A theory of the infinite horizon LQ-problem for composite systems of PDEs with boundary control

We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential Equations (PDE) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall `predominant' hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic components of the dynamics has been introduced by the authors in 2005, and a full theory of the LQ-problem on a finite time horizon has been developed. The present paper provides the infinite time horizon theory, culminating in well-posedness of the corresponding (algebraic) Riccati equations. New technical challenges are encountered and new tools are needed, especially in order to pinpoint the differentiability of the optimal solution. The theory is illustrated by means of a boundary control problem arising in thermoelasticity.Comment: 50 pages, submitte

PADUS, SANDALUS, GENS FADIENA. UNDERWATER SURVEYS IN PALAEO-WATERCOURSES (FERRARA DISTRICT – ITALY)

In the ambit of our program of researches on ancient rivers in Ferrara hinterland (Italy), we have been joining a Scientific – Didactic Project between Soprintendenza per i Beni Archeologici dell'Emilia Romagna, Comune di Portomaggiore Assessorato alla Cultura, CMAS A.CDCI. - Confédération Mondiale des Activités Subaquatiques Federation ITA F07 – Associazione CMAS Diving Center Italia. The Project is focused on underwater archaeological surveys in ex quarry lakes, following the Rivers Padus and Sandalus between Voghiera, Gambulaga and Portomaggiore (Ferrara District). Here we are going to introduce our most recent results, after the last immersions and a 3D bathymetrical survey completed by echo-side scan sonar in Tramonto Lake at Gambulaga, explaining the connection with remote sensing investigations and direct surveys applied to underwater archaeology of the inland water. The main submerged structure individuated is a part of wooden dock on the left side of Padus, in front of the Necropolis of Fadieni (1st-3rd cent. A.D.). Thanks to the study of 183 finds coming from the lake, involving students and young collaborators of the Archaeological National Museum of Ferrara, we are reconstructing the ancient landscape between Proto-Imperial Age and Late Antique

Spectral properties of incommensurate charge-density wave systems

The concept of frustrated phase separation is applied to investigate its consequences for the electronic structure of the high T_c cuprates. The resulting incommensurate charge density wave (CDW) scattering is most effective in creating local gaps in k-space when the scattering vector connects states with equal energy. Starting from an open Fermi surface we find that the resulting CDW is oriented along the (10)- and (or) (01)-direction which allows for a purely one-dimensional or a two-dimensional ``eggbox type'' charge modulation. In both cases the van Hove singularities are substantially enhanced, and the spectral weight of Fermi surface states near the M-points, tends to be suppressed. Remarkably, a leading edge gap arises near these points, which, in the eggbox case, leaves finite arcs of the Fermi surface gapless. We discuss our results with repect to possible consequences for photoemission experiments

Effectiveness of surgical procedures in the acceleration of orthodontic tooth movement: Findings from systematic reviews and meta-analyses

The current overview aimed to summarise the findings provided by systematic reviews (SRs) on the effect of surgical procedures in the acceleration of tooth movement and to assess the methodological quality of the included SRs. Three electronic databases have been explored. SRs addressing the effects of surgical procedures on the acceleration of tooth movement were included. The methodological quality of the included SRs was assessed using the updated version of “A Measurement Tool to Assess Systematic Review” (AMSTAR-2). Twenty-eight (28) SRs were included. The methodological quality of the included reviews ranged between critically low (6 studies) and high (12 studies). The most common critical weakness in the included reviews was the absence of clearly a-prior established review methods and any significant deviations from the protocol. The most studied surgical procedure was corticotomy, followed by micro-osteoperforation, piezocision and periodontally accelerated osteogenic orthodontics. The majority of the included SRs supported short-term favourable effects of corticotomy on treatment time and tooth movement rate, in the short-term. However, the authors of the included SRs reported that results were based on weak quality evidence. Conflicting results arise from the existent SRs with regards to the effectiveness of piezocision and micro-osteoperforation. Few SRs summarised complications and side effects of surgical techniques, supporting absence of loss of tooth vitality, periodontal problems, or severe root resorption. The current overview of SRs highlighted the need of high quality SRs comparing different surgical approaches for tooth movement acceleration though network meta-analysis, in order to determine the most efficient instrument for orthodontic movement acceleration

Nitric oxide and hydrogen sulfide: the gasotransmitter paradigm of the vascular system.

There are several reviews on NO and hydrogen sulfide (H2 S) and their role in vascular diseases in the current relevant literature. The aim of this review is to discuss, within the limits of present knowledge, the interconnection between these two gasotransmitters in vascular function. In particular, the review focuses on the role played by the balance between the NO and H2 S pathways in either physiological or pathological conditions. The distinction between physiology and pathology has been made in order to dissect the molecular basis of this crosstalk, highlighting how and if this balance varies, depending upon the vascular status. Perspectives and possible novel therapeutic approaches are also discussed

Variety, Competition, and Population in Economic Growth: Theory and Empirics

We provide aggregate macroeconomic evidence on how, in the long-run, a diverse degree of production-complexity may affect not only the rate of economic growth, but also the correlation between the latter, population growth and the monopolistic (intermediate) markups. For a sample of OECD economies, we find that the losses due to more complexity in production are lower than the corresponding specialization gains. According to our theoretical model, this implies that the impact of population change on economic growth is slightly positive. Using a Finite Mixture Model, we also classify the countries in the sample and verify for each cluster the impact that the population growth rate and the intermediate sector's markups exert on the 5-year average real GDP growth rate

Variety, Competition, and Population in Economic Growth : Theory and Empirics

We provide aggregate macroeconomic evidence on how, in the long-run, a diverse degree of complexity in production may affect not only the rate of economic growth, but also the correlation between the latter, population growth and the monopolistic (intermediate) markups. For a sample of OECD countries, we find that the impact of population change on economic growth is slightly positive. According to our the- oretical model, this implies that the losses due to more complexity in production are lower than the corresponding specialization gains. Using a Finite Mixture Model, we also classify the countries in the sample and verify for each cluster the impact that the population growth rate and the intermediate sector\u2019s markups exert on the 5-year average real GDP growth rate