SPACES OF FIBONACCI DIFFERENCE IDEAL CONVERGENT SEQUENCES IN RANDOM 2–NORMED SPACE

In this article, by using Fibonacci difference matrix  and the notion of ideal convergence of sequences in random 2–normed space, we introduce some new spaces of Fibonacci difference ideal convergent sequences with respect to random -norm and study some inclusion relations, topological and algebraic properties of these spaces.

Strategic lacunes and their relationship to cognitive impairment in cerebral small vessel disease.

Objectives: Lacunes are an important disease feature of cerebral small vessel disease (SVD) but their relationship to cognitive impairment is not fully understood. To investigate this we determined (1) the relationship between lacune count and total lacune volume with cognition, (2) the spatial distribution of lacunes and the cognitive impact of lacune location, and (3) the whole brain anatomical covariance associated with these strategically located regions of lacune damage. Methods: One hundred and twenty one patients with symptomatic lacunar stroke and radiological leukoaraiosis were recruited and multimodal MRI and neuropsychological data acquired. Lacunes were mapped semi-automatically and their volume calculated. Lacune location was automatically determined by projection onto atlases, including an atlas which segments the thalamus based on its connectivity to the cortex. Lacune locations were correlated with neuropsychological results. Voxel based morphometry was used to create anatomical covariance maps for these ‘strategic’ regions. Results: Lacune number and lacune volume were positively associated with worse executive function (number p < 0.001; volume p < 0.001) and processing speed (number p < 0.001; volume p < 0.001). Thalamic lacunes, particularly those in regions with connectivity to the prefrontal cortex, were associated with impaired processing speed (Bonferroni corrected p = 0.016). Regions of associated anatomical covariance included the medial prefrontal, orbitofrontal, anterior insular cortex and the striatum. Conclusion: Lacunes are important predictors of cognitive impairment in SVD. We highlight the importance of spatial distribution, particularly of anteromedial thalamic lacunes which are associated with impaired information processing speed and may mediate cognitive impairment via disruption of connectivity to the prefrontal cortex

Three-year follow-up and event rates in the international REduction of Atherothrombosis for Continued Health Registry

To determine 3-year event rates in outpatients with vascular disease enrolled in the REduction of Atherothrombosis for Continued Health (REACH) Registry. Methods and results REACH enrolled 67 888 outpatients with atherothrombosis [ established coronary artery disease (CAD), cerebrovascutar disease, or peripheral arterial disease (PAD)], or with at least three atherothrombotic risk factors, from 44 countries . Among the 55 499 patients at baseline with symptomatic disease, 39 675 were eligible for 3-year follow-up, and 32 247 had data available (81% retention rate). Among the symptomatic patients at 3 years, 92% were taking an antithrombotic agent, 91% an anti hypertensive, and 76% were on Upid- lowering therapy. For myocardial infarction (Ml)/ stroke/vascutar death, 1 - and 3-year event rates for all patients were 4.2 and 11.0%, respectively. Event rates (MI/ stroke/vascutar death) were significantly higher for patients with symptomatic disease vs. those with risk factors only at 1 year (4.7 vs. 2.3%, P < 0.001) and at 3 years (12.0 vs. 6.0%, P < 0.001). One and 3-year rates of MI /stroke/vascular cleath/ rehospitatization were 14.4 and 28.4 %, respectively, for patients with symptomatic disease. Rehospitalization for a vascular event other than Mi/ stroke/ vascular death was common at 3 years (19.0% overall; 33.6% for PAD ; 23.0% for CAD). For patients with symptomatic vascular disease in one vascular bed vs. multiple vascular beds, 3-year event rates for MI/stroke/ vascular death/ rehospitalization were 25.5 vs. 40.5% (P < 0.001). Conclusion Despite contemporary therapy, outpatients with symptomatic atherothrombotic vascular disease experience high rates of recurrent vascular events and rehospitalizations

Insights into the formation mechanism of two-dimensional lead halide nanostructures

We present a colloidal synthesis strategy for lead halide nanosheets with a thickness of far below 100 nm. Due to the layered structure and the synthesis parameters the crystals of PbI2 are initially composed of many polytypes. We propose a mechanism which gives insight into the chemical process of the PbI2 formation. Further, we found that the crystal structure changes with increasing reaction temperature or by performing the synthesis for longer time periods changing for the final 2H structure. In addition, we demonstrate a route to prepare nanosheets of lead bromide as well as lead chloride in a similar way. Lead halides can be used as a detector material for high-energy photons including gamma and X-rays