John's ellipsoid and the integral ratio of a log-concave function

We extend the notion of John’s ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the log-concave function maximizing the integral ratio. A reverse functional affine isoperimetric inequality will be given, written in terms of this integral ratio. This can be viewed as a stability version of the functional affine isoperimetric inequality.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalConsejería de Industria, Turismo, Empresa e Innovación (Comunidad Autónoma de la Región de Murcia)Coordenação de aperfeiçoamento de pessoal de nivel superiorInstituto Nacional de Matemática Pura e Aplicad

Tutorial de Qt4 Designer

Con el presente proyecto se pretende unificar y actualizar a la versión 4.0 de Qt, dos tutoriales existentes en línea, que son: Clive Cooper: How to Create a Linux Desktop App in 14 Minutes for Beginners. Jean Pierre Charalambos: Tutorial de Qt4 Designer. El tutorial deberá estar disponible mediante soporte online, por lo que a modo de ampliación se ha optado por el desarrollo de una aplicación web. De este modo un usuario podrá interactuar con cada capítulo del tutorial, valorándolo y escribiendo comentarios que considere oportunos

Best approximation of functions by log-polynomials

Lasserre [La] proved that for every compact set $K\subset\mathbb R^n$ and every even number $d$ there exists a unique homogeneous polynomial $g_0$ of degree $d$ with $K\subset G_1(g_0)=\{x\in\mathbb R^n:g_0(x)\leq 1\}$ minimizing $|G_1(g)|$ among all such polynomials $g$ fulfilling the condition $K\subset G_1(g)$. This result extends the notion of the L\"owner ellipsoid, not only from convex bodies to arbitrary compact sets (which was immediate if $d=2$ by taking convex hulls), but also from ellipsoids to level sets of homogeneous polynomial of an arbitrary even degree. In this paper we extend this result for the class of non-negative log-concave functions in two different ways. One of them is the straightforward extension of the known results, and the other one is a suitable extension with uniqueness of the solution in the corresponding problem and a characterization in terms of some 'contact points'.Comment: 26 pages, 2 figure

An extension of Berwald's inequality and its relation to Zhang's inequality

In this note prove the following Berwald-type inequality, showing that for any integrable log-concave function f:Rn→[0, ∞)and any concave function h :L →[0, ∞), where L ={(x, t) ∈Rn×[0, ∞) :f(x) ≥e−t‖f‖∞}, then p→⎛⎝1Γ(1 +p)∫Le−tdtdx∫Lhp(x, t)e−tdtdx⎞⎠1p is decreasing in p ∈(−1, ∞), extending the range of pwhere the monotonicity is known to hold true.As an application of this extension, we will provide a new proof of a functional form of Zhang’s reverse Petty projection inequality, recently obtained in [2]

What drives unhappiness? A cross-country analysis

We study the sources of misery (lowest level of life satisfaction) using the European Quality of Life 2016, a cross-sectional survey for 28 European Union countries. We use the decomposition of misery, multivariate analysis and a structural equation model to assess which are the main sources to explain misery: risk of depression (mental health), unemployment, poverty or chronic health problems (physical health). Regardless of the methodological approach followed, we found consistently that the effect of mental health on misery is the largest, exceeding poverty and unemployment. Nonetheless, stigma and low access are the main barriers for mental health attention; therefore, policy goals should proactively promote attention, efficient prevention and early diagnosis of mental health problems.Funding for open access charge: Universidad de Málaga / CBU

Volume inequalitites for the i-th convolution bodies

We obtain a new extension of Rogers–Shephard inequality providing an upper bound for the volume of the sum of two convex bodies K and L. We also give lower bounds for the volume of the k-th limiting convolution body of two convex bodies K and L. Special attention is paid to the (n - 1)-th limiting convolution body, for which a sharp inequality, which is equality only when K = -L is a simplex, is given. Since the n-th limiting convolution body of K and -K is the polar projection body of K, these inequalities can be viewed as an extension of Zhang’s inequality

Size and emission wavelength control of InAs/InP quantum wires

For a certain heteroepitaxial system, the optical properties of self-assembled nanostructures basically depend on their size. In this work, we have studied different ways to modify the height of InAs/InP quantum wires (QWrs) in order to change the photoluminescence emission wavelength. One procedure consists of changing the QWr size by varying the amount of InAs deposited. The other two methods explored rely on the control of As/P exchange process, in one case during growth of InAs on InP for QWr formation and in the other case during growth of InP on InAs for QWr capping. The combination of the three approaches provides a fine tuning of QWr emission wavelength between 1.2 and 1.9 μm at room [email protected]

Distant emitters in ultrastrong waveguide QED: Ground-state properties and non-Markovian dynamics

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ansätze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime