The classical density topology is derived from the Lebesgue density points of Lebesgue measurable sets. Wilczynski proposed a more general scheme for defining density points. It turns out that his scheme works in the category sense in addition to the measure-theoretic one. The sets of density points necessitate some properties of the operator of density points. Such an operator is named the lower density operator. In this theme, we introduce lower density soft operators on (abstract) chargeable soft spaces along with their basic properties. Among others, we show that each lower density soft operator defines a system of parametric lower density operators. Then, we study density soft topologies, the soft topologies generated by lower density soft operators. The main attributes and topological properties of density soft topologies are analyzed. We finalize this work by demonstrating several characterizations of (simple) soft density topologies. In particular, we prove that in density soft topologies, the Borel soft -algebra coincides with the soft -algebra of soft sets with the Baire property.
Download full-text PDF |
Source |
---|---|
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11647939 | PMC |
http://dx.doi.org/10.1016/j.heliyon.2024.e35280 | DOI Listing |
Sci Adv
December 2024
Beijing Key Laboratory of Micro-Nano Energy and Sensor, Center for High-Entropy Energy and Systems, Beijing Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 101400, P. R. China.
Tissue imaging is usually captured by hospital-based nuclear magnetic resonance. Here, we present a wearable triboelectric impedance tomography (TIT) system for noninvasive imaging of various biological tissues. The imaging mechanism relies on the obtained impedance information from the different soft human tissues.
View Article and Find Full Text PDFJ Control Release
December 2024
Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway.
The delivery of nanoparticles to tumors has been shown preclinically to be improved by microbubble-mediated ultrasound. However, the mechanisms and biological effects not fully understood. In this study, we explored the influence of the tumor microenvironment on nanoparticle uptake and microdistribution both with and without ultrasound and microbubble treatment.
View Article and Find Full Text PDFSoft Matter
December 2024
Federal Research Center for Chemical Physics, Kosygina Street, 4 Building 1, Moscow 119991, Russian Federation.
Redox-active polymer gels are promising materials for various applications, such as energy conversion and storage systems, organic electronics, soft-robotics, sensors and others. This is in part due to the remarkable structural tunability of these materials. The gel may adopt different conformations depending on the crosslinking density, solvent temperature and other conditions.
View Article and Find Full Text PDFAdv Mater
December 2024
Dynamic Colloidal Systems Laboratory, Department of Chemistry, Indian Institute of Technology, Roorkee, 247667, India.
The design of chemomechanical self-oscillators, which execute oscillations in the presence of constant stimuli lacking periodicity, is a step toward the development of autonomous and interactive soft robotic systems. This work presents a simple design of prolonged chemomechanical oscillatory movement in a microgel system capable of buoyant motility within stratified chemical media containing spatially localized sinking and floating stimuli. Three design elements are developed: a stimuli-responsive membranized calcium alginate microgel, a Percoll density gradient for providing stratified antagonistic chemical media, and transduction of microgel particle size actuation into buoyant motility via membrane-mediated displacement of the Percoll media.
View Article and Find Full Text PDFBMC Med Imaging
December 2024
Department of Radiology, The Second Hospital, Dalian Medical University, 467 Zhongshan Rd, Dalian, 116023, China.
Background: The vascular endothelial growth factor (VEGF) and microvessel density (MVD) have been widely employed as angiogenesis indicators in the diagnosis and treatment of soft tissue sarcomas. While diffusion kurtosis imaging (DKI) and proton magnetic resonance spectroscopy (H-MRS) imaging hold potential in assessing angiogenesis in other tumors, their reliability in correlating with angiogenesis in soft tissue sarcomas remains uncertain, contingent upon accurately acquiring the region of interest (ROI).
Methods: 23 patients with soft tissue sarcomas (STSs) confirmed by pathology were selected, underwent DKI and H-MRS at 3.
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!