Characteristic approximation properties of quadratic irrationals

Some characteristic approximation properties of quadratic irrationals are studied in this paper. It is shown that the limit points of the sequence δn form a subset C(x), and D(x) can be generated from C(x) in a relatively simple way. Another proof of Lekkerkerker's theorem is given using relations between δn−1, δn, δn+1 which are independent of x and n

On Kaluza's sign criterion for reciprocal power series

T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzy\.z is applied.Comment: 13 page

Fascial tissue research in sports medicine: from molecules to tissue adaptation, injury and diagnostics.

The fascial system builds a three-dimensional continuum of soft, collagen-containing, loose and dense fibrous connective tissue that permeates the body and enables all body systems to operate in an integrated manner. Injuries to the fascial system cause a significant loss of performance in recreational exercise as well as high-performance sports, and could have a potential role in the development and perpetuation of musculoskeletal disorders, including lower back pain. Fascial tissues deserve more detailed attention in the field of sports medicine. A better understanding of their adaptation dynamics to mechanical loading as well as to biochemical conditions promises valuable improvements in terms of injury prevention, athletic performance and sports-related rehabilitation. This consensus statement reflects the state of knowledge regarding the role of fascial tissues in the discipline of sports medicine. It aims to (1) provide an overview of the contemporary state of knowledge regarding the fascial system from the microlevel (molecular and cellular responses) to the macrolevel (mechanical properties), (2) summarise the responses of the fascial system to altered loading (physical exercise), to injury and other physiological challenges including ageing, (3) outline the methods available to study the fascial system, and (4) highlight the contemporary view of interventions that target fascial tissue in sport and exercise medicine. Advancing this field will require a coordinated effort of researchers and clinicians combining mechanobiology, exercise physiology and improved assessment technologies

Hypokalemic Periodic Paralysis: a case report and review of the literature

Hypokalemic Periodic Paralysis is one form of Periodic Paralysis, a rare group of disorders that can cause of sudden onset weakness. A case of a 29 year old male is presented here. The patient presented with sudden onset paralysis of his extremities. Laboratory evaluation revealed a markedly low potassium level. The patient's paralysis resolved upon repletion of his low potassium and he was discharged with no neurologic deficits. An association with thyroid disease is well established and further workup revealed Grave's disease in this patient. Although rare, Periodic Paralysis must differentiated from other causes of weakness and paralysis so that the proper treatment can be initiated quickly

Strong approximation of lacunary series with random gaps

We investigate the asymptotic behavior of sums (Formula presented.), where f is a mean zero, smooth periodic function on (Formula presented.) and (Formula presented.) is a random sequence such that the gaps (Formula presented.) are i.i.d. Our result shows that, in contrast to the classical Salem–Zygmund theory, the almost sure behavior of lacunary series with random gaps can be described very precisely without any assumption on the size of the gaps. © 2017 Springer-Verlag Wie

In-situ observations of young contrails – overview and selected results from the CONCERT campaign

Lineshaped contrails were detected with the research aircraft Falcon during the CONCERT – CONtrail and Cirrus ExpeRimenT – campaign in October/November 2008. The Falcon was equipped with a set of instruments to measure the particle size distribution, shape, extinction and chemical composition as well as trace gas mixing ratios of sulfur dioxide (SO<sub>2</sub>), reactive nitrogen and halogen species (NO, NO<sub>y</sub>, HNO<sub>3</sub>, HONO, HCl), ozone (O<sub>3</sub>) and carbon monoxide (CO). During 12 mission flights over Europe, numerous contrails, cirrus clouds and a volcanic aerosol layer were probed at altitudes between 8.5 and 11.6 km and at temperatures above 213 K. 22 contrails from 11 different aircraft were observed near and below ice saturation. The observed NO mixing ratios, ice crystal and soot number densities are compared to a process based contrail model. On 19 November 2008 the contrail from a CRJ-2 aircraft was penetrated in 10.1 km altitude at a temperature of 221 K. The contrail had mean ice crystal number densities of 125 cm<sup>−3</sup> with effective radii <i>r</i><sub>eff</sub> of 2.6 μm. The presence of particles with <i>r</i>>50 μm in the less than 2 min old contrail suggests that natural cirrus crystals were entrained in the contrail. Mean HONO/NO (HONO/NO<sub>y</sub>) ratios of 0.037 (0.024) and the fuel sulfur conversion efficiency to H<sub>2</sub>SO<sub>4</sub> (ε<sub><i>S</i>↓</sub>) of 2.9 % observed in the CRJ-2 contrail are in the range of previous measurements in the gaseous aircraft exhaust. On 31 October 2010 aviation NO emissions could have contributed by more than 40% to the regional scale NO levels in the mid-latitude lowest stratosphere. The CONCERT observations help to better quantify the climate impact from contrails and will be used to investigate the chemical processing of trace gases on contrails

Channelopathies in Cav1.1, Cav1.3, and Cav1.4 voltage-gated L-type Ca2+ channels

Voltage-gated Ca2+ channels couple membrane depolarization to Ca2+-dependent intracellular signaling events. This is achieved by mediating Ca2+ ion influx or by direct conformational coupling to intracellular Ca2+ release channels. The family of Cav1 channels, also termed L-type Ca2+ channels (LTCCs), is uniquely sensitive to organic Ca2+ channel blockers and expressed in many electrically excitable tissues. In this review, we summarize the role of LTCCs for human diseases caused by genetic Ca2+ channel defects (channelopathies). LTCC dysfunction can result from structural aberrations within their pore-forming α1 subunits causing hypokalemic periodic paralysis and malignant hyperthermia sensitivity (Cav1.1 α1), incomplete congenital stationary night blindness (CSNB2; Cav1.4 α1), and Timothy syndrome (Cav1.2 α1; reviewed separately in this issue). Cav1.3 α1 mutations have not been reported yet in humans, but channel loss of function would likely affect sinoatrial node function and hearing. Studies in mice revealed that LTCCs indirectly also contribute to neurological symptoms in Ca2+ channelopathies affecting non-LTCCs, such as Cav2.1 α1 in tottering mice. Ca2+ channelopathies provide exciting disease-related molecular detail that led to important novel insight not only into disease pathophysiology but also to mechanisms of channel function

Working conditions and Work-Family Conflict in German hospital physicians: psychosocial and organisational predictors and consequences

<p>Abstract</p> <p>Background</p> <p>Germany currently experiences a situation of major physician attrition. The incompatibility between work and family has been discussed as one of the major reasons for the increasing departure of German physicians for non-clinical occupations or abroad. This study investigates predictors for one particular direction of Work-Family Conflict – namely work interfering with family conflict (WIF) – which are located within the psychosocial work environment or work organisation of hospital physicians. Furthermore, effects of WIF on the individual physicians' physical and mental health were examined. Analyses were performed with an emphasis on gender differences. Comparisons with the general German population were made.</p> <p>Methods</p> <p>Data were collected by questionnaires as part of a study on <it>Psychosocial work hazards and strains of German hospital physicians </it>during April–July 2005. Two hundred and ninety-six hospital physicians (response rate 38.9%) participated in the survey. The Copenhagen Psychosocial Questionnaire (COPSOQ), work interfering with family conflict scale (WIF), and hospital-specific single items on work organisation were used to assess WIF, its predictors, and consequences.</p> <p>Results</p> <p>German hospital physicians reported elevated levels of WIF (mean = 74) compared to the general German population (mean = 45, <it>p </it>< .01). No significant gender difference was found. Predictors for the WIF were lower age, high quantitative demands at work, elevated number of days at work despite own illness, and consequences of short-notice changes in the duty roster. Good sense of community at work was a protective factor. Compared to the general German population, we observed a significant higher level of quantitative work demands among hospital physicians (mean = 73 vs. mean = 57, <it>p </it>< .01). High values of WIF were significantly correlated to higher rates of personal burnout, behavioural and cognitive stress symptoms, and the intention to leave the job. In contrast, low levels of WIF predicted higher job satisfaction, better self-judged general health status, better work ability, and higher satisfaction with life in general. Compared to the German general population, physicians showed significantly higher levels of individual stress and quality of life as well as lower levels for well-being. This has to be judged as an alerting finding regarding the state of physicians' health.</p> <p>Conclusion</p> <p>In our study, work interfering with family conflict (WIF) as part of Work-Family Conflict (WFC) was highly prevalent among German hospital physicians. Factors of work organisation as well as factors of interpersonal relations at work were identified as significant predictors for WIF. Some of these predictors are accessible to alteration by improving work organisation in hospitals.</p