From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere

We prove a sharp multiplier theorem of Mihlin-H\"ormander type for the Grushin operator on the unit sphere in $\mathbb{R}^3$, and a corresponding boundedness result for the associated Bochner-Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics.Comment: 32 page

Technical Debt Prioritization: State of the Art. A Systematic Literature Review

Background. Software companies need to manage and refactor Technical Debt issues. Therefore, it is necessary to understand if and when refactoring Technical Debt should be prioritized with respect to developing features or fixing bugs. Objective. The goal of this study is to investigate the existing body of knowledge in software engineering to understand what Technical Debt prioritization approaches have been proposed in research and industry. Method. We conducted a Systematic Literature Review among 384 unique papers published until 2018, following a consolidated methodology applied in Software Engineering. We included 38 primary studies. Results. Different approaches have been proposed for Technical Debt prioritization, all having different goals and optimizing on different criteria. The proposed measures capture only a small part of the plethora of factors used to prioritize Technical Debt qualitatively in practice. We report an impact map of such factors. However, there is a lack of empirical and validated set of tools. Conclusion. We observed that technical Debt prioritization research is preliminary and there is no consensus on what are the important factors and how to measure them. Consequently, we cannot consider current research conclusive and in this paper, we outline different directions for necessary future investigations

Uniform pointwise estimates for ultraspherical polynomials

We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in arbitrary dimension, and are instrumental in the proof of sharp multiplier theorems for those operators.Comment: 12 pages. This work extends the estimates for spherical harmonics initially proved in arXiv:1705.0706

Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators

We study degenerate elliptic operators of Grushin type on the $d$-dimensional sphere, which are singular on a $k$-dimensional sphere for some $k < d$. For these operators we prove a spectral multiplier theorem of Mihlin-H\"ormander type, which is optimal whenever $2k \leq d$, and a corresponding Bochner-Riesz summability result. The proof hinges on suitable weighted spectral cluster bounds, which in turn depend on precise estimates for ultraspherical polynomials.Comment: 39 pages. This work extends the multiplier theorem proved in arXiv:1705.07068 and is based on estimates for ultraspherical polynomials in arXiv:2009.0232

La rappresentanza degli amministratori delle persone giuridiche del Libro Primo del Codice Civile

The focus of this work, which deals with the powers of representation granted to the directors of legal entities pursuant to the First Book of the Italian Civil Code, is the examination of the cases of pathological management of the representative power and the reconnaissance - and analysis - of the main forms of limitations, both statutory or legal, to such power, with particular reference to the effect of said restrictions on the relationships with third parties who deal with the legal representative. The work therefore has been structured moving from a prior recall to concepts and institutions that constitute the foundation of the subject under consideration, such as the various theories on the legal entity and the legal representation. The analysis, about the main limiting cases of the representative power and about the fate of the acts executed by the representative of non-corporate bodies in violation of the abovementioned limits, was carried out on the basis of a dialectical confrontation with the reformed rules applicable to corporate companies, in order to seize which principles - accrued within the corporate purview - are subject to analogous application and which instead should be disregarded, with the application of the general rules for voluntary representation. The research concludes with an examination of the applicability, with reference to the legal representation, of the principles of apparent representation, as a form of protection for third parties otherwise exposed to excessively detrimental consequences

New insights on the multidimensionality of fatigue and on its relationship with cognitive impairments in multiple sclerosis

Multiple Sclerosis (MS) is an inflammatory disease of the central nervous system (CNS), and it represents the most common cause of irreversible impairment in young adults, affecting about 2.5 million individuals worldwide. In MS, acute attacks of inflammation, leading to demyelination and axonal loss, determine the accumulation of disabilities, varying in number, nature, and severity. Indeed, motor, sensory, cognitive, and behavioral symptoms may manifest at different times during the disease's variable clinical course. Fatigue is a complex and multifaceted phenomenon and one of the most prevalent and disabling symptoms of MS, affecting 75%–90% of patients. Despite its prevalence, MS- related fatigue is still poorly understood. The absence of a well-validated definition and of clear insights into its pathophysiological causes makes fatigue a hybrid symptom, approached within the context of different disciplines, each with their own methods and tools. As a result, the scientific literature abounds with irreconcilable data, leaving fatigue in a dark shadow zone, at the expense of MS patients still lacking adequate therapies and strategies of management. The main topic of this thesis relates to the multidimensional nature of fatigue, to its variability, and its effects on attentional processes, most commonly affected in MS patients. Specifically, studies presented in the current thesis address four research issues: (i) are physical and mental fatigue two distinct constructs? (ii) how do physical and mental fatigue vary within a short (within a day) and long (within a year) period? (iii) how do induced physical and mental fatigue impact the attentional functions of alerting, orienting, and conflict resolution in MS? The main results of the studies are reported: a) A clear distinction between physical and mental fatigue has been psychometrically documented in MS patients. b) MS patients reported experiencing more overall fatigue than Controls. c) A gradual increase in overall fatigue from the morning to the evening was reported by MS participants. d) Across experiments physical fatigue was significantly more pronounced in MS patients as compared to Controls. e) Both MS patients and Controls reported having experienced more overall fatigue in the past (one year ago) than in the present (the last 24 hours). f) MS patients were slower as compared to Controls in performing attentional tasks; however, inconclusive results have emerged regarding the effects of physical and mental fatigue on attentional processes. g) Sleep quality and depression were both associated with fatigue across the experiments. The relationship between self-efficacy, general cognitive functioning, functional deterioration, and physical and mental fatigue is fragmented, thus preventing a clear conclusion

Does Geographical Proximty Matters for Innovation? The Case for European Regions

The increasing globalization, challenges for the competitiveness, and resources prioritization are among the causes forcing the European (EU) regions to rethink their overall approach to regional economic development. To deal with such a complexity, EU policy makers deployed a program called Smart Specialisation Strategies (SSS) which aims at consolidating the sources of regional competitive advantage by making effective and efficient use of public investment in R&D. By promoting SSS, national and regional governments are attempting to enhance the competitiveness of firms and clusters. Then, the study of clusters along with their evolutionary and spatial dynamics is put on top of the agenda of EU policy makers. To better understand the determinants of clusters in Europe we first, investigate the role played by technological specialization and diversification; second, find empirical evidence to whether the link between geographical proximity and regional innovation activity exists; finally, explore the co-existence of cluster dynamics and the deployment of SSS

Targeting Brutons Tyrosine Kinase in Chronic Lymphocytic Leukemia at the Crossroad between Intrinsic and Extrinsic Pro-survival Signals

Chemo immunotherapies for chronic lymphocytic leukemia (CLL) showed a positive impact on clinical outcome, but many patients relapsed or become refractory to the available treatments. The main goal of the researchers in CLL is the identification of specific targets in order to develop new therapeutic strategies to cure the disease. The B cell receptor-signalling pathway is necessary for survival of malignant B cells and its related molecules recently become new targets for therapy. Moreover, leukemic microenvironment delivers survival signals to neoplastic cells also overcoming the apoptotic effect induced by traditional drugs. In this context, the investigation of Bruton\u2019s tyrosine kinase (Btk) is useful in: i) dissecting CLL pathogenesis; ii) finding new therapeutic approaches striking simultaneously intrinsic as well as extrinsic pro-survival signals in CLL. This paper will review these main topics