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Journal articles on the topic 'Tonelli's theorem'

Author: Grafiati

Published: 24 April 2022

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1

Cid, José Ángel, and Rodrigo López Pouso. "A generalization of Montel–Tonelli's Uniqueness Theorem." Journal of Mathematical Analysis and Applications 429, no. 2 (2015): 1173–77. http://dx.doi.org/10.1016/j.jmaa.2015.04.064.

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2

Hatvani, László. "The Growth Condition Guaranteeing Small Solutions for a Linear Oscillator with an Increasing Elasticity Coefficient." gmj 14, no. 2 (2007): 269–78. http://dx.doi.org/10.1515/gmj.2007.269.

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Abstract The second order linear differential equation is considered, where 𝑞 : [0, ∞) → (0, ∞) is continuous, piecewise continuously differentiable, non-decreasing, and lim𝑡→∞ 𝑞(𝑡) = ∞. A solution 𝑥0 is called small if lim𝑡→∞ 𝑥0(𝑡) = 0. It is known that the equation always has at least one nontrivial small solution, but, in general, it can have also solutions not small. The Armellini–Tonelli–Sansone Theorem says that if the function 𝑞 grows “regularly” in some sense, then all solutions are small. A generalization of this growth condition is given in terms only of the integral of 𝑞 and . It is proved that the result is a real generalization of the earlier theorems.

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3

CLARKE, FRANCIS. "A Lipschitz regularity theorem." Ergodic Theory and Dynamical Systems 27, no. 6 (2007): 1713–18. http://dx.doi.org/10.1017/s0143385707000132.

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AbstractThis paper gives a direct and elementary proof of the fact that under hypotheses of Tonelli type, solutions to the basic problem in the calculus of variations are Lipschitz when the Lagrangian is autonomous. This fact was first proved by Clarke and Vinter in 1985, using other methods.

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4

de Amo, E., and M. Díaz Carrillo. "Fubini-Tonelli theorems with local integrals." Acta Mathematica Hungarica 72, no. 3 (1996): 221–27. http://dx.doi.org/10.1007/bf00050684.

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5

Robdera, Mangatiana A. "On Cartesian Nets and Fubini-Tonelli Type Theorem." International Journal of Applied Physics and Mathematics 7, no. 2 (2017): 118–27. http://dx.doi.org/10.17706/ijapm.2017.7.2.118-127.

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6

Asselle, Luca, and Marco Mazzucchelli. "Waist theorems for Tonelli systems in higher dimensions." manuscripta mathematica 163, no. 1-2 (2019): 185–99. http://dx.doi.org/10.1007/s00229-019-01154-5.

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7

Asselle, Luca, and Gabriele Benedetti. "The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles." Journal of Topology and Analysis 08, no. 03 (2016): 545–70. http://dx.doi.org/10.1142/s1793525316500205.

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Let [Formula: see text] be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian [Formula: see text] and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if [Formula: see text] is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of [Formula: see text].

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8

Zaslavski, Alexander J. "Generic existence of solutions of nonconvex optimal control problems." Abstract and Applied Analysis 2005, no. 4 (2005): 375–421. http://dx.doi.org/10.1155/aaa.2005.375.

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The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrandsfwhich satisfy convexity and growth conditions. In 1996, the author obtained a generic existence and uniqueness result (with respect to variations of the integrand of the integral functional) without the convexity condition for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we survey this result and its recent extensions, and establish several new results in this direction.

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9

Lee, Tuo-Yeong. "Product variational measures and Fubini–Tonelli type theorems for the Henstock–Kurzweil integral." Journal of Mathematical Analysis and Applications 298, no. 2 (2004): 677–92. http://dx.doi.org/10.1016/j.jmaa.2004.05.033.

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10

Lee, Tuo-Yeong. "Product variational measures and Fubini–Tonelli type theorems for the Henstock–Kurzweil integral II." Journal of Mathematical Analysis and Applications 323, no. 1 (2006): 741–45. http://dx.doi.org/10.1016/j.jmaa.2005.10.045.

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11

Torres, D. F. M. "Carathéodory Equivalence, Noether Theorems, and Tonelli Full-Regularity in the Calculus of Variations and Optimal Control." Journal of Mathematical Sciences 120, no. 1 (2004): 1032–50. http://dx.doi.org/10.1023/b:joth.0000013565.78376.fb.

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12

Masani, P. R., and H. Niemi. "The integration theory of Banach space valued measures and the Tonelli-Fubini theorems. II. Pettis integration." Advances in Mathematics 75, no. 2 (1989): 121–67. http://dx.doi.org/10.1016/0001-8708(89)90035-2.

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13

Mandorino, Vito. "Connecting orbits for families of Tonelli Hamiltonians." Journal of Modern Dynamics 6, no. 4 (2012): 499–538. http://dx.doi.org/10.3934/jmd.2012.6.499.

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14

Brix, M. "NERVAL: DE CORILLA A LA TONELLI." French Studies Bulletin LXI, no. 102 (2007): 15–17. http://dx.doi.org/10.1093/frebul/ktl048.

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15

Masani, P. R., та H. Niemi. "The integration theory of Banach space valued measures and the Tonelli-Fubini theorems I. Scalar-valued measures on δ-rings". Advances in Mathematics 73, № 2 (1989): 204–41. http://dx.doi.org/10.1016/0001-8708(89)90069-8.

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16

Ávila, Paula Aparecida, and Juliana Reichert Assunção Tonelli. "As motivações para a implementação do ensino de língua inglesa nos anos iniciais de escolarização em uma escola municipal pública." Acta Scientiarum. Language and Culture 42, no. 1 (2020): e50986. http://dx.doi.org/10.4025/actascilangcult.v42i1.50986.

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Neste artigo investigamos as motivações para a implementação da Língua Inglesa nos anos iniciais em uma escola situada no norte do Paraná. Os dados analisados constam de entrevistas com os sujeitos envolvidos direta ou indiretamente com a inserção da língua na escola, a saber: as secretárias de educação, as diretoras e as professoras de inglês. Para esta pesquisa qualitativa interpretativista, caracterizada como um estudo de caso, ancoramo-nos teoricamente nos preceitos da Abordagem do Ciclo de Políticas (ACP) (Bowe, Ball, & Gold, 1992; Mainardes, 2006; Ball & Mainardes, 2011) e em autores como Santos (2005), Muñoz (2014), Chaguri e Tonelli (2013), dentre outros, sobre ensino de inglês para crianças. Os resultados revelam motivações de diferentes naturezas para a inserção da Língua Inglesa na escola investigada, dentre elas: a motivação política; 2) motivação pedagógica; 3) motivação administrativa e 4) a motivação mercantilista. Desse modo, a influência que o inglês exerce nos dias atuais, impulsionado pela força da globalização, pauta-se na maior motivação ao se pensar na oferta de uma língua estrangeira, além de ser considerada pelas participantes da pesquisa como ‘porta de entrada’ para o mercado de trabalho e como sinônimo de sucesso profissional.

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17

Goldhill, Simon. "(F.) Tonelli Sophocles' Oedipus and the tale of the theatre. (Speculum artium, 12.) Ravenna: Longo. 1983. Pp. 199. L 18,000." Journal of Hellenic Studies 106 (November 1986): 209–10. http://dx.doi.org/10.2307/629673.

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18

Kay, Tristan. "Natascia Tonelli, Fisiologia della passione: Poesia d’amore e medicina da Cavalcanti a Boccaccio. Florence: SISMEL Edizioni del Galluzzo, 2015. Pp. xvi, 253. €54. ISBN: 978-88-8450-671-9." Speculum 94, no. 1 (2019): 293–94. http://dx.doi.org/10.1086/701308.

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19

Arnaud, Marie-Claude, and Andrea Venturelli. "A multidimensional Birkhoff theorem for time-dependent Tonelli Hamiltonians." Calculus of Variations and Partial Differential Equations 56, no. 4 (2017). http://dx.doi.org/10.1007/s00526-017-1210-0.

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20

Asselle, Luca, Gabriele Benedetti, and Marco Mazzucchelli. "Minimal Boundaries in Tonelli Lagrangian Systems." International Mathematics Research Notices, November 11, 2019. http://dx.doi.org/10.1093/imrn/rnz246.

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Abstract We prove several new results concerning action minimizing periodic orbits of Tonelli Lagrangian systems on an oriented closed surface $M$. More specifically, we show that for every energy larger than the maximal energy of a constant orbit and smaller than or equal to the Mañé critical value of the universal abelian cover, the Lagrangian system admits a minimal boundary, that is, a global minimizer of the Lagrangian action on the space of smooth boundaries of open sets of $M$. We also extend the celebrated graph theorem of Mather in this context: in the tangent bundle $\textrm{T} M$, the union of the supports of all lifted minimal boundaries with a given energy projects injectively to the base $M$. Finally, we prove the existence of action minimizing simple periodic orbits on energies just above the Mañé critical value of the universal abelian cover. This provides in particular a class of nonreversible Finsler metrics on the two-sphere possessing infinitely many closed geodesics.

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21

Biacino, Loredana. "Development of the Theory of the Functions of Real Variables in the First Decades of the Twentieth Century." Transversal: International Journal for the Historiography of Science, no. 9 (December 19, 2020). http://dx.doi.org/10.24117/2526-2270.2020.i9.01.

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In (Biacino 2018) the evolution of the concept of a real function of a real variable at the beginning of the twentieth century is outlined, reporting the discussions and the polemics, in which some young French mathematicians of those years as Baire, Borel and Lebesgue were involved, about what had to be considered a genuine real function. In this paper a technical survey of the arising function and measure theory is given with a particular regard to the contribution of the Italian mathematicians Vitali, Beppo Levi, Fubini, Severini, Tonelli etc … and also with the purpose of exposing the intermediate steps before the final formulation of Radom-Nicodym-Lebesgue Theorem and the Italian method of calculus of variations.

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22

Sarkar, Palash. "Computing square roots faster than the Tonelli-Shanks/Bernstein algorithm." Advances in Mathematics of Communications, 2022, 0. http://dx.doi.org/10.3934/amc.2022007.

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<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula> be a prime such that <inline-formula><tex-math id="M2">\begin{document}$ p = 1+2^nm $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M3">\begin{document}$ n\geq 1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ m $\end{document}</tex-math></inline-formula> is odd. Given a square <inline-formula><tex-math id="M5">\begin{document}$ u $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M6">\begin{document}$ \mathbb{Z}_p $\end{document}</tex-math></inline-formula> and a non-square <inline-formula><tex-math id="M7">\begin{document}$ z $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M8">\begin{document}$ \mathbb{Z}_p $\end{document}</tex-math></inline-formula>, we describe an algorithm to compute a square root of <inline-formula><tex-math id="M9">\begin{document}$ u $\end{document}</tex-math></inline-formula> which requires <inline-formula><tex-math id="M10">\begin{document}$ \mathfrak{T}+O(n^{3/2}) $\end{document}</tex-math></inline-formula> operations (i.e., squarings and multiplications), where <inline-formula><tex-math id="M11">\begin{document}$ \mathfrak{T} $\end{document}</tex-math></inline-formula> is the number of operations required to exponentiate an element of <inline-formula><tex-math id="M12">\begin{document}$ \mathbb{Z}_p $\end{document}</tex-math></inline-formula> to the power <inline-formula><tex-math id="M13">\begin{document}$ (m-1)/2 $\end{document}</tex-math></inline-formula>. This improves upon the Tonelli-Shanks (TS) algorithm which requires <inline-formula><tex-math id="M14">\begin{document}$ \mathfrak{T}+O(n^{2}) $\end{document}</tex-math></inline-formula> operations. Bernstein had proposed a table look-up based variant of the TS algorithm which requires <inline-formula><tex-math id="M15">\begin{document}$ \mathfrak{T}+O((n/w)^{2}) $\end{document}</tex-math></inline-formula> operations and <inline-formula><tex-math id="M16">\begin{document}$ O(2^wn/w) $\end{document}</tex-math></inline-formula> storage, where <inline-formula><tex-math id="M17">\begin{document}$ w $\end{document}</tex-math></inline-formula> is a parameter. A table look-up variant of the new algorithm requires <inline-formula><tex-math id="M18">\begin{document}$ \mathfrak{T}+O((n/w)^{3/2}) $\end{document}</tex-math></inline-formula> operations and the same storage. In concrete terms, the new algorithm is shown to require significantly fewer operations for particular values of <inline-formula><tex-math id="M19">\begin{document}$ n $\end{document}</tex-math></inline-formula>.</p>

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23

Vilella, Eduard. "«Natascia Tonelli, Fisologia della passione. Poesia d’amore e medicina da Cavalcanti a Boccaccio, Firenze, Edizioni del Galluzzo, 2015, 253 pp.»." Revista de Literatura Medieval, December 2, 2016, 317–20. http://dx.doi.org/10.37536/rlm.2016.28.0.62063.

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