Maltsiniotis's first conjecture for K_1

We show that K_1 of an exact category agrees with K_1 of the associated triangulated derivator. More generally we show that K_1 of a Waldhausen category with cylinders and a saturated class of weak equivalences coincides with K_1 of the associated right pointed derivator.Comment: 23 pages, the main results have been generalize

Quasinormal Modes of Charged Dilaton Black Holes in 2+1 Dimensions

We have studied the scalar perturbation of static charged dilaton black holes in 2+1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2+1 dimensions. It is asymptotic to the anti-de Sitter space. The exact values of quasinormal modes for the scalar perturbations are calculated. For both the charged and uncharged cases, the quasinormal frequencies are pure-imaginary leading to purely damped modes for the perturbations.Comment: 12 pages, LaTex, references added, some typos corrected. notations change

Robust Stability Under Mixed Time Varying, Time Invariant and Parametric Uncertainty

Robustness analysis is considered for systems with structured uncertainty involving a combination of linear time-invariant and linear time-varying perturbations, and parametric uncertainty. A necessary and sufficient condition for robust stability in terms of the structured singular value μ is obtained, based on a finite augmentation of the original problem. The augmentation corresponds to considering the system at a fixed number of frequencies. Sufficient conditions based on scaled small-gain are also considered and characterized

Slowly Oscillating Solution of the Cubic Heat Equation

In this paper, we are considering the Cauchy problem of the nonlinear heat equation $u\_t -\Delta u= u^{3 },\ u(0,x)=u\_0$. After extending Y. Meyer's result establishing the existence of global solutions, under a smallness condition of the initial data in the homogeneous Besov spaces $\dot{B}\_{p}^{-\sigma, \infty}(\mathbb{R}^{3})$, where 3 \textless{} p \textless{} 9 and $\sigma=1-3/p$, we prove that initial data $u\_0\in \mathcal{S}(\mathbb{R}^{3})$, arbitrarily small in ${\dot B^{-2/3,\infty}\_{9}}(\mathbb{R}^{3})$, can produce solutions that explode in finite time. In addition, the blowup may occur after an arbitrarily short time

Analytic quantification of the singlet nonlocality for the first Bell's inequality

Recently an alternative way to quantify Bell nonlocality has been proposed [Phys. Rev. A {\bf 92}, 030101(R) (2015)]. In this work we further develop this concept, the volume of violation, and analytically calculate its value for the spin-singlet state with respect to the settings of the first Bell's inequality. These settings correspond to three directions in space, or three arbitrary points on the unit sphere. It is shown that the triples of directions that lead to violations in local causality correspond to $1/3$ of all possible configurations. From the perspective of quantum communications, this means that two distant parties that were capable of align their measurements in one direction only (the remaining direction in each site being random), have a probability of about 33.3$\%$ to be able to certify their entanglement.Comment: Accepted for publicitar in Phys. Rev.