Sarabia et al. (1999) present a basic model to create ordered families of Lorenz curves, along with basic theorems that describe the conditions for the models to satisfy the definition of the Lorenz curve. Using these basic models, they suggest a family which includes several well-known Lorenz models as special cases. This paper first shows that their basic theorems can be generalized. The pape...

20 Prolonged exposure to a single direction of motion alters perception of subsequent 21 static or dynamic stimuli and induces substantial changes in behaviors of motion22 sensitive neurons, but it remains unclear about an origin of neural adaptation and 23 neural correlates of perceptual consequences of motion adaptation in human brain. 24 Using functional magnetic resonance imaging (fMRI), we...

We address the problem of how to perform prescribed shape modification of NURBS curves merely by the modification of the weight of some of their control points. As is known, NURBS curves can be considered as central projections of nonrational B-spline curves. Making use of the property that there is an infinite number of nonrational B-spline curves the central projection of which is a given NUR...

The DEplot command in Maple is used to show the direction field and solution curves of a differential equation or system of differential equations. We present new options created for the DEplot command for enhancing the visualization of a direction field and for animating a direction field and the solution curves in time. We present a new Maplet, DEplotlet(DEplotInteractive), which simplifies t...

This paper considers the problem of constructing a smooth surface to fit rows of data points. A special class of T-spline surfaces is examined, which is characterized to have a global knot vector in one parameter direction and individual knot vectors from row to row in the other parameter direction. These T-spline surfaces are suitable for lofted surface interpolation or approximation. A skinni...

Suppose n points are scattered uniformly at random in the unit square [0, 1]. Question: How many of these points can possibly lie on some curves of length λ? Answer, proved here: OP (λ · √ n). We consider a general class of such questions; in each case, we are given a class Γ of curves in the square, and we ask: in a cloud of n uniform random points, how many can lie on some curve γ ∈ Γ? Classe...

To characterize muscle synergy organization underlying multidirectional control of stance posture, electromyographic activity was recorded from 11 lower limb and trunk muscles of 7 healthy subjects while they were subjected to horizontal surface translations in 12 different, randomly presented directions. The latency and amplitude of muscle responses were quantified for each perturbation direct...

A binary chain code for representing 3D curves is presented. 3D curves are digitalized and represented as 3D discrete curves. 3D discrete curves are composed of constant straight-line segments using only orthogonal directions. The proposed binary notation is based on the orthogonal direction change chain code. Thus, using the proposed binary chain code it is possible to represent any 3D curve b...

We present two new corner detectors; one works by using dissimilarity along the contour direction to detect curves in the image contour and the other estimates image curvature along the contour direction. These operators are fast, robust to noise, and require no subjective thresholding.

Let π be a Hecke-Maass cusp form for SL(3,Z) and χ = χ1χ2 a Dirichlet character with χi primitive modulo Mi. Suppose that M1, M2 are primes such that max{(M |t|)1/3+2δ/3,M2/5|t|−9/20,M1/2+2δ|t|−3/4+2δ}(M |t|)ε < M1 < min{(M |t|)2/5, (M |t|)1/2−8δ}(M |t|)−ε for any ε > 0, where M = M1M2, |t| ≥ 1 and 0 < δ < 1/52. Then we have L ( 1 2 + it, π ⊗ χ ) ≪π,ε (M |t|).