Upper and lower bounds for a reactive-diffuse system with Arrhenius kinetics.
Al-Refai, Mohammed, Katatbeh, Qutaibeh (2006)
International Journal of Mathematics and Mathematical Sciences
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Al-Refai, Mohammed, Katatbeh, Qutaibeh (2006)
International Journal of Mathematics and Mathematical Sciences
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Olivier Ramaré (2001)
Acta Arithmetica
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Pedro Freitas, Batłomiej Siudeja (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove some new upper and lower bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. In particular, we improve Pólya and Szegö's [ (1951)] lower bound for quadrilaterals and extend Hersch's [ (1966) 457–460] upper bound for parallelograms to general quadrilaterals.
L. Gajek (1987)
Applicationes Mathematicae
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J. Kaczorowski, A. Perelli (2012)
Acta Arithmetica
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Kulikov, A.S., Fedin, S.S. (2004)
Zapiski Nauchnykh Seminarov POMI
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Paturi, R., Pudlák, P. (2004)
Zapiski Nauchnykh Seminarov POMI
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Antunes, Pedro, Freitas, Pedro (2006)
Experimental Mathematics
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Bianchi, Monica, Torriero, Anna (2000)
Journal of Inequalities and Applications [electronic only]
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Morosi, Carlo, Pizzocchero, Livio (2001)
Journal of Inequalities and Applications [electronic only]
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A. Adamus (1970)
Annales Polonici Mathematici
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S. Laurens, S. Tordeux, A. Bendali, M. Fares, P. R. Kotiuga (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational...