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Composition of some singular Fourier integral operators and estimates for restricted X -ray transforms

Allan Greenleaf, Gunther Uhlmann (1990)

Annales de l'institut Fourier

We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations C ( T * X 0 ) × ( T * Y 0 ) . These canonical relations, which arise naturally in integral geometry, are such that π : C T * Y is a Whitney fold and ρ : C T * X is a blow-down mapping. If A I m ( C ) , B I m ' ( C t ) , then B A I m + m ' , 0 ( Δ , Λ ) a class of pseudodifferential operators with singular symbols. From this follows L 2 boundedness of A with a loss of 1/4 derivative.

Compositions, Generated by Special Nets in Affinely Connected Spaces

Zlatanov, Georgi (2002)

Serdica Mathematical Journal

Special nets which characterize Cartesian, geodesic, Chebyshevian, geodesic- Chebyshevian and Chebyshevian-geodesic compositions are introduced. Con- ditions for the coefficients of the connectedness in the parameters of these special nets are found.

Computational studies of conserved mean-curvature flow

Miroslav Kolář, Michal Beneš, Daniel Ševčovič (2014)

Mathematica Bohemica

The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are...

Computational studies of non-local anisotropic Allen-Cahn equation

Michal Beneš, Shigetoshi Yazaki, Masato Kimura (2011)

Mathematica Bohemica

The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.

Concentrated monotone measures with non-unique tangential behavior in 3

Robert Černý, Jan Kolář, Mirko Rokyta (2011)

Czechoslovak Mathematical Journal

We show that for every ε > 0 there is a set A 3 such that 1 A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and 1 A has the 1 -dimensional density between 1 and 2 + ε everywhere in the support.

Conditions for integrability of a 3-form

Jiří Vanžura (2017)

Archivum Mathematicum

We find necessary and sufficient conditions for the integrability of one type of multisymplectic 3-forms on a 6-dimensional manifold.

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