Displaying similar documents to “Lower and upper bounds for the Rayleigh conductivity of a perforated plate”

A comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai equations

Peter Wall (1997)

Applications of Mathematics

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In this paper we study a unidirectional and elastic fiber composite. We use the homogenization method to obtain numerical results of the plane strain bulk modulus and the transverse shear modulus. The results are compared with the Hashin-Shtrikman bounds and are found to be close to the lower bounds in both cases. This indicates that the lower bounds might be used as a first approximation of the plane strain bulk modulus and the transverse shear modulus. We also point out the connection...

Explicit upper bounds for |L(1,χ)| when χ(3) = 0

David J. Platt, Sumaia Saad Eddin (2013)

Colloquium Mathematicae

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Let χ be a primitive Dirichlet character of conductor q and denote by L(z,χ) the associated L-series. We provide an explicit upper bound for |L(1,χ)| when 3 divides q.

Bounds and numerical results for homogenized degenerated p -Poisson equations

Johan Byström, Jonas Engström, Peter Wall (2004)

Applications of Mathematics

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In this paper we derive upper and lower bounds on the homogenized energy density functional corresponding to degenerated p -Poisson equations. Moreover, we give some non-trivial examples where the bounds are tight and thus can be used as good approximations of the homogenized properties. We even present some cases where the bounds coincide and also compare them with some numerical results.

Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals

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.