Carath\'eodory metric on some generalized Teichm\"uller spaces

We study the Carath\'eodory metric on some generalized Teichm\"uller spaces. Earle showed that the Carath\'eodory metric is complete on any Teichmu\"uller space. Miyachi extended this result for Asymptotic Teichm\"uller spaces. We study the completeness of the Carath\'eodory metric on product Teichm\"uller spaces and on the Teichm\"uller space of a closed set in the Riemann sphere.Comment: 13 page

On complex extension of the Liouville map

The Liouville map assigns to each point in the Teichm\"uller space a positive Radon measure on the space of geodesics of the universal covering of the base Riemann surface. This construction which was introduced by Bonahon is valid for both finite and infinite Riemann surfaces. Bonahon and S\"ozen proved that the Liouville map is differentiable for closed Riemann surfaces and the second author extended this result to all other Riemann surfaces. Otal proved that the Liouville map is real analytic using an idea from the geometric analysis. The purpose of this note is to give another proof of Otal's result using a complex analysis approach.Comment: 15 pages, Lemma 6 adde

Differentiability of the Liouville Map via Geodesic Currents

For a conformally hyperbolic Riemann surface, the Teichmüller space is the space of quasiconformal maps factored by an equivalence relation, and it is a complex Banach manifold. The space of geodesic currents endowed with the uniform weak* topology is a subset of a Fréchet space of Hölder distributions. We introduce an appropriate topology on the space of Hölder distributions and this new topology coincides with the uniform weak* topology on the space of geodesic currents. The Liouville map of the Teichmüller space becomes differentiable in the Fréchet sense. In particular, the derivative of Liouville currents exists and belongs to the space of Hölder distributions, and the tangent map of the Liouville map is continuous and linear. The elements of the Teichmüller space can be represented by earthquake maps. Since an earthquake path is a differentiable path in the Teichmüller space, then the image of an earthquake path under the Liouville map is a differentiable path in the space of Hölder distributions. We compute the image of the tangent vector to an earthquake path in the space of Hölder distributions

B7-H4 Expression Is Associated with Tumor Progression and Prognosis in Patients with Osteosarcoma

Increasing evidences have demonstrated that B7-H4 is associated with tumor development and prognosis. However, the clinical significance of B7-H4 expression in human osteosarcoma (OS) remains unclear. The aim of present study was to examine the B7-H4 expression and to explore its contribution in OS. B7-H4 expression in OS tissues was examined by immunohistochemistry. Soluble B7-H4 (sB7-H4) levels in blood were examined by ELISA. The association of B7-H4 expression with clinicopathological factors or prognosis was statistically analyzed. Our findings demonstrated that B7-H4 expression in OS tissues was significantly higher than those in paired normal bone tissues (P<0.001). sB7-H4 level in OS serum samples was significantly higher than that in healthy controls (P=0.005). High B7-H4 expression in tissues and sB7-H4 level were both correlated with advanced tumor stage (P<0.001, P=0.017, resp.) and distant metastasis (P=0.034, P=0.021, resp.). Additionally, high B7-H4 expression or serum sB7-H4 levels were significantly related to poor overall survival (P=0.028, P=0.005, resp.). B7-H4 in tissues and serum samples were an independent factor for affecting the survival time of OS patients (P=0.004, P=0.041, resp.). Collectively, our data suggest that the evaluation of B7-H4 expression in tissues and blood is a useful tool for predicting the progression of osteosarcoma and prognosis

Carathéodory metric on some generalized Teichmüller spaces

We study the Carathéodory metric on some generalized Teichmüller spaces. Our paper is especially inspired by the papers by Earle (1974) and Miyachi (2006). Earle (1974) showed that the Carathéodory metric is complete on any Teichmüller space. Miyachi (2006) extended this result for asymptotic Teichmüller spaces. We study the completeness of the Carathéodory metric on product Teichmüller spaces and on the Teichmüller space of a closed set in the Riemann sphere

Roles and therapeutic potential of different extracellular vesicle subtypes on traumatic brain injury

Abstract Traumatic brain injury (TBI) is a leading cause of injury-related disability and death around the world, but the clinical stratification, diagnosis, and treatment of complex TBI are limited. Due to their unique properties, extracellular vesicles (EVs) are emerging candidates for being biomarkers of traumatic brain injury as well as serving as potential therapeutic targets. However, the effects of different extracellular vesicle subtypes on the pathophysiology of traumatic brain injury are very different, or potentially even opposite. Before extracellular vesicles can be used as targets for TBI therapy, it is necessary to classify different extracellular vesicle subtypes according to their functions to clarify different strategies for EV-based TBI therapy. The purpose of this review is to discuss contradictory effects of different EV subtypes on TBI, and to propose treatment ideas based on different EV subtypes to maximize their benefits for the recovery of TBI patients. Video Abstrac

Magnetic properties in Pd doped ZnS from ab initio calculations

First-principles calculations based on density functional theory within the general gradient approximation (GGA) are performed to study the electronic structure and magnetic properties of Pd doped ZnS. It is found that an isolated Pd atom doped 2 × 2 × 2 ZnS supercell shows half-metallic ferromagnetic character with a total magnetic moment of 2.0μB per supercell, which is significantly enhanced compared with the pure ZnS supercell. The strong ferromagnetic coupling of the local magnetic moments can be explained in terms of strong hybridisation between Pd-4d and S-3p states. The hybridisation between Pd and the neighbouring S atoms leads to a strong coupling chain Pd(4d)-S(3p)-Zn(3d)-S(3p)-Pd(4d), which induces strong indirect long range FM coupling between Pd dopants. The results of several doping configurations demonstrate that ferromagnetic coupling exists between the two doped palladium atoms. These results suggest that Pd doped ZnS can also be considered as suitable candidates for exploring new half-metallic ferromagnetism in semiconductors