Minimal sets in monotone and sublinear skew-product semiflows I: The general case

The dynamics of a general monotone and sublinear skew-product semiflow is analyzed, paying special attention to the long-term behavior of the strongly positive semiorbits and to the minimal sets. Four possibilities arise depending on the existence or absence of strongly positive minimal sets and bounded semiorbits, as well as on the coexistence or not of bounded and unbounded strongly positive semiorbits. Previous results are unified and extended, and scenarios which are impossible in the autonomous or periodic cases are described.     

Manipulation games in economies with indivisible goods

In this paper we study the strategic aspects of the No-Envy solution for the problem of allocating a finite set of indivisible goods among a group of agents when monetary compensations are possible. In the first part of the paper we consider the case where each agent receives, at most, one indivisible good. We prove that the set of equilibrium allocations of any direct revelation game associated with a subsolution of the No-Envy solution coincides with the set of envy-free allocations for the true preferences. Under manipulation all the subsolutions of the No-Envy solution are equivalent. In the second part of the paper, we allow each agent to receive more than one indivisible good. In this situation the above characterization does not hold any more. We prove that any Equal Income Walrasian allocation for the true preferences can be supported as an equilibrium allocation of any direct revelation game associated with subsolutions of the No-Envy solution, but also non-efficient allocations can be supported.     

Epidemiological Study of Voice Disorders Among Teaching Professionals of La Rioja, Spain

The purpose of the present study was to calculate the prevalence and incidence of voice disorders among teaching staff and find out the associated occupational risk factors. A case-control study was performed with 905 teachers, 579 cases and 326 controls; 492 were randomly selected and 413 volunteered. All teachers were asked to fill out a standard questionnaire. Next, a complete laryngeal exam was performed including a general ear, nose, and throat evaluation and videolaryngostroboscopy. The prevalence of voice disorders among teaching staff was 57%. The most prevalent lesions were vocal overstrain (18%), nodular lesions (14%), and hyperfunctional dysphonia (8%). The incidence rate was 3.87 new cases per year per 1000 teachers. Women had organic lesions three times more than men (odds ratio [OR]: 3.52, confidence interval [CI]: 2.04-6.09). However, men had chronic laryngitis three times more than women (OR: 2.93, CI: 1.50-5.71) and functional dysphonia nearly twice more than women (OR: 1.81, CI: 1.21-2.69). We find a significant risk of suffering voice disorders in teachers who smoke daily (OR: 2.31, CI: 1.58-3.37) and who drink several cups of coffee or tea (OR: 1.87, CI: 1.36-2.56). It is advisable to carry out an annual evaluation of all teaching staff on account of the high prevalence of voice disorders among them.     

Light-Induced Tetrazole-Quinone 1,3-Dipolar Cycloadditions

Quinones were firstly used as dipolarophiles in a photoclick 1,3-cycloaddition with 2,5-diaryltetrazoles, as photoactivatable predipoles, providing a novel and efficient access to three types of pyrazole-fused quinones (indazoledione derivatives). Distinctive features of this protocol include the use of light as the unique reagent and readily available, stable, and easy to handle starting materials and good to excellent yields. Photophysical and electrochemical properties of the quinones and their potential application as photoredox catalysts are also detailed.     

Bipolar Electrochemistry Exfoliation of Layered Metal Chalcogenides Sb2S3 and Bi2S3 and their Hydrogen Evolution Applications

Efficient exfoliation and downsizing of Sb₂S₃ and Bi₂S₃ layered compounds by using scalable bipolar electrochemistry on their suspensions in aqueous media are here demonstrated. The resulting samples were characterized in detail by transmission electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray photoelectron spectroscopy; their electrochemistry toward hydrogen evolution was also investigated. Hydrogen evolution ability of exfoliated Sb₂S₃ and Bi₂S₃ was investigated and compared to the bulk counterparts.     

Production and characterization of refractive index gratings in high-birefringence fibre optics

In this work, we report production and modelling of both Bragg gratings and rocking filters in high birefringence fibre optics. Bragg gratings are produced by UV (257.0 nm) external interferometric exposition of a frequency-doubled Ar⁺ ion laser, whereas for rocking filters formation the visible Ar⁺ ion laser lines in 488.0 and 514.5 nm are used in an internal method. The spectral characteristics due to the birefringence properties are studied through numerical methods and experimental techniques. The spectral responsivity of the structures under temperature changes and stress application is presented.     

Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems

We investigate how to adapt the Q-Arnoldi method for the case of symmetric quadratic eigenvalue problems, that is, we are interested in computing a few eigenpairs \((\lambda ,x)\) of \((\lambda ^2M+\lambda C+K)x=0\) with M, C, K symmetric \(n\times n\) matrices. This problem has no particular structure, in the sense that eigenvalues can be complex or even defective. Still, symmetry of the matrices can be exploited to some extent. For this, we perform a symmetric linearization \(Ay=\lambda By\), where A, B are symmetric \(2n\times 2n\) matrices but the pair (A, B) is indefinite and hence standard Lanczos methods are not applicable. We implement a symmetric-indefinite Lanczos method and enrich it with a thick-restart technique. This method uses pseudo inner products induced by matrix B for the orthogonalization of vectors (indefinite Gram-Schmidt). The projected problem is also an indefinite matrix pair. The next step is to write a specialized, memory-efficient version that exploits the block structure of A and B, referring only to the original problem matrices M, C, K as in the Q-Arnoldi method. This results in what we have called the Q-Lanczos method. Furthermore, we define a stabilized variant analog of the TOAR method. We show results obtained with parallel implementations in SLEPc.     

Snapshot location for POD in control of a linear heat equation

In the present work, we study the approximation of a distributed optimal control problem for a linear heat equation with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). We show that snapshot location for control problems is crucial in model reduction. For the determination of the time instances (snapshot locations) we utilize an a-posteriori error control concept which is based on a reformulation of the optimality system of the underlying optimal control problem as a second order in time and fourth order in space elliptic system. Finally, we present a numerical test to illustrate our approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Demonstration of a 100 Hz repetition rate gain-saturated diode-pumped table-top soft x-ray laser

We demonstrate the operation of a gain-saturated table-top soft x-ray laser at 100?Hz repetition rate. The laser generates an average power of 0.15?mW at λ=18.9 nm, the highest laser power reported to date from a sub-20-nm wavelength compact source. Picosecond laser pulses of 1.5?μJ energy were produced at λ=18.9 nm by amplification in a Mo plasma created by tailoring the temporal intensity profile of single pump pulses with 1?J energy produced by a diode-pumped chirped pulse amplification Yb:YAG laser. Lasing was also obtained in the 13.9?nm line of Ni-like Ag. These results increase by an order of magnitude the repetition rate of plasma-based soft x-ray lasers opening the path to milliwatt average power table-top lasers at sub-20?nm wavelengths.     

Gabor systems and almost periodic functions

Inspired by results of Kim and Ron, given a Gabor frame in $L^2(\mathbb{R})$, we determine a non-countable generalized frame for the non-separable space ${\mathit{AP}}_2(\mathbb{R})$ of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of ${\mathit{AP}}_2(\mathbb{R})$ are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.