Imaging interfacial micro‐ and nano‐bubbles by scanning transmission soft X‐ray microscopy

Synchrotron‐based scanning transmission soft X‐ray microscopy (STXM) with nanometer resolution was used to investigate the existence and behavior of interfacial gas nanobubbles confined between two silicon nitride windows. The observed nanobubbles of SF₆ and Ne with diameters smaller than 2.5 µm were quite stable. However, larger bubbles became unstable and grew during the soft X‐ray imaging, indicating that stable nanobubbles may have a length scale, which is consistent with a previous report using atomic force microscopy [Zhang et al. (2010), Soft Matter, 6 , 4515–4519]. Here, it is shown that STXM is a promising technique for studying the aggregation of gases near the solid/water interfaces at the nanometer scale.     

Orthogonality and quintic functional equations

Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.     

A continuous-review inventory model with random disruptions at the primary supplier

We consider a continuous-review inventory problem for a retailer facing constant customer demand for a single product. This retailer is assumed to follow the well known and widely used order-up-to policy in making replenishment decisions, and can order from two suppliers who differ in reliability and costs. Supplier 1, the primary supplier, is cheaper, but is subject to random disruptions. Supplier 2, the backup supplier or the contingent source, is more expensive, but is perfectly reliable. If Supplier 1 is available when the inventory level at the retailer reaches the reorder point, the retailer orders from Supplier 1. Otherwise, it will wait for a while to see if Supplier 1 can recover from the disruption quickly. If so, it will still get replenishment from Supplier 1 to take advantage of its lower charge. However, the retailer will reroute to the backup supplier if Supplier 1 still does not recover from the disruption when the cap of waiting (the maximal waiting time of the retailer if Supplier 1 is disrupted) is reached. We analytically study the optimal sourcing and replenishment decisions at the retailer, and the impacts of various problem parameters on the optimal decisions. We also conduct extensive numerical experiments to compare different sourcing and replenishment decisions the retailer can make and get further managerial insights into the problem.     

Near unity quantum yield of light-driven redox mediator reduction and efficient H2 generation using colloidal nanorod heterostructures

The advancement of direct solar-to-fuel conversion technologies requires the development of efficient catalysts as well as efficient materials and novel approaches for light harvesting and charge separation. We report a novel system for unprecedentedly efficient (with near-unity quantum yield) light-driven reduction of methylviologen (MV(2+)), a common redox mediator, using colloidal quasi-type II CdSe/CdS dot-in-rod nanorods as a light absorber and charge separator and mercaptopropionic acid as a sacrificial electron donor. In the presence of Pt nanoparticles, this system can efficiently convert sunlight into H(2), providing a versatile redox mediator-based approach for solar-to-fuel conversion. Compared to related CdSe seed and CdSe/CdS core/shell quantum dots and CdS nanorods, the quantum yields are significantly higher in the CdSe/CdS dot-in-rod structures. Comparison of charge separation, recombination and hole filling rates in these complexes showed that the dot-in-rod structure enables ultrafast electron transfer to methylviologen, fast hole removal by sacrificial electron donor and slow charge recombination, leading to the high quantum yield for MV(2+) photoreduction. Our finding demonstrates that by controlling the composition, size and shape of quantum-confined nanoheterostructures, the electron and hole wave functions can be tailored to produce efficient light harvesting and charge separation materials.     

孔径透射率调制对外差探测的影响

信号光与本地光的夹角是影响探测器输出外差信号强度的主要因素。当夹角过大时,甚至不能检测到外差信号。通过分析提出,外差信号的振幅实际上是接收孔径透射率函数的傅里叶变换,以此为依据提出一种降低失配角对外差信号影响的方法,即在接收孔径处放置透射率分布满足一定函数形式的透过型元件,使其傅里叶频谱满足预定的要求,这种情况下两光束夹角增大时,探测器输出的外差信号强度能得到增强,从而降低了对探测系统瞄准精度的要求。     

Product of Toeplitz operators on the harmonic Dirichlet space

In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.     

Time-varying coefficient estimation in differential equation models with noisy time-varying covariates

We study the problem of estimating time-varying coefficients in ordinary differential equations. Current theory only applies to the case when the associated state variables are observed without measurement errors as presented in Chen and Wu (2008) [4] and [5]. The difficulty arises from the quadratic functional of observations that one needs to deal with instead of the linear functional that appears when state variables contain no measurement errors. We derive the asymptotic bias and variance for the previously proposed two-step estimators using quadratic regression functional theory.     

Rh2(S-biTISP)2-catalyzed asymmetric functionalization of indoles and pyrroles with vinylcarbenoids

Asymmetric functionalization of N-heterocycles by vinylcarbenoids in the presence of catalytic amounts of Rh(2)(S-biTISP)(2) has been successfully developed. This bridged dirhodium catalyst not only selectively enforces the reaction to occur at the vinylogous position of the carbenoid but also affords high levels of asymmetric induction.     

Experimental and theoretical study of the charge transport property of 4,4′-N,N′-dicarbazole-biphenyl

The hole and electron mobilities of the amorphous films of the organic semiconductor 4,4′-N,N′-dicarbazole-biphenyl (CBP) at different electric fields were measured through the time of flight (TOF) method. Based on its crystalline structure, the hole and electron mobilities of CBP were calculated. A detailed comparison between experimental and theoretical results is necessary for further understanding its charge transport properties. In order to do this, charge mobilities at zero electric field, μ(0), were deduced from experimental data as a link between experimental and theoretical data. It was found that the electron transport of CBP is less affected by traps compared with its hole transport. This unusual phenomenon can be understood through the distributions of frontier molecular orbitals. We showed that designing materials with frontier molecular orbitals localized at the center of the molecule has the potency to reduce the influence of traps on charge transport and provide new insights into designing high mobility charge transport materials.