A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under L2 norm but with less segmentation. The re-parameterization functions we used are C continuous piecewise rational linear functions, which provide more flexibility and can b...

we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

It is possible for medium-frequency (MF) radar systems to estimate kinetic energy dissipation rates by measuring signal fading times. Here, we present approximately 5 years of such results from Tromsø (69 N, 19 E) and in particular, investigate the periodicities present at different altitudes in the regime 80 to 100 km. We detect the known annual variation in the mesosphere and the semiannual v...

Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L 2-loss function. The unknown function f is assumed to be m times diierentiable except for an unknown, though nite, number of jumps, with piecewise mth derivative bounded in L 2-norm. An estimator is constructed, attaining the same o...

We have developed a novel loss function that embeds largemargin classification into Minimum Classification Error (MCE) training. Unlike previous efforts this approach employs a loss function that is bounded, does not require incremental adjustment of the margin or prior MCE training. It extends the Bayes risk formulation of MCE using Parzen Window estimation to incorporate large– margin classif...

Support vector machines (SVMs) belong to the class of modern statistical machine learning techniques and can be described as M-estimators with a Hilbert norm regularization term for functions. SVMs are consistent and robust for classification and regression purposes if based on a Lipschitz continuous loss and a bounded continuous kernel with a dense reproducing kernel Hilbert space. For regress...

According to Jordan Decomposition Theorem, every real function of bounded variation can be decomposed to a difference of two increasing functions. In this paper we will show, among others, that an effective version of this theorem does not hold for computable function of bounded variation.

This paper considers estimation of normal mean ? when the variance is unknown, using the LINEX loss function. The unique Bayes estimate of ? is obtained when the precision parameter has an Inverse Gaussian prior density

We present several examples which show that the well known statements about Markov Decision Processes can fail if the loss function is not bounded.