As an intial step towards low-rank optimization algorithms using hierarchical tensors, the aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety M≤k of real m × n matrices of rank at most k. Such methods extend successfully used Riemannian optimization methods on the smooth manifold Mk of rank-k matrices to its closure by taking steps...

Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...

In this letter, our objective is to explore how two well-known projection dynamics can be used as dynamic controllers for stabilization of nonlinear systems. Combining the properties operators, Lyapunov stability theory and LaSalle’s theorem, we confirm that on feasible set tangent cone are Krasovskii passive. To show effectiveness proposed approach, use stabilizing boost converters in a DC mic...

This work proposes a texture descriptor based on fractal theory. The method is based on the Bouligand-Minkowski descriptors. We decompose the original image recursively into 4 equal parts. In each recursion step, we estimate the average and the deviation of the Bouligand-Minkowski descriptors computed over each part. Thus, we extract entropy features from both average and deviation. The propose...

Arapaima gigas, a fresh water fish found in the Amazon Basin, resist predation by piranhas through the strength and toughness of their scales, which act as natural dermal armour. Arapaima scales consist of a hard, mineralized outer shell surrounding a more ductile core. This core region is composed of aligned mineralized collagen fibrils arranged in distinct lamellae. Here we show how the Bouli...