Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Heart Failure Association of the European Society of Cardiology Quality of Care Centres Programme: design and accreditation document

Heart failure (HF) is the major contributor to cardiovascular morbidity and mortality. Given its rising prevalence, the costs of HF care can be expected to increase. Multidisciplinary management of HF can improve quality of care and survival. However, specialized HF programmes are not widely available in most European countries. These circumstances underlie the suggestion of the Heart Failure Association (HFA). of the European Society of Cardiology (ESC) for the development of quality of care centres (QCCs). These are defined as health care institutions that provide multidisciplinary HF management at all levels of care (primary, secondary and tertiary), are accredited by the HFA/ESC and are implemented into existing health care systems. Their major goals are to unify and improve the quality of HF care, and to promote collaboration in education and research activities. Three types of QCC are suggested: community QCCs (primary care facilities able to provide non-invasive assessment and optimal therapy); specialized QCCs (district hospitals with intensive care units, able to provide cardiac catheterization and device implantation services), and advanced QCCs (national reference centres able to deliver advanced and innovative HF care and research). QCC accreditation will require compliance with general and specific HFA/ESC accreditation standards. General requirements include confirmation of the centre's existence, commitment to QCC implementation, and collaboration with other QCCs. Specific requirements include validation of the centre's level of care, service portfolio, facilities and equipment, management, human resources, process measures, quality indicators and outcome measures. Audit and recertification at 4–6-year intervals are also required. The implementation of QCCs will evolve gradually, following a pilot phase in selected countries. The present document summarizes the definition, major goals, development, classification and crucial aspects of the accreditation process of the HFA/ESC QCC Programme. © 2020 European Society of Cardiolog

Heart failure in cardiomyopathies: a position paper from the Heart Failure Association of the European Society of Cardiology

Cardiomyopathies are a heterogeneous group of heart muscle diseases and an important cause of heart failure (HF). Current knowledge on incidence, pathophysiology and natural history of HF in cardiomyopathies is limited, and distinct features of their therapeutic responses have not been systematically addressed. Therefore, this position paper focuses on epidemiology, pathophysiology, natural history and latest developments in treatment of HF in patients with dilated (DCM), hypertrophic (HCM) and restrictive (RCM) cardiomyopathies. In DCM, HF with reduced ejection fraction (HFrEF) has high incidence and prevalence and represents the most frequent cause of death, despite improvements in treatment. In addition, advanced HF in DCM is one of the leading indications for heart transplantation. In HCM, HF with preserved ejection (HFpEF) affects most patients with obstructive, and ∼10% of patients with non-obstructive HCM. A timely treatment is important, since development of advanced HF, although rare in HCM, portends a poor prognosis. In RCM, HFpEF is common, while HFrEF occurs later and more frequently in amyloidosis or iron overload/haemochromatosis. Irrespective of RCM aetiology, HF is a harbinger of a poor outcome. Recent advances in our understanding of the mechanisms underlying the development of HF in cardiomyopathies have significant implications for therapeutic decision-making. In addition, new aetiology-specific treatment options (e.g. enzyme replacement therapy, transthyretin stabilizers, immunoadsorption, immunotherapy, etc.) have shown a potential to improve outcomes. Still, causative therapies of many cardiomyopathies are lacking, highlighting the need for the development of effective strategies to prevent and treat HF in cardiomyopathies. © 2019 The Authors. European Journal of Heart Failure © 2019 European Society of Cardiolog