An Engel condition with two generalized derivations in prime rings
COMMUNICATIONS IN ALGEBRA
Authors: Liu, Cheng-Kai
Abstract
Let R be a noncommutative prime ring with extended centroid C and maximal right ring of quotients Q. Let I be a nonzero ideal of R, and let g, h be two generalized derivations of R. Suppose that [g(x(m))x(n) = x(s)h(x(t)), x(r)](k) = 0 for all x is an element of I, where m, n, s, t, r, k are fixed positive integers. Then, one of the following conditions holds: 1. there exist alpha, beta is an element of C such that g(x) = alpha x and h(x) = beta x for all x is an element of R; 2. m = s, n = t and there exist a is an element of Q and alpha is an element of C such that g(x) = xa and h(x) = (a + alpha)x for all x is an element of R; 3. C is a finite field, R = Q similar or equal to M-l(C), the l x l matrix ring over C for some integer l >= 2 and there exist a, u is an element of R such that g(x) = xa and h(x) = ux for all x is an element of R.
Deep brain stimulation effects on lower urinary tract function: Systematic review and meta-analysis
PARKINSONISM & RELATED DISORDERS
Authors: Joerg, Elisa; Sartori, Andrea M.; Hofer, Anna-Sophie; Baumann, Christian R.; Kessler, Thomas M.
Abstract
Introduction: While efficacy of deep brain stimulation for motor symptoms of neurological disorders is well accepted, its effects on the autonomic system remain controversial. We aimed to systematically assess all available evidence of deep brain stimulation effects on lower urinary tract function. Methods: This systematic review was performed according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Studies were identified by electronic search of Cochrane Central Register of Controlled Trials, Embase, Medline, Scopus, and Web of Science (last search July 12, 2019) and by screening of reference lists and reviews. Results: After screening 577 articles, we included 29 studies enrolling a total of 1293 patients. Deep brain stimulation of the globus pallidus internus (GPi), pedunculopontine nucleus (PPN), and subthalamic nucleus (STN) had an inhibitory effect on detrusor function, while deep brain stimulation of the ventral intermediate nucleus of the thalamus (VIM) showed an excitatory effect. In the meta-analysis, deep brain stimulation of the STN led to a significant increase in maximum bladder capacity (mean difference 124 mL, 95% confidence interval 60-187 mL, p = 0.0001) but had no clinically relevant effects on other urodynamic parameters. Adverse events (reported in thirteen studies) were most commonly respiratory issues, postural instability, and dysphagia. Risk of bias and confounding was relatively low. Conclusions: Deep brain stimulation does not impair lower urinary tract function and might even have beneficial effects. This needs to be considered in the deep brain stimulation decision-making process helping to encourage and to reassure prospective patients.