O 3 ), possessing a bandgap of 1.9-2.2 eV and theoretically enabling a photocurrent density of 12.6 mA cm −2 at 1.23 V versus reversible hydrogen electrode (RHE) for water splitting, [6] become one of the most investigated photoanode materials. Additionally, Hematite has stable properties, abundant reserves, and nontoxicity compared with other photoanode materials. [7] However, the photoelectrochemical performance of hematite is severely restricted by its short hole diffusion length (≈2-4 nm), low conductivity, and short lifetime of the excited state carriers (≈10 −12 s). Furthermore, a high concentration of surface states and slow kinetics for sluggish oxygen evolution reaction (OER) at the surface of Fe 2 O 3 call for the necessary modifications to improve the PEC performance.Cu 2 S, a p-type semiconductor with a narrow bandgap (1.2 eV), is attracting broad interest for solar energy conversion and storage in numerous applications. [8][9][10] It is ideally suitable for harvesting sunlight in a wide wavelength range and simultaneously the high conductivity allows for efficient photogenerated charge transfer. Moreover, copper vacancies are generated once copper(I) sulfide is exposed to oxygen, and then an localized surface plasmon resonance band will emerge. [11,12] This property of copper sulfide enables the utilization of sunlight with the wavelength up to the near-infrared region. Due to the photothermal effect, CuS compound nanocrystals have been used widely for energy storage and photothermal therapy. [13,14] Importantly, a recent report demonstrates that the derivatives of Cu 2 S under the condition of OER The severe charge recombination and the sluggish kinetic for oxygen evolution reaction have largely limited the application of hematite (α-Fe 2 O 3 ) for water splitting. Herein, the construction of Cu 2 S/Fe 2 O 3 heterojunction and discover that the formation of covalent SO bonds between Cu 2 S and Fe 2 O 3 can significantly improve the photoelectrochemical performance and stability for water splitting is reported. Compared with bare Fe 2 O 3 , the heterostructure of Cu 2 S/Fe 2 O 3 endows the resulting electrode with enhanced charge separation and transfer, extended range for light absorption, and reduced charge recombination rate. Additionally, due to the photothermal properties of Cu 2 S, the heterostructure exhibits locally a higher temperature under illumination, profitable for increasing the rate of oxygen evolution reaction. Consequently, the photocurrent density of the heterostructure is enhanced by 177% to be 1.19 mA cm −2 at 1.23 V versus reversible hydrogen electrode. This work may provide guideline for future in the design and fabrication of highly efficient photoelectrodes for various reactions.

Wnt signaling plays critical roles in dorsoventral fate specification and anteroposterior patterning, as well as in morphogenetic cell movements. Dishevelled proteins, or Dvls, mediate the activation of Wnt/ß-catenin and Wnt/planar cell polarity pathways. There are at least three highly conserved Dvl proteins in vertebrates, but the implication of each Dvl in key early developmental processes remains poorly understood. In this study, we use genome-editing approach to generate different combinations of maternal and zygotic dvl mutants in zebrafish, and examine their functions during early development. Maternal transcripts for dvl2 and dvl3a are most abundantly expressed, whereas the transcript levels of other dvl genes are negligible. Phenotypic and molecular analyses show that early dorsal fate specification is not affected in maternal and zygotic dvl2 and dvl3a double mutants, suggesting that the two proteins may be dispensable for the activation of maternal Wnt/ß-catenin signaling. Interestingly, convergence and extension movements and anteroposterior patterning require both maternal and the zygotic functions of Dvl2 and Dvl3a, but these processes are more sensitive to Dvl2 dosage. Zygotic dvl2 and dvl3a double mutants display mild axis extension defect with correct anteroposterior patterning. However, maternal and zygotic double mutants exhibit most strongly impaired convergence and extension movements, severe trunk and posterior deficiencies, and frequent occurrence of cyclopia and craniofacial defects. Our results suggest that Dvl2 and Dvl3a products are required for the activation of zygotic Wnt/ß-catenin signaling and Wnt/planar cell polarity pathway, and regulate zygotic developmental processes in a dosage-dependent manner. This work provides insight into the mechanisms of Dvl-mediated Wnt signaling pathways during early vertebrate development.

We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to lower levels, the other is based on a recursive expression for the deviation matrix.We revisit the link between a solution of Poisson's equation and perturbation analysis and we show that it applies to QBDs. We conclude with the PH/M/1 queue as an illustrative example, and we measure the sensitivity of the expected queue size to the initial value.

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In this paper, subgeometric ergodicity is investigated for continuous-time Markov chains. Several equivalent conditions, based on the first hitting time or the drift function, are derived as the main theorem. In its corollaries, practical drift criteria are given forergodicity and computable bounds on subgeometric convergence rates are obtained for stochastically monotone Markov chains. These results are illustrated by examples.