The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. ...

Given the periodicity of our model problem, it suffices to consider a single period cell (the dotted square in Figure 1), which has side length d. The front of the evolving step in this cell can be described by a simple 1D curve in the plane. We first discretize this 1D curve in space with N grid points, (xi, yi), i = 1, 2, . . . , N , which are uniformly spaced with respect to the arc length, ...

The length of a noun phrase has been shown to influence choices such as syntactic role assignment (e.g., whether the noun phrase is realized as the subject or the object). But does length also affect the choice between different forms of referring expressions? Three experiments investigated the effect of antecedent length on the choice between pronouns (e.g., he) and repeated nouns (e.g., the a...

Homotopy continuation provides a numerical tool for computing the equivalence of a smooth variety in an intersection product. Intersection theory provides a theoretical tool for relating the equivalence of a smooth variety in an intersection product to the degrees of the Chern classes of the variety. A combination of these tools leads to a numerical method for computing the degrees of Chern cla...

This paper describes a simple technique for evaluating the length of a parametric curve. The technique approximates sections of the curve to the arc of a circle using only sample points on the curve: no computation of derivatives or other properties is required. This method is almost as quick to implement and compute as chord-length summation but is much more accurate : it also provides recursi...

We demonstrate that the apparent length of a thin white arc on a black disk, rotating concentrically at 2.5 rps, varies with angular length and exposure duration. While short arcs (9-18 degrees ) gradually expand, long arcs (36-72 degrees ) first undergo a brief contraction, before they also expand. On average, perceived elongation asymptotes after 15 s equivalent to visual persistencies rangin...

The robust detection of lines and arcs in scanned documents or technical drawings is an important problem in document image understanding. We present a new solution to this problem that works directly on run-length encoded data. The method finds globally optimal solutions to parameterized thick line and arc models. Line thickness is part of the model and directly used during the matching proces...