Given a function b, holomorphic on the disc and bounded by 1, one can construct an associated reproducing kernel Hilbert space called the de Branges–Rovnyak space H(b). We explore representations of such spaces via descriptions of the corresponding families of orthogonal polynomials. We find relevant structures in the linear systems involved in a diversity of cases when b is rational. We also establish a form of invariance under some composition operators on H(b) spaces.
A new alternative numerical procedure to the Szego quadrature formulas for the estimation of integrals with respect to a positive Borel measure & micro; supported on the unit circle is presented. As in many practical situations, we assume that the values of the integrand F are only known at a finite number of points, which we will assume to be equispaced on the unit circle. Our technique consists of obtaining an approximating Laurent polynomial L to F by interpolation in the Hermite sense in a collection of these points that mimic the zeros of a para-orthogonal polynomial with respect to & micro;, and to use the values of F at the remaining nodes to improve the accuracy of the approximation by a process of simultaneous complex regression. Some numerical examples are carried out.
Three decades after the Stiglitz Commission's call to measure “beyond GDP”, multidimensional prosperity frameworks have proliferated, yet cross-linguistic mappings of their paradigmatic and territorial composition remain scarce; existing reviews rely on English-only searches.This article characterises the conceptual, methodological and territorial structure of multidimensional prosperity frameworks published between 1995 and 2026, and tests the robustness of the resulting patterns to alternative definitions of the review scope.Following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA 2020), we searched Web of Science and Scopus in English, Spanish, French, Italian and Portuguese, retrieving 23,048 unique records. Title-and-abstract screening used a deterministic rule-based classifier specified and refined by the two reviewers, who adjudicated every record it passed forward at full text, yielding 583 included studies. Paradigm was coded at two levels — the identity of the framework referenced and the analytical framing of the study deploying it — because the two do not coincide. Robustness was assessed across three nested corpora (n = 583, 551, 503).The Human Development Index (HDI) of the United Nations Development Programme (UNDP) and the Multidimensional Poverty Index (MPI) of the Oxford Poverty and Human Development Initiative (OPHI) jointly account for 46.3–50.4% of the corpus. Frameworks with a social paradigmatic identity account for 79.0%, ecological for 8.9%, holistic for 8.3%, economic for 2.2% and two-dimensional hybrids for 1.6%. Insular contexts represent 1.0% of studies, and paradigm is not associated with territorial scale (Monte-Carlo p = 0.39), so the concentration is field-wide rather than confined to any territorial tier. Framework paradigm and study-level analytical framing diverge for 73.2% of the studies in which both are determinable: 184 of the 348 studies invoking a social-paradigm instrument (52.9%) are framed economically. Among the 162 bespoke frameworks, 58 integrate all three substantive dimensions but only one imposes an explicit biophysical boundary. All patterns are stable across the three corpus definitions.Three decades after the Beyond GDP critique, the field remains concentrated on a narrow canon of capability-based instruments that are predominantly deployed within income- and growth-centred analytical framings, while ecological-paradigm frameworks and insular territories remain marginal. Paradigmatic plurality appears to require editorial and institutional intervention rather than further conceptual elaboration.
This study is grounded in a novel approach of sustainable tourism through the concept of the Tourism Cooperative (TC). Its theoretical foundation lies in the broad understanding of the natural world and environment as well as their interconnectedness with human factors. In order to establish a balance between tourism sustainability and human actions, four constructs were examined: market orientation, circular economy, innovation, and Sustainable Development Goals (SDGs). A sample of 108 tourism firms in Tenerife was used to explore the theoretical and practical relevance of the four constructs and their role in shaping sustainable tourism practices. The reliability analysis confirmed the constructs’ formulation. The TC model views sustainability as an ongoing and adaptive process that emphasizes knowledge sharing and power dynamics. Therefore, this research demonstrated that mutual cooperation among all tourism stakeholders is fundamental for tourism companies to adopt sustainable business models and thus contribute to tourist destinations being directed towards sustainable development. Limitations and future research directions concern mainly construct interrelations and the application of the study in different contexts.
Alzheimer's disease (AD) is a progressive neurodegenerative disorder characterized by amyloid-beta (A beta) accumulation and neuronal loss. Despite extensive research, the early biophysical events underlying A beta-induced neurotoxicity remain poorly understood. Quantitative Phase Imaging (QPI) is a label-free optical technique that enables non-invasive measurement of cellular morphology, refractive index, and dry-mass distribution, offering a powerful approach for studying early pathological alterations in living cells. In this work, we employed QPI to investigate AD-associated cellular phenotypes in two complementary models: SH-SY5Y neuroblastoma cells exposed to soluble A beta 42 and primary olfactory neuronal precursors (ONPs) derived from AD patients. Time-lapse QPI recordings revealed that acute exposure of SH-SY5Y cells to 10 mu M A beta 42 induced a significant reduction in the integrated phase signal within 1 h, consistent with rapid cellular shrinkage, osmotic imbalance, and intracellular mass redistribution. These findings demonstrate that QPI can sensitively detect early neurotoxic responses before the appearance of overt pathological hallmarks. To evaluate the applicability of QPI in patient-derived models, ONPs from AD patients and cognitively healthy controls were imaged after fixation as a proof-of-concept study. QPI revealed heterogeneous intracellular optical signatures, including localized hyper-refractive puncta and alterations in phase topography in representative AD-derived ONPs. Line-scan analysis further illustrated examples of cells displaying pronounced somatic optical-thickness peaks (similar to 50 nm) and compartmentalized mass accumulation, while distal neurites exhibited lower-amplitude signals (similar to 10-20 nm). These features are consistent with early intracellular aggregation and structural remodeling associated with neurodegeneration. Together, our results establish QPI as a sensitive, label-free platform for detecting early biophysical signatures of AD in live experimental models and demonstrate its feasibility for the analysis of patient-derived ONPs, supporting future studies in larger clinical cohorts.
