On extensions of representations for compact Lie groups

Let $H$ be a closed normal subgroup of a compact Lie group $G$ such that $G/H$ is connected. This paper provides a necessary and sufficient condition for every complex representation of $H$ to be extendible to $G$, and also for every complex $G$-vector bundle over the homogeneous space $G/H$ to be trivial. In particular, we show that the condition holds when the fundamental group of $G/H$ is torsion free.Comment: 10 pages, AMS-LaTeX v1.

Porous Carbon Materials as Supreme Metal-Free Counter Electrode for Dye-Sensitized Solar Cells

Counter electrode (CE), as one of the key components of dye-sensitized solar cells (DSSCs), plays a significant role in the overall efficiency and cost of the device. Platinum metal has long been considered one of the most efficient CEs for DSSCs, but its scarcity, high cost, and low stability in I−/I3− redox couple limit its application in the large scale. In this chapter, we provide a broad overview on porous carbon materials as supreme metal-free counter electrode for DSSCs. In the first part, we concisely discuss on the importance and working principle of DSSCs and then the influence of counter electrode on the photovoltaic performance of DSSCs. Afterward, we review different synthetic methods and precursors of porous carbon materials and their efficiency in DSSCs. In the last section, we discuss in detail with example how to characterize and evaluate the device performance using porous carbon materials as counter electrode. Finally, we finish this chapter with a brief summary and outlook of porous carbon materials as counter electrodes in DSSCs

Lymphangiography to treat postoperative lymphatic leakage: a technical review.

In addition to imaging the lymphatics and detecting various types of lymphatic leakage, lymphangiography is a therapeutic option for patients with chylothorax, chylous ascites, and lymphatic fistula. Percutaneous thoracic duct embolization, transabdominal catheterization of the cisterna chyli or thoracic duct, and subsequent embolization of the thoracic duct is an alternative to surgical ligation of the thoracic duct. In this pictorial review, we present the detailed technique, clinical applications, and complications of lymphangiography and thoracic duct embolization

Electrochemical Investigation of High-Performance Dye-Sensitized Solar Cells Based on Molybdenum for Preparation of Counter Electrode

In order to improve the photocurrent conversion efficiency of dye-sensitized solar cells (DSSCs), we studied an alternative conductor for the counter electrode and focused on molybdenum (Mo) instead of conventional fluorine-doped tin oxide (FTO). Because Mo has a similar work function to FTO for band alignment, better formability of platinum (Pt), and a low electric resistance, using a counter electrode made of Mo instead of FTO lead to the enhancement of the catalytic reaction of the redox couple, reduce the interior resistance of the DSSCs, and prevent energy-barrier formation. Using electrical measurements under a 1-sun condition (100 mW/cm(2), AM 1.5), we determined that the fill factor (FF) and photocurrent conversion efficiency (eta) of DSSCs with a Mo electrode were respectively improved by 7.75% and 5.59% with respect to those of DSSCs with an FTO electrode. Moreover, we have investigated the origin of the improved performance through surface morphology analyses such as scanning electron microscopy and electrochemical analyses including cyclic voltammetry and impedance spectroscopy