Article history: Received 2 November 2011 Available online xxxx Communicated by Luchezar L. Avramov MSC: primary 16E40, 55P35 secondary 16E45, 16T10, 16T15, 18G55, 55P40, 55U10, 55U15, 57T05, 57T30

Resumen—A second order sliding mode controller, the so-called “Twisting” algorithm is under study. A non-smooth strict Lyapunov function is proposed, so global finite time stability for this algorithm can be proved, even in the case when it is affected by bounded external perturbations. The strict Lyapunov function gives the possibility to estimate an upper bound for the time convergence of the...

1. Introduction. In [5] Mazur constructed a homotopy 4-sphere which looked like one of the strongest candidates for a counterexample to the 4-dimensional Poincaré Conjecture. In this paper we show that Mazur's example is in fact a true 4-sphere after all. This raises the odds in favour of the 4-dimensional Poincaré Conjecture. The proof involves a smooth knot of S2 in S4 with unusual properties.

We generalize graded Hecke algebras to include a twisting twococycle for the associated finite group. We give examples where the parameter spaces of the resulting twisted graded Hecke algebras are larger than that of the graded Hecke algebras. We prove that twisted graded Hecke algebras are particular types of deformations of a crossed product.

Edwards’ elliptic curve form is popular in modern cryptographic implementations thanks to their fast, strongly unified addition formulas. Twisted Edwards curves with a = −1 are slightly faster, but their addition formulas are not complete over Fp where p ≡ 3 (mod 4). In this short note, we propose that designers specify Edwards curves, but implement scalar multiplications and the like using an ...

1 2004 (1) References [1] M. Cho and S. Y. Rhee. Optimization of laminates with free edges under bounded uncertainty subject to extension, bending and twisting. International Journal of Solids and Structures, 41:227–245, 2004. [2] C. Lin and Y. Lee. Stacking sequence optimization of laminated composite structures using genetic algorithm with local improvement. Composite Structures, 63:339–345, ...

A novel super-twisting adaptive sliding mode control law is derived using Lyapunov function technique. The both drift uncertain term and multiplicative perturbation are assumed to be bounded with unknown boundaries. The proposed approach consists in using dynamically adapted control gains that ensure the establishment, in a finite time, of a real second order sliding mode. The efficacy of the p...

In this paper, a new smooth second order sliding mode control is proposed. This algorithm is a modified form of Super Twisting algorithm. The Super Twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular Lyapunov function. The Proposed algorithm which is able to control nonlinear systems with matched structured u...