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

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

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

Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets

Frustration refers to competition between different interactions that cannot be simultaneously satisfied, a familiar feature in many magnetic solids. Strong frustration results in highly degenerate ground states, and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism are characterizing the fluctuating spin-liquid regime and determining the mechanism of eventual order at lower temperature. Here, we study a model of a diamond lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration a massive ground state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional ``spiral surface'' in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomena called order-by-disorder. A broad ``spiral spin-liquid'' regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed via spin correlations. We discuss the agreement between these predictions and the well characterized spinel MnSc2S4

Eosinophil and T Cell Markers Predict Functional Decline in COPD Patients

BACKGROUND. The major marker utilized to monitor COPD patients is forced expiratory volume in one second (FEV1). However, asingle measurement of FEV1 cannot reliably predict subsequent decline. Recent studies indicate that T lymphocytes and eosinophils are important determinants of disease stability in COPD. We therefore measured cytokine levels in the lung lavage fluid and plasma of COPD patients in order to determine if the levels of T cell or eosinophil related cytokines were predictive of the future course of the disease. METHODS. Baseline lung lavage and plasma samples were collected from COPD subjects with moderately severe airway obstruction and emphysematous changes on chest CT. The study participants were former smokers who had not had a disease exacerbation within the past six months or used steroids within the past two months. Those subjects who demonstrated stable disease over the following six months (ΔFEV1 % predicted = 4.7 ± 7.2; N = 34) were retrospectively compared with study participants who experienced a rapid decline in lung function (ΔFEV1 % predicted = -16.0 ± 6.0; N = 16) during the same time period and with normal controls (N = 11). Plasma and lung lavage cytokines were measured from clinical samples using the Luminex multiplex kit which enabled the simultaneous measurement of several T cell and eosinophil related cytokines. RESULTS AND DISCUSSION. Stable COPD participants had significantly higher plasma IL-2 levels compared to participants with rapidly progressive COPD (p = 0.04). In contrast, plasma eotaxin-1 levels were significantly lower in stable COPD subjects compared to normal controls (p < 0.03). In addition, lung lavage eotaxin-1 levels were significantly higher in rapidly progressive COPD participants compared to both normal controls (p < 0.02) and stable COPD participants (p < 0.05). CONCLUSION. These findings indicate that IL-2 and eotaxin-1 levels may be important markers of disease stability in advanced emphysema patients. Prospective studies will need to confirm whether measuring IL-2 or eotaxin-1 can identify patients at risk for rapid disease progression.National Heart, Lung, and Blood Institute (NO1-HR-96140, NO1-HR-96141-001, NO1-HR-96144, NO1-HR-96143; NO1-HR-96145; NO1-HR-96142, R01HL086936-03); The Flight Attendant Medical Research Institute; the Jo-Ann F. LeBuhn Center for Chest Diseas