Comparison of electrohysterogram characteristics during uterine contraction and non-contraction during labor

Uterine contraction is one of the most important indication in the labor progression. Electrohysterogram (EHG) is a promising method for monitoring uterine contraction and discriminating efficient and inefficient contractions. This study aims to analyze the difference of EHG signals between two groups. EHG signals are recorded with abdominal electrodes from 20 pregnant women, including 10 in term labor group and 10 in non-labor group. Typical linear and nonlinear characteristics of EHG signals, including root mean square (RMS), peak frequency (PF), median frequency (MDF), mean frequency (MNF), parameters from wavelet decomposition (W4, W5) and time reversibility (Tr) are extracted. These characteristics are compared between contraction and non-contraction in term labor group and non-labor group. The result shows that RMS, W4 and W5 of contraction are significantly larger than non-contraction both within term labor group and between two groups (all p<;0.001). However, MDF and MNF are significantly smaller (all p<;0.05). Furthermore, all characteristics of non-contraction show no significant difference between two groups, except MNF. The variability of RMS, W4, W5 and Tr of contraction are significantly larger than non-contraction both within term labor group and between two groups (all p<;0.05, with p<;0.001 for W5 and Tr). However, the variability of MDF, PF and MNF are significantly smaller (all p<;0.05). Moreover, the variability of all characteristics of non-contraction shows no significant difference between two groups, except MNF. We have shown that characteristics of EHG signals and their variability during contraction are quite different from non-contraction. Therefore, it is feasible to separate uterine contractions and monitor uterine activity with EHG signals

C1,1C^{1,1}-rectifiability and Heintze-Karcher inequality on Sn+1\mathbf{S}^{n+1}

In this paper, by isometrically embedding $(\mathbf{S}^{n+1},g_{\mathbf{S}^{n+1}})$ into $\mathbf{R}^{n+2}$, and using nonlinear analysis on the codimension-2 graphs, we will show that the level sets of distance function from the boundary of any Borel set in sphere, are $C^{1,1}$-rectifiable. As a by-product, we establish a Heintze-Karcher inequality.Comment: 23 pages, 2 figure

Quantitative Alexandrov theorem for capillary hypersurfaces in the half-space

In this paper, we prove the quantitative version of the Alexandrov theorem for capillary hypersurfaces in the half-space. The proof is based on the quantitative analysis of the Montiel-Ros-type argument, carried out in the joint works with Wang-Xia \cites{JWXZ22-B,JWXZ23}. As by-products, we obtain new Michael-Simon-type inequality and Topping-type inequality for capillary hypersurfaces in the half-space.Comment: 49 pages, comments are welcome

Volume-constraint local energy-minimizing sets in a ball

In this paper, we prove a Poincar\'e inequality for any volume-constraint local energy-minimizing sets, provided its singular set is of Hausdorff dimension at most $n-3$. With this inequality, we prove that the only volume-constraint local energy-minimizing sets in the Euclidean unit ball, whose singular set is closed and of Hausdorff dimension at most $n-3$, are totally geodesic balls or spherical caps intersecting the unit sphere with constant contact angle; for stable sets in a wedge-shaped domain or in a half space, provided the same condition of the singular set, must be spherical. In particular, they are smooth.Comment: 35 pages, 2 figures; added some arguments on stable measure-theoretic capillary hyper surfaces in a half space or in a domain with planar boundaries in section 6; typos correcte

Capillary Schwarz symmetrization in the half-space

In this paper, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half-space. A key ingredient is a special anisotropic gauge, which enables us to transform the capillary symmetrization to the convex symmetrization introduced in \cite{AFT97}.Comment: 15 page

Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains

In this paper, we prove an optimal Heintze-Karcher-type inequality for anisotropic free boundary hypersurfaces in general convex domains. The equality is achieved for anisotropic free boundary Wulff shapes in a convex cone. As applications, we prove various Alexandrov-type theorems.Comment: 15 pages, 1 figur

Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces

In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the second part, we prove quantitative stability results for the Serrin-type partially overdetermined problem, as well as capillary almost constant mean curvature hypersurfaces in the half-space

A characterization of capillary spherical caps by a partially overdetermined problem in a half ball

In this note, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160, 2019. https://doi.org/10.1007/s00526-019-1603-3, and prove a rigidity result that characterizes capillary spherical caps in a half ball

Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space

In this paper, we show that any embedded capillary hypersurface in the half-space with anisotropic constant mean curvature is a truncated Wulff shape. This extends Wente's result \cite{Wente80} to the anisotropic case and He-Li-Ma-Ge's result \cite{HLMG09} to the capillary boundary case. The main ingredients in the proof are a new Heintze-Karcher inequality and a new Minkowski formula, which have their own inetrest.Comment: 16 page

Grassland Certification, Grazing Behavior, and Ecological Consequences: Evidence from Pastoral China

This paper investigates the effects of grassland certification reform on grassland quality and livestock output in China. Using remote sensing and household surveyed data, we found that the Normalized Difference Vegetation Index (NDVI) of our research area decreased by 9.37% after the implementation of the certification reform. Two potential mechanisms can be responsible for the tragic ecological consequences. The initial factor is the intensified grassland fragmentation. Contiguous large-scale grasslands were divided into small-scale fragmented grasslands after the certification reform, resulting in increased grazing intensity. The imperfection of grassland use rights could be the second potential mechanism. Herders have transferred their grazing intensity from their personally owned grazing area to the leased grazing field due to the volatility of grassland tenure and the inadequacy of agreements. Conversely, the aggregate output of villages increased by 15.5%, and the grassland rental markets became more efficient. We contend that property rights reforms have increased the vulnerability of grassland ecology and the livelihoods of herders despite the anticipated enhancement in output resulting from the reforms. These findings suggest that the trade-off between grassland sustainability and livestock productivity capacity led by the grassland property rights reform has impeded the development of more comprehensive strategies to withstand grassland degradation