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

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

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

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

Remarks on the Cauchy functional equation and variations of it

This paper examines various aspects related to the Cauchy functional equation $f(x+y)=f(x)+f(y)$, a fundamental equation in the theory of functional equations. In particular, it considers its solvability and its stability relative to subsets of multi-dimensional Euclidean spaces and tori. Several new types of regularity conditions are introduced, such as a one in which a complex exponent of the unknown function is locally measurable. An initial value approach to analyzing this equation is considered too and it yields a few by-products, such as the existence of a non-constant real function having an uncountable set of periods which are linearly independent over the rationals. The analysis is extended to related equations such as the Jensen equation, the multiplicative Cauchy equation, and the Pexider equation. The paper also includes a rather comprehensive survey of the history of the Cauchy equation.Comment: To appear in Aequationes Mathematicae (important remark: the acknowledgments section in the official paper exists, but it appears before the appendix and not before the references as in the arXiv version); correction of a minor inaccuracy in Lemma 3.2 and the initial value proof of Theorem 2.1; a few small improvements in various sections; added thank

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Coping with stress in medical students: results of a randomized controlled trial using a mindfulness-based stress prevention training (MediMind) in Germany

BACKGROUND: High prevalence rates of psychological distress in medical training and later professional life indicate a need for prevention. Different types of intervention were shown to have good effects, but little is known about the relative efficacy of different types of stress management interventions, and methodological limitations have been reported. In order to overcome some of these limitations, the present study aimed at evaluating the effect of a specifically developed mindfulness-based stress prevention training for medical students (MediMind) on measures of distress, coping and psychological morbidity. METHODS: We report on a prospective randomized controlled trial with three study conditions: experimental treatment (MediMind), standard treatment (Autogenic Training) and a control group without treatment. The sample consisted of medical or dental students in the second or eighth semester. They completed self-report questionnaires at baseline, after the training and at one year follow-up. Distress (Trier Inventory for the Assessment of Chronic Stress, TICS) was assessed as the primary outcome and coping (Brief COPE) as a co-primary outcome. Effects on the psychological morbidity (Brief Symptom Inventory, BSI) as a secondary outcome were expected one year after the trainings. RESULTS: Initially, N = 183 students were randomly allocated to the study groups. At one year follow-up N = 80 could be included into the per-protocol analysis: MediMind (n =31), Autogenic Training (n = 32) and control group (n = 17). A selective drop-out for students who suffered more often from psychological symptoms was detected (p = .020). MANCOVA’s on TICS and Brief COPE revealed no significant interaction effects. On the BSI, a significant overall interaction effect became apparent (p = .002, η2partial = .382), but post hoc analyses were not significant. Means of the Global Severity Index (BSI) indicated that MediMind may contribute to a decrease in psychological morbidity. CONCLUSION: Due to the high and selective dropout rates, the results cannot be generalized and further research is necessary. Since the participation rate of the trainings was high, a need for further prevention programs is indicated. The study gives important suggestions on further implementation and evaluation of stress prevention in medical schools. TRIAL REGISTRATION: This trial is recorded at German Clinical Trials Register under the number DRKS00005354 (08.11.2013)