Tobias Wang | Searcharxiv

arXiv2026

The Usual Square Function on Weakly Flat Sets

We study the usual square function estimate associated with the Cauchy single-layer kernel in the plane, without assuming Ahlfors-David regularity. We prove that a finite Radon measure with positive and finite upper density is rectifiable if it satisfies the usual square function estimate and a weak flatness condition. We also prove that, under the same finiteness and density hypotheses, the weak flatness condition follows when the support is contained in a locally two-sided NTA curve. As a corollary, rectifiability follows when the support is contained in a quasicircle.

math.CA↗

arXiv2014

Superparamagnetic iron oxide polyacrylic acid coated γ-Fe2O3 nanoparticles does not affect kidney function but causes acute effect on the cardiovascular function in healthy mice

This study describes the distribution of intravenously injected polyacrylic acid (PAA) coated γ-Fe2O3 NPs (10 mg kg-1) at the organ, cellular and subcellular levels in healthy BALB/cJ mice and in parallel addresses the effects of NP injection on kidney function, blood pressure and vascular contractility. Magnetic resonance imaging (MRI) and transmission electron microscopy (TEM) showed accumulation of NPs in the liver within 1h after intravenous infusion, accommodated by intracellular uptake in endothelial and Kupffer cells with subsequent intracellular uptake in renal cells, particularly the cytoplasm of the proximal tubule, in podocytes and mesangial cells. The renofunctional effects of NPs were evaluated by arterial acid-base status and measurements of glomerular filtration rate (GFR) after instrumentation with chronically indwelling catheters. Arterial pH was 7.46 and 7.41 in mice 0.5 h after injections of saline or NP, and did not change over the next 12h. In addition, the injections of NP did not affect arterial PCO2 or [HCO3-] either. Twenty-four and 96h after NP injections, the GFR averaged 11.0 and 13.0 ml min-1 g-1, respectively, values which were statistically comparable with controls (14.0 and 14.0 ml min-1 g-1). Mean arterial blood pressure (MAP) decreased 12-24h after NP injections (111 vs 123 min-1) associated with a decreased contractility of small mesenteric arteries revealed by myography to characterise endothelial function. In conclusion, our study demonstrates that accumulation of superparamagnetic iron oxide nanoparticles does not affect kidney function in healthy mice but temporarily decreases blood pressure.

physics.med-ph↗