Results 71 to 80 of about 6,349 (218)

Completions of uniform convergence spaces [PDF]

Proceedings of the American Mathematical Society, 1971
H. J. Biesterfeldt has shown that a uniform convergence space which satisfies the completion axiom has a completion. In the present paper, we show that every uniform convergence space has a completion. Furthermore, if the uniform convergence space is Hausdorff and satisfies the completion axiom, then it has a Hausdorff completion, which reduces to the ...
openaire   +2 more sources

Functional Connectivity Linked to Cognitive Recovery After Minor Stroke

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Patients with minor stroke exhibit slowed processing speed and generalized alterations in functional connectivity involving frontoparietal cortex (FPC). The pattern of connectivity evolves over time. In this study, we examine the relationship of functional connectivity patterns to cognitive performance, to determine ...
Vrishab Commuri, Isabella Dallasta, Ciaran Stone, Sophia Girgenti, Neda Gould, Rafael H. Llinas, Jonathan Z. Simon, Elisabeth Breese Marsh   +7 more
wiley   +1 more source

A Machine Proof of the Filter-Method Construction for Real Numbers

Mathematics
This paper presents a machine verification of a real number theory where real numbers are constructed using concepts related to filters. The theory encompasses a special filter, namely the non-principal arithmetical ultrafilter whose existence can be ...
Guowei Dou, Wensheng Yu
doaj   +1 more source

A hyperspace for convergence spaces [PDF]

Proceedings of the American Mathematical Society, 1973
The purpose of this note is to introduce a convergence structure h ( t ) h(t) on the collection C ( E ) C(E) of nonempty, compact subsets of a Hausdorff convergence space (E, t). It is shown that if (E, t) is topological, then h (
openaire   +2 more sources

Super‐Refractory Status Epilepticus (SRSE) in a Patient With Compound Heterozygous OPA1 Variants: Case Report and Literature Review

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Super‐Refractory Status Epilepticus (SRSE) is a rare, life‐threatening neurological emergency with unclear etiology in many cases. Mitochondrial dysfunction, often due to disease‐causing genetic variants, is increasingly recognized as a cause, with each gene producing distinct pathophysiological mechanisms.
Pouria Mohammadi, Lara Basovic, Christopher Michael McGraw   +2 more
wiley   +1 more source

Unraveling the Molecular Mechanisms of Glioma Recurrence: A Study Integrating Single‐Cell and Spatial Transcriptomics

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Glioma recurrence severely impacts patient prognosis, with current treatments showing limited efficacy. Traditional methods struggle to analyze recurrence mechanisms due to challenges in assessing tumor heterogeneity, spatial dynamics, and gene networks.
Lei Qiu, Yinjiao Fei, Jiaxuan Ding, Kexin Shi, Jinyan Luo, Yuchen Zhu, Xingjian Sun, Gefei Jiang, Yuandong Cao, Weilin Xu, Shu Zhou   +10 more
wiley   +1 more source

p-topological and p-regular: dual notions in convergence theory

International Journal of Mathematics and Mathematical Sciences, 1999
The natural duality between “topological” and “regular,” both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space.
Scott A. Wilde, D. C. Kent
doaj   +1 more source

Paranorm I-convergent sequence spaces

Mathematica Slovaca, 2009
Abstract In this article we introduced the sequence spaces c I(p), c 0I(p), m I(p) and m 0I(p) for p = (p k), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces.
Tripathy, Binod Chandra, Hazarika, Bipan
openaire   +2 more sources

Impact of Asymptomatic Intracranial Hemorrhage on Outcome After Endovascular Stroke Treatment

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Background Endovascular treatment (EVT) achieves high rates of recanalization in acute large‐vessel occlusion (LVO) stroke, but functional recovery remains heterogeneous. While symptomatic intracranial hemorrhage (sICH) has been well studied, the prognostic impact of asymptomatic intracranial hemorrhage (aICH) after EVT is less certain ...
Shihai Yang, Chengsong Yue, Zhuang Li, Xiaolei Shi, Haoxuan Zhu, Jie Yang, Linyu Li, Jiaxing Song, Shitao Fan, Gaoming Li, Wenzhe Sun, Zhixian Ye, Jiacheng Huang, Dahong Yang, Jinfu Ma, Xu Xu, Zhixi Wang, Lilan Wang, Guojian Liu, Fengli Li, Changwei Guo, Li Qi, Wenjie Zi   +22 more
wiley   +1 more source

A Rocq-Based Formalization of Hilbert’s Geometry: Building a Reusable Foundation for 3D Perpendicularity Theory and Verification

Mathematical and Computational Applications
Hilbert’s axiom system for geometry is a landmark in formal methods. This paper presents a complete formalization of spatial perpendicularity—a theory not fully developed in Hilbert’s original work—using the Rocq proof assistant.
Qimeng Zhang, Wensheng Yu
doaj   +1 more source