Geometric methods from dynamical systems are used to study Lagrangian transport in numerically-generated, time-dependent, two-dimensional vector elds. The ows analyzed here are numerical solutions to the barotropic, -plane, potential vorticity equation with viscosity, where the pde parameters have been chosen so that the solution evolves to a meandering jet. Numerical methods for approximating ...

We address the question if a point inside a domain bounded by a simple closed arc spline is circularly visible from a specified arc from the boundary. We provide a simple and numerically stable linear time algorithm that solves this problem. In particular, we present an easy to check criterion that implies that a point is not visible from a specified boundary arc.

The fundamental construct of numerical algebraic geometry is the representation of an irreducible algebraic set, A, by a witness set, which consists of a polynomial system, F , for which A is an irreducible component of V(F ), a generic linear space L of complementary dimension to A, and a numerical approximation to the set of witness points, L ∩A. Given F , methods exist for computing a numeri...

Robust semi-definite programming problems with rational dependence on uncertainties are known to have a wide range of applications, in particular in robust control. It is well-established how to systematically construct relaxations on the basis of the full block S-procedure. In general such relaxations are expected to be conservative, but for concrete problem instances they are often observed t...

The Betz theory expresses that no horizontal axis wind turbine can extract more than 16/27 (59.3%) of the kinetic energy of the wind. The factor 16/27 (0.593) is known as the Betz limit. Horizontal Axis wind turbine designers try to improve the power performance to reach the Betz limit. Modern operational wind turbines achieve at peak 75% to 80% of the Betz limit. In 1919, Albert Betz used an a...

We consider the problem of numerical stability and model density growth when training a sparse linear model from massive data. We focus on scalable algorithms that optimize certain loss function using gradient descent, with either l0 or l1 regularization. We observed numerical stability problems in several existing methods, leading to divergence and low accuracy. In addition, these methods typi...

We propose a knot insertion algorithm for splines that are piecewisely in L{1, x, sin x, cos x}. Since an ECC–system on [0, 2π] in this case does not exist, we construct a CCC–system by choosing the appropriate measures in the canonical representation. In this way, a B-basis can be constructed in much the same way as for weighted and tension splines. Thus we develop a corner cutting algorithm f...

The presentation explores diplophonia via numerical simulations of glottal vibrations. The aim of the study is to improve the understanding of glottal wall vibration and area waveform patterns of nonmodal phonation as observed via laryngeal highspeed videos. Diplophonia has been described as the simultaneous perception of two pitches during voicing. A broader definition is the vibration of diff...

The syntactic nature and compositionality characteristic of stochastic process algebras make models to be easily understood by human beings, but not convenient for machines as well as people to directly carry out mathematical analysis and stochastic simulation. This paper presents a numerical representation schema for the stochastic process algebra PEPA, which can provide a platform to directly...

Gaussian elimination with partial pivoting is performed routinely, millions times per day around the world, but partial pivoting (that is, row interchange of an input matrix) is communication intensive and has become the bottleneck of the elimination algorithm in the present day computer environment, in both cases of matrices of large and small size. Gaussian elimination with no pivoting as wel...