Continued fractions for some transcendental numbers

We consider series of the form $p/q + \sum_{j=2}^\infty 1/x_j$, where $x_1=q$ and the integer sequence $x_n$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for n?1. It is shown that the terms of the sequence, and multiples of the ratios of successive terms, appear interlaced in the continued fraction expansion of the sum of the series, which is a transcendental number

Reactive Polymorphic Nanoparticles: Preparation via Polymerization-Induced Self-Assembly and Postsynthesis Thiol-para-Fluoro Core Modification

The use of 2,3,4,5,6-pentafluorobenzyl methacrylate (PFBMA) as a core-forming monomer in ethanolic reversible addition-fragmentation chain transfer dispersion polymerization formulations is presented. Poly[poly(ethylene glycol) methyl ether methacrylate] (pPEGMA) macromolecular chain transfer agents were chain-extended with PFBMA leading to nanoparticle formation via polymerization-induced self-assembly (PISA). pPEGMA-pPFBMA particles exhibited the full range of morphologies (spheres, worms, and vesicles), including pure and mixed phases. Worm phases formed gels that underwent a thermo-reversible degelation and morphological transition to spheres (or spheres and vesicles) upon heating. Postsynthesis, the pPFBMA cores were modified through thiol-para-fluoro substitution reactions in ethanol using 1,8-diazabicyclo[5.4.0]undec-7-ene as the base. For monothiols, conversions were 64% (1-octanethiol) and 94% (benzyl mercaptan). Spherical and worm-shaped nano-objects were core cross-linked using 1,8-octanedithiol, which prevented their dissociation in nonselective solvents. For a temperature-responsive worm sample, cross-linking additionally resulted in the loss of the temperature-triggered morphological transition. The use of the reactive monomer PFBMA in PISA formulations presents a simple method to prepare well-defined nano-objects similar to those produced with nonreactive monomers (e.g., benzyl methacrylate) and to retain morphologies independent of solvent and temperature

Cation distribution in manganese cobaltite spinels Co3−xMnxO4 (0 ≤ x ≤ 1) determined by thermal analysis

Thermogravimetric analysis was used in order to study the reduction in air of submicronic powders of Co3−x Mn x O4 spinels, with 0 ≤ x ≤ 1. For x = 0 (i.e. Co3O4), cation reduction occurred in a single step. It involved the CoIII ions at the octahedral sites, which were reduced to Co2+ on producing CoO. For 0 < x ≤ 1, the reduction occurred in two stages at increasing temperature with increasing amounts of manganese. The first step corresponded to the reduction of octahedral CoIII ions and the second was attributed to the reduction of octahedral Mn4+ ions to Mn3+. From the individual weight losses and the electrical neutrality of the lattice, the CoIII and Mn4+ ion concentrations were calculated. The distribution of cobalt and manganese ions present on each crystallographic site of the spinel was determined. In contrast to most previous studies that took into account either CoIII and Mn3+ or Co2+, CoIII and Mn4+ only, our thermal analysis study showed that Co2+/CoIII and Mn3+/Mn4+ pairs occupy the octahedral sites. These results were used to explain the resistivity measurements carried out on dense ceramics prepared from our powders sintered at low temperature (700–750 °C) in a Spark Plasma Sintering apparatus

Aspirin use and knowledge in the community: a population- and health facility based survey for measuring local health system performance

BACKGROUND: Little is known about the relationship between cardiovascular risk, disease and actual use of aspirin in the community. METHODS: The Measuring Disparities in Chronic Conditions (MDCC) study is a community and health facility-based survey designed to track disparities in the delivery of health interventions for common chronic diseases. MDCC includes a survey instrument designed to collect detailed information about aspirin use. In King County, WA between 2011 and 2012, we surveyed 4633 white, African American, or Hispanic adults (45% home address-based sample, 55% health facility sample). We examined self-reported counseling on, frequency of use and risks of aspirin for all respondents. For a subgroup free of CAD or cerebral infarction that underwent physical examination, we measured 10-year coronary heart disease risk and blood salicylate concentration. RESULTS: Two in five respondents reported using aspirin routinely while one in five with a history of CAD or cerebral infarction and without contraindication did not report routine use of aspirin. Women with these conditions used less aspirin than men (65.0% vs. 76.5%) and reported more health problems that would make aspirin unsafe (29.4% vs. 21.2%). In a subgroup undergoing phlebotomy a third of respondents with low cardiovascular risk used aspirin routinely and only 4.6% of all aspirin users had no detectable salicylate in their blood. CONCLUSIONS: In this large urban county where health care delivery should be of high quality, there is insufficient aspirin use among those with high cardiovascular risk or disease and routine aspirin use by many at low risk. Further efforts are needed to promote shared-decision making between patients and clinicians as well as inform the public about appropriate use of routine aspirin to reduce the burden of atherosclerotic vascular disease

Ischaemic heart disease in the former Soviet Union 1990-2015 according to the Global Burden of Disease 2015 Study.

OBJECTIVE: The objective of this study was to compare ischaemic heart disease (IHD) mortality and risk factor burden across former Soviet Union (fSU) and satellite countries and regions in 1990 and 2015. METHODS: The fSU and satellite countries were grouped into Central Asian, Central European and Eastern European regions. IHD mortality data for men and women of any age were gathered from national vital registration, and age, sex, country, year-specific IHD mortality rates were estimated in an ensemble model. IHD morbidity and mortality burden attributable to risk factors was estimated by comparative risk assessment using population attributable fractions. RESULTS: In 2015, age-standardised IHD death rates in Eastern European and Central Asian fSU countries were almost two times that of satellite states of Central Europe. Between 1990 and 2015, rates decreased substantially in Central Europe (men -43.5% (95% uncertainty interval -45.0%, -42.0%); women -42.9% (-44.0%, -41.0%)) but less in Eastern Europe (men -5.6% (-9.0, -3.0); women -12.2% (-15.5%, -9.0%)). Age-standardised IHD death rates also varied within regions: within Eastern Europe, rates decreased -51.7% in Estonian men (-54.0, -47.0) but increased +19.4% in Belarusian men (+12.0, +27.0). High blood pressure and cholesterol were leading risk factors for IHD burden, with smoking, body mass index, dietary factors and ambient air pollution also ranking high. CONCLUSIONS: Some fSU countries continue to experience a high IHD burden, while others have achieved remarkable reductions in IHD mortality. Control of blood pressure, cholesterol and smoking are IHD prevention priorities

Increased Matrix Metalloproteinase (MMPs) Levels Do Not Predict Disease Severity or Progression in Emphysema

Rationale: Though matrix metalloproteinases (MMPs) are critical in the pathogenesis of COPD, their utility as a disease biomarker remains uncertain. This study aimed to determine whether bronchoalveolar lavage (BALF) or plasma MMP measurements correlated with disease severity or functional decline in emphysema. Methods: Enzyme-linked immunosorbent assay and luminex assays measured MMP-1, -9, -12 and tissue inhibitor of matrix metalloproteinase-1 in the BALF and plasma of non-smokers, smokers with normal lung function and moderate-to-severe emphysema subjects. In the cohort of 101 emphysema subjects correlative analyses were done to determine if MMP or TIMP-1 levels were associated with key disease parameters or change in lung function over an 18-month time period. Main Results: Compared to non-smoking controls, MMP and TIMP-1 BALF levels were significantly elevated in the emphysema cohort. Though MMP-1 was elevated in both the normal smoker and emphysema groups, collagenase activity was only increased in the emphysema subjects. In contrast to BALF, plasma MMP-9 and TIMP-1 levels were actually decreased in the emphysema cohort compared to the control groups. Both in the BALF and plasma, MMP and TIMP-1 measurements in the emphysema subjects did not correlate with important disease parameters and were not predictive of subsequent functional decline. Conclusions: MMPs are altered in the BALF and plasma of emphysema; however, the changes in MMPs correlate poorly with parameters of disease intensity or progression. Though MMPs are pivotal in the pathogenesis of COPD, these findings suggest that measuring MMPs will have limited utility as a prognostic marker in this disease. © 2013 D'Armiento et al

The SNAPSHOT study protocol : SNAcking, Physical activity, Self-regulation, and Heart rate Over Time

Peer reviewedPublisher PD

Synthesis of ‘unfeasible’ zeolites

R.E.M. thanks the Royal Society and the E.P.S.R.C. (Grants EP/L014475/1, EP/K025112/1 and EP/K005499/1) for funding work in this area. J.Č. and P.N. acknowledge the Czech Science Foundation for the project of the Centre of Excellence (P106/12/G015) and the European Union Seventh Framework Programme (FP7/ 2007-­‐2013) under grant agreement n°604307. The research leading to these results has received funding from the European Union Seventh Framework Programme under Grant Agreement 312483 – ESTEEM2 (Integrated Infrastructure Initiative–I3). We thank Professor Wuzong Zhou and Dr. Fengjiao Yu for their expertise in TEM and Daniel Dawson for help with NMR.Zeolites are porous aluminosilicate materials that have found applications in many different technologies. However, although simulations suggest that there are millions of possible zeolite topologies, only a little over 200 zeolite frameworks of all compositions are currently known, of which about 50 are pure silica materials. This is known as the zeolite conundrum - why have only so few of all the possible structures been made? Several criteria have been formulated to explain why most zeolites are unfeasible synthesis targets. Here we demonstrate the synthesis of two such 'unfeasible' zeolites, IPC-9 and IPC-10, through the assembly-disassembly-organization-reassembly mechanism. These new high-silica zeolites have rare characteristics, such as windows that comprise odd-membered rings. Their synthesis opens up the possibility of preparing other zeolites that have not been accessible by traditional solvothermal synthetic methods. We envisage that these findings may lead to a step change in the number and types of zeolites available for future applications.PostprintPeer reviewe