"

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Volmer, Julia, Andreas Ammon, Alan Genz, Tobias Hartung, Karl Jansen, and Hernan Leövey. "Applying recursive numerical integration techniques for solving high dimensional integrals." In 34th annual International Symposium on Lattice Field Theory. Sissa Medialab, 2017. http://dx.doi.org/10.22323/1.256.0335.

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