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

On globally defined semianalytic sets

In this work we present the concept of $C$-semianalytic subset of a real analytic manifold and more generally of a real analytic space. $C$-semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analytic sets introduced by Cartan ($C$-analytic sets for short). More precisely $S$ is a $C$-semianalytic subset of a real analytic space $(X,{\mathcal O}_X)$ if each point of $X$ has a neighborhood $U$ such that $S\cap U$ is a finite boolean combinations of global analytic equalities and strict inequalities on $X$. By means of paracompactness $C$-semianalytic sets are the locally finite unions of finite boolean combinations of global analytic equalities and strict inequalities on $X$. The family of $C$-semianalytic sets is closed under the same operations as the family of semianalytic sets: locally finite unions and intersections, complement, closure, interior, connected components, inverse images under analytic maps, sets of points of dimension $k$, etc. although they are defined involving only global analytic functions. In addition, we characterize subanalytic sets as the images under proper analytic maps of $C$-semianalytic sets. We prove also that the image of a $C$-semianalytic set $S$ under a proper holomorphic map between Stein spaces is again a $C$-semianalytic set. The previous result allows us to understand better the structure of the set $N(X)$ of points of non-coherence of a $C$-analytic subset $X$ of a real analytic manifold $M$. We provide a global geometric-topological description of $N(X)$ inspired by the corresponding local one for analytic sets due to Tancredi-Tognoli (1980), which requires complex analytic normalization. As a consequence it holds that $N(X)$ is a $C$-semianalytic set of dimension $\leq\dim(X)-2$.Comment: 32 pages, 3 figure

Classification of obstruction for separation of semialgebraic sets in dimension 3

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Smooth and Analytic Salutions for Analytic Linear System

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The Walking Test: Use in clinical practice

Exercise Capacity is the expression of the cardiovascular and of metabolic organic efficiency and represents a important prognostic marker. The Six Minute Walking Test is adopted in the practice for exercise capacity evaluation in the normal subject as in pneumologic or cardiac rehabilitation programs, and in both pediatric and elderly ages. The aim of the work is to present a practical summary of the application of the six minutes walking test, according to the American Thoracic Society statement. We reviewed the various experiences of its application, and reported the indications, clinical interpretation parameters, relationship and correlation between functional and clinical parameters (hospitalization, quality of life, therapy and exercise control response and compliance), the basic and advanced protocol, the application modality, the reporting models, and the educational checklist

2019 Italian Society of Cardiology census on telemedicine in cardiovascular disease : a report from the working group on telecardiology and informatics

Background The aim of this study was to assess by a census supported by the Italian Society of Cardiology (Societ\ue0 Italiana di Cardiologia, SIC) the present implementation of telemedicine in the field of cardiovascular disease in Italy. Methods A dedicated questionnaire was sent by email to all the members of the SIC: data on telemedicine providers, service provided, reimbursement, funding and organisational solutions were collected and analysed. Results Reported telemedicine activities were mostly stable and public hospital based, focused on acute cardiovascular disease and prehospital triage of suspected acute myocardial infarction (prehospital ECG, always interpreted by a cardiologist and not automatically reported by computerised algorithms). Private companies delivering telemedicine services in cardiology (ECGs, ambulatory ECG monitoring) were also present. In 16% of cases, ECGs were also delivered through pharmacies or general practitioners. ICD/CRT-D remote control was performed in 42% of cases, heart failure patient remote monitoring in 37% (21% vital parameters monitoring, 32% nurse telephone monitoring). Telemedicine service was public in 74% of cases, paid by the patient in 26%. About half of telemedicine service received no funding, 17% received State and/or European Union funding. Conclusions Several telemedicine activities have been reported for the management of acute and chronic cardiovascular disease in Italy. The whole continuum of cardiovascular disease is covered by telemedicine solutions. A periodic census may be useful to assess the implementation of guidelines recommendations on telemedicine