This paper derives an algorithm which determines the invertibility of arbitrary two-dimensional quadratic isoparametric finite element transformations. Theorems verifying the algorithm and guiding the construction of invertible transformations are proven.

This paper considers estimation of moving average (MA) models with non-Gaussian errors. Information in higher order cumulants allows identification of the parameters without imposing invertibility. By allowing for an unbounded parameter space, the generalized method of moments estimator of the MA(1) model has classical (root-T and asymptotic normal) properties when the moving average root is in...

Motion artifacts are a significant issue in medical image reconstruction. There are many methods for incorporating motion information into image reconstruction. However, there are fewer studies that focus on deformation regularization in motioncompensated image reconstruction. The usual choice for deformation regularization has been penalty functions based on the assumption that tissues are ela...

We present a test for the invertibility of second order Bézier elements. Our test that can determine precisely if such the function is invertible in only a constant number of operations. Although our formulation is specific to triangles, it is simple to extend it to other polygonal domains. Our test is used in the routines of the Lagrangian finite element fluid solver Tumble. Tumble uses moving...

We show that the hyperbolic volume of a hyperbolic knot is a quandle cocycle invariant. Further we show that it completely determines invertibility and positive/negative amphicheirality of hyperbolic knots.