Irrational Numbers of Constant Type --- A New Characterization

We obtain a new characterization for irrational numbers of constant type -- defined as irrationals with bounded partial quotients in their continued fraction expansion. The result is essential in the formulation of stability criteria for orbits of quantum twist maps in a class of dynamical systems.Comment: 7 pages, AMS-LaTeX, with changes in reference

Hilfeplanung im Jugendamt Landkreis Hildesheim. Eine Arbeitsbroschüre für die Mitarbeiter_innen des Jugendamts-Erziehungshilfe im Landkreis Hildesheim

In der Zeit von Juli 2015 bis September 2017 fand in Zusammenarbeit des Jugendamts-Erziehungshilfe des Landkreises Hildesheim und der Universität Hildesheim das Projekt „Hilfeplanung in den Hilfen zur Erziehung“ statt. Das Projekt hatte zum Ziel, gemeinsame Standards in den einzelnen Arbeitsschritten der Hilfeplanung festzulegen. Die folgende Broschüre stellt die zentralen Diskussionen und Ergebnisse des Projekts dar und gibt somit einen Überblick über die im Projekt erarbeiteten und die für das Jugendamt-Erziehungshilfe konstitutiven Standards im Rahmen des Hilfeplanungsprozesses

Irrational Numbers of Constant Type — A New Characterization

Abstract. Given an irrational number α and a positive integer m, the distinct fractional parts of α, 2α, ·· ·,mα determine a partition of the interval [0, 1]. Defining dα(m) and d ′ α(m) to be the maximum and minimum lengths, respectively, of the subintervals of�the partition corresponding to the integer dα(m) m, it is shown that the sequence d ′ α (m) � ∞ is bounded if and only if α m=1 is of constant type. (The proof of this assertion is based on the continue

Hilfeplanung im Jugendamt Landkreis Hildesheim. Eine Arbeitsbroschüre für die Mitarbeiter_innen des Jugendamts-Erziehungshilfe im Landkreis Hildesheim

In der Zeit von Juli 2015 bis September 2017 fand in Zusammenarbeit des Jugendamts-Erziehungshilfe des Landkreises Hildesheim und der Universität Hildesheim das Projekt „Hilfeplanung in den Hilfen zur Erziehung“ statt. Das Projekt hatte zum Ziel, gemeinsame Standards in den einzelnen Arbeitsschritten der Hilfeplanung festzulegen. Die folgende Broschüre stellt die zentralen Diskussionen und Ergebnisse des Projekts dar und gibt somit einen Überblick über die im Projekt erarbeiteten und die für das Jugendamt-Erziehungshilfe konstitutiven Standards im Rahmen des Hilfeplanungsprozesses

Risk factors for executive dysfunction after subthalamic nucleus stimulation in Parkinson's disease

International audienceA slight decline in cognitive functions and especially in executive functioning after deep brain stimulation (DBS) of the nucleus subthalamicus (STN) in patients with Parkinson's disease (PD) has been described. This study evaluated baseline parameters that contribute to a deterioration of cognitive functioning after DBS. We analyzed data from the neuropsychological protocol in a randomized controlled study comparing DBS with best medical treatment (BMT). Change scores were calculated for the cognitive domains "global cognitive functioning," "memory," "working memory," "attention," and "executive function." These domain-specific change scores were correlated with previously defined preoperative parameters. Compared with the BMT group (63 patients), the STN-DBS group (60 patients) showed a significant decline only in the domain executive function 6 months after DBS, which was significantly correlated with age, levodopa-equivalence dosage (LED) and axial subscore of the UPDRS in the off-medication state at baseline. Multiple regression analysis showed that these three factors explained, however, only about 23% of the variance. Patients with higher age, higher baseline LED, and/or higher axial subscore of the UPDRS at baseline have an increased risk for worsening of executive function after STN-DBS. High scores of these factors might reflect an advanced stage of disease progression. As these baseline factors explained the variance of the change score executive function only to a minor proportion, other factors including the surgical procedure, the exact placement of the electrode or postsurgical management might be more relevant for a decline in executive functioning after STN-DBS

Neuropsychological and psychiatric changes after deep brain stimulation for Parkinson's disease: a randomised, multicentre study

International audienceBACKGROUND: Deep brain stimulation (DBS) of the subthalamic nucleus (STN) reduces motor symptoms in patients with Parkinson's disease (PD) and improves their quality of life; however, the effect of DBS on cognitive functions and its psychiatric side-effects are still controversial. To assess the neuropsychiatric consequences of DBS in patients with PD we did an ancillary protocol as part of a randomised study that compared DBS with the best medical treatment. METHODS: 156 patients with advanced Parkinson's disease and motor fluctuations were randomly assigned to have DBS of the STN or the best medical treatment for PD according to the German Society of Neurology guidelines. 123 patients had neuropsychological and psychiatric examinations to assess the changes between baseline and after 6 months. The primary outcome was the comparison of the effect of DBS with the best medical treatment on overall cognitive functioning (Mattis dementia rating scale). Secondary outcomes were the effects on executive function, depression, anxiety, psychiatric status, manic symptoms, and quality of life. Analysis was per protocol. The study is registered at ClinicalTrials.gov, number NCT00196911. FINDINGS: 60 patients were randomly assigned to receive STN-DBS and 63 patients to have best medical treatment. After 6 months, impairments were seen in executive function (difference of changes [DBS-best medical treatment] in verbal fluency [semantic] -4.50 points, 95% CI -8.07 to -0.93, Cohen's d=-;0.4; verbal fluency [phonemic] -3.06 points, -5.50 to -0.62, -0.5; Stroop 2 naming colour error rate -0.37 points, -0.73 to 0.00, -0.4; Stroop 3 word reading time -5.17 s, -8.82 to -1.52, -0.5; Stroop 4 colour naming time -13.00 s, -25.12 to -0.89, -0.4), irrespective of the improvement in quality of life (difference of changes in PDQ-39 10.16 points, 5.45 to 14.87, 0.6; SF-36 physical 16.55 points, 10.89 to 22.21, 0.9; SF-36 psychological 9.74 points, 2.18 to 17.29, 0.5). Anxiety was reduced in the DBS group compared with the medication group (difference of changes in Beck anxiety inventory 10.43 points, 6.08 to 14.78, 0.8). Ten patients in the DBS group and eight patients in the best medical treatment group had severe psychiatric adverse events. INTERPRETATION: DBS of the STN does not reduce overall cognition or affectivity, although there is a selective decrease in frontal cognitive functions and an improvement in anxiety in patients after the treatment. These changes do not affect improvements in quality of life. DBS of the STN is safe with respect to neuropsychological and psychiatric effects in carefully selected patients during a 6-month follow-up period. FUNDING: German Federal Ministry of Education and Research (01GI0201)