This paper considers k-monotone estimation and the related asymptotic performance analysis over a suitable Hölder class for general k. A novel two stage k-monotone B-spline estimator is proposed: in the first stage, an unconstrained estimator with optimal asymptotic performance is considered; in the second stage, a k-monotone B-spline estimator is constructed by projecting the unconstrained est...

Let K be a number field with ring of integers ZK . We prove two asymptotic formulas connected with the distribution of irreducible elements in ZK . First, we estimate the maximum number of nonassociated irreducibles dividing a nonzero element of ZK of norm not exceeding x (in absolute value), as x → ∞. Second, we count the number of irreducible elements of ZK of norm not exceeding x lying in a ...

It can be checked that this is a valid norm (on the set of random variables for which the left side of the above display is finite). Of special interest to us will be the Orlicz norms corresponding to the functions {ψp : p ≥ 1} where ψp(x) = exp(xp) − 1. Lemma 8.1 of Kosorok (2008) provides a necessary and sufficient condition for the ψp Orlicz norm to be finite in terms of the tail-behavior of...

To investigate the effects of hypoxia and incremental exercise on muscle contractility, membrane excitability, and maximal Na(+)-K(+)-ATPase activity, 10 untrained volunteers (age = 20 +/- 0.37 yr and weight = 80.0 +/- 3.54 kg; +/- SE) performed progressive cycle exercise to fatigue on two occasions: while breathing normal room air (Norm; Fi(O(2)) = 0.21) and while breathing a normobaric hypoxi...

In recent years, the eeect of the curse of high dimensionality has been studied in great detail on several problems such as clustering, nearest neighbor search, and indexing. In high dimensional space the data becomes sparse, and traditional indexing and algorithmic techniques fail from a eeciency and/or eeectiveness perspective. Recent research results show that in high dimensional space, the ...

Abstract In this article, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in $\mathcal {L}(E, F)$ . By using a theorem due to Pfitzner on James boundaries, show that if there exists relatively compact set K (in weak operator topology) such $0$ is an element its closure but it not norm-closed convex hull, then can guarantee does attain norm. This ...

This paper introduces a new locking–free formulation that combines the discontinuous Galerkin methods with weakly over-penalized techniques for Reissner– Mindlin plates. We derive optimal a priori error estimates in both the energy norm and L2 norm for polynomials of degree k = 2, and we extend the results concerning the energy norm to higher-order polynomial degrees. Numerical tests confirm ou...

We consider the numerical approximation of a flrst order stationary hyperbolic équation by the method of characteristics with pseudo time step k using discontinuous finite éléments on a mesh Th. For this method, we exhibit a "natural" norm || \\h,k for which we show that the discrete variational problem P^ is welî posed and we obtain an error estimate. We show that when k goes to zero problem (...

In this paper, we propose a novel robust and pragmatic feature selection approach. Unlike those sparse learning based feature selection methods which tackle the approximate problem by imposing sparsity regularization in the objective function, the proposed method only has one `2,1-norm loss term with an explicit `2,0-Norm equality constraint. An efficient algorithm based on augmented Lagrangian...