On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

An Estimated New-Keynesian Model with Unemployment as Excess Supply of Labor

Wage stickiness is incorporated to a New-Keynesian model with variable capital to drive endogenous unemployment uctuations de ned as the log di¤erence between aggregate labor supply and aggregate labor demand. We estimated such model using Bayesian econometric techniques and quarterly U.S. data. The second-moment statistics of the unemployment rate in the model give a good t to those observed in U.S. data. Our results also show that wage-push shocks, demand shifts and monetary policy shocks are the three major determinants of unemployment fl uctuations. Compared to an estimated New-Keynesian model without unemployment (Smets and Wouters, 2007): wage stickiness is higher, labor supply elasticity is lower, the slope of the New-Keynesian Phillips curve is flatter, and the importance of technology innovations on output variability increases.

The prevalence of diabetes-related complications and multimorbidity in the population with type 2 diabetes mellitus in the Basque Country

Background: Type 2 diabetes mellitus is associated with a diverse range of pathologies. The aim of the study was to determine the incidence of diabetes-related complications, the prevalence of coexistent chronic conditions and to report multimorbidity in people with type 2 diabetes living in the Basque Country. Methods: Administrative databases, in four cross sections (annually from 2007 to 2011) were consulted to analyse 149,015 individual records from patients aged >= 35 years with type 2 diabetes mellitus. The data observed were: age, sex, diabetes-related complications (annual rates of acute myocardial infarction, major amputations and avoidable hospitalisations), diabetes-related pathologies (prevalence of ischaemic heart disease, renal failure, stroke, heart failure, peripheral neuropathy, foot ulcers and diabetic retinopathy) and other unrelated pathologies (44 diseases). Results: The annual incidence for each condition progressively decreased during the four-year period: acute myocardial infarction (0.47 to 0.40%), major amputations (0.10 to 0.08%), and avoidable hospitalisations (5.85 to 5.5%). The prevalence for diabetes-related chronic pathologies was: ischaemic heart disease (11.5%), renal failure (8.4%), stroke (7.0%), heart failure (4.3%), peripheral neuropathy (1.3%), foot ulcers (2.0%) and diabetic retinopathy (7.2%). The prevalence of multimorbidity was 90.4%. The highest prevalence for other chronic conditions was 73.7% for hypertension, 13.8% for dyspepsia and 12.7% for anxiety. Conclusions: In the type 2 diabetes mellitus population living in the Basque Country, incidence rates of diabetes complications are not as high as in other places. However, they present a high prevalence of diabetes related and unrelated diseases. Multimorbidity is very common in this group, and is a factor to be taken into account to ensure correct clinical management.

Temperature-and pH-Sensitive Nanohydrogels of Poly(N-Isopropylacrylamide) for Food Packaging Applications: Modelling the Swelling-Collapse Behaviour

Temperature-sensitive poly(N-isopropylacrylamide) (PNIPA) nanohydrogels were synthesized by nanoemulsion polymerization in water-in-oil systems. Several cross-linking degrees and the incorporation of acrylic acid as comonomer at different concentrations were tested to produce nanohydrogels with a wide range of properties. The physicochemical properties of PNIPA nanohydrogels, and their relationship with the swelling-collapse behaviour, were studied to evaluate the suitability of PNIPA nanoparticles as smart delivery systems (for active packaging). The swelling-collapse transition was analyzed by the change in the optical properties of PNIPA nanohydrogels using ultraviolet-visible spectroscopy. The thermodynamic parameters associated with the nanohydrogels collapse were calculated using a mathematical approach based on the van't Hoff analysis, assuming a two-state equilibrium (swollen to collapsed). A mathematical model is proposed to predict both the thermally induced collapse, and the collapse induced by the simultaneous action of two factors (temperature and pH, or temperature and organic solvent concentration). Finally, van't Hoff analysis was compared with differential scanning calorimetry. The results obtained allow us to solve the problem of determining the molecular weight of the structural repeating unit in cross-linked NIPA polymers, which, as we show, can be estimated from the ratio of the molar heat capacity (obtained from the van't Hoff analysis) to the specific heat capacity (obtained from calorimetric measurements).

Temperature-and pH-Sensitive Nanohydrogels of Poly(N-Isopropylacrylamide) for Food Packaging Applications: Modelling the Swelling-Collapse Behaviour

Temperature-sensitive poly(N-isopropylacrylamide) (PNIPA) nanohydrogels were synthesized by nanoemulsion polymerization in water-in-oil systems. Several cross-linking degrees and the incorporation of acrylic acid as comonomer at different concentrations were tested to produce nanohydrogels with a wide range of properties. The physicochemical properties of PNIPA nanohydrogels, and their relationship with the swelling-collapse behaviour, were studied to evaluate the suitability of PNIPA nanoparticles as smart delivery systems (for active packaging). The swelling-collapse transition was analyzed by the change in the optical properties of PNIPA nanohydrogels using ultraviolet-visible spectroscopy. The thermodynamic parameters associated with the nanohydrogels collapse were calculated using a mathematical approach based on the van't Hoff analysis, assuming a two-state equilibrium (swollen to collapsed). A mathematical model is proposed to predict both the thermally induced collapse, and the collapse induced by the simultaneous action of two factors (temperature and pH, or temperature and organic solvent concentration). Finally, van't Hoff analysis was compared with differential scanning calorimetry. The results obtained allow us to solve the problem of determining the molecular weight of the structural repeating unit in cross-linked NIPA polymers, which, as we show, can be estimated from the ratio of the molar heat capacity (obtained from the van't Hoff analysis) to the specific heat capacity (obtained from calorimetric measurements).