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We investigate moduli of planar circular quadrilaterals symmetric with respect to both the coordinate axes. First we develop an analytic approach which reduces this problem to ODEs and devise a numeric method to find out the accessory parameters. This method uses the Schwarz equation to determine conformal mapping of the unit disk onto a given circular quadrilateral. We also give an example of a circular quadrilateral for which the value of the conformal modulus can be found in the analytic form; this example is used to validate the numeric calculations. We also use another method, so called hpFEM, for the numeric calculation of the moduli. These two different approaches provide results agreeing with high accuracy.
We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when possible, compari
The unsigned p-Willmore functional introduced in cite{mondino2011} generalizes important geometric functionals which measure the area and Willmore energy of immersed surfaces. Presently, techniques from cite{dziuk2008} are adapted to compute the firs
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bound
The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a given cubic pyramid into a conforming set of congruent cubic pyramids
We study the problem of finding orthogonal low-rank approximations of symmetric tensors. In the case of matrices, the approximation is a truncated singular value decomposition which is then symmetric. Moreover, for rank-one approximations of tensors