The convergence order of finite elements is related to the polynomial order of the basis functions used on each element, with higher order polynomials yielding better convergence orders. However, two issues can prevent this convergence order from being achieved: the poor approximation of curved boundaries by polygonal meshes and lack of regularity of the PDE solution. We show studies for Lagran...

Phenotypic similarity of species occupying similar habitats has long been taken as strong evidence of adaptation, but this approach implicitly assumes that similarity is evolutionarily derived. However, even derived similarities may not represent convergent adaptation if the similarities did not evolve as a result of the same selection pressures; an alternative possibility is that the similar f...

BACKGROUND The purpose of this study was to help determine the most appropriate target to be used for the assessment of the nearpoint of convergence, normative data for the break and recovery in adults, and the diagnostic value of the red-glass modification and repetition of the nearpoint of convergence. METHODS A total of 175 subjects with normal binocular vision and 38 subjects with converg...

The famous ratio test of d’Alembert for convergence of series depends on the limit of the simple ratio an+1 an (J. d’Alembert, 1717–1783). If the limit is 1, the test fails. Most notable is its failure in situations where it is expected to succeed. For example, it often fails on series with terms containing factorials or finite products. Such terms appear in Taylor series of many functions. The...

We describe a new and simple method to aid in the analysis of retrieved pulses from inverted frequency-resolved optical gating (FROG) traces. The analysis can separate noise from distortion and shows that distortion is more deleterious to the retrieved pulse than is pure noise. The analysis relies on the fact that FROG traces can be constructed from a single outer product of two vectors, wherea...

In this paper we use Wynn’s -algorithm to accelerate certain numerical sequences, in order to study empirically their rate of convergence, for the sequence of successive approximations associated with some test functions and ordinary differential equations. For the great majority of the test sequences, the -algorithm does not improve the convergence rate. Subject Classification: [2000] 47H10, 6...