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Solutions of hypersingular integral equations over circular domains by a spectral method

Farina, Leandro, Ziebell, Juliana S. (2013)

Applications of Mathematics 2013

The problem of a solving a class of hypersingular integral equations over the boundary of a nonplanar disc is considered. The solution is obtained by an expansion in basis functions that are orthogonal over the unit disc. A Fourier series in the azimuthal angle, with the Fourier coefficients expanded in terms of Gegenbauer polynomials is employed. These integral equations appear in the study of the interaction of water waves with submerged thin plates.

Some examples of homogeneous Einstein manifolds

Rodionov, E. D. (1993)

Proceedings of the Winter School "Geometry and Physics"

The author obtains the classification of all invariant Einstein metrics on the following homogeneous spaces: S U ( 3 ) / T max , S p ( 3 ) / S p ( 1 ) × S p ( 1 ) × S p ( 1 ) , F 4 / spin ( 8 ) , S U ( 5 ) / S p ( 2 ) × T 1 . Combining this with the results of other authors, the classification of all invariant Einstein metrics on all compact simply connected homogeneous spaces admitting a homogeneous Riemannian metric of positive sectional curvature is obtained.

Some natural operations between connections on fibred manifolds

Doupovec, Miroslav, Vondra, Alexandr (1996)

Proceedings of the Winter School "Geometry and Physics"

Given a fibered manifold Y → X , a 2-connection on Y means a section J 1 Y → J 2 Y . The authors determine all first order natural operators transforming a 2-connection on Y and a classical linear connection on X into a connection on J 1 Y → Y . (The proof implies that there is no first order natural operator transforming 2-connections on Y into connections on J 1 Y → Y .) Using this result, the authors deduce several properties of characterizable connections on J 1 Y → X .

Some practical aspects of parallel adaptive BDDC method

Šístek, Jakub, Mandel, Jan, Sousedík, Bedřich (2012)

Applications of Mathematics 2012

We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may...

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