Change of variable formulas for non-anticipative functionals on path space

We derive a change of variable formula for non-anticipative functionals defined on the space of Rd-valued right-continuous paths with left limits. The functionals are only required to possess certain directional derivatives, which may be computed pathwise. Our results lead to functional extensions of the Itô formula for a large class of stochastic processes, including semimartingales and Dirichlet processes. In particular, we show the stability of the class of semimartingales under certain functional transformations.     

CdS纳米晶颗粒薄膜的制备及其光学特性研究

采用化学浴沉积法,以CdCl2·H2O、CS(NH2)2、NH4Cl、NH3·H2O和去离子水作为反应前驱物,在不同的氨水浓度下制备CdS纳米晶颗粒薄膜.通过扫描电镜、X射线衍射、X射线能量色散谱、紫外-可见光透射光谱、椭圆偏振光谱等方法,研究了反应前驱物中氨水浓度对CdS纳米晶颗粒薄膜的表面形貌、晶体结构、S/Cd原子比、光透过率、光学带隙、折射率、消光系数和光学吸收边等物理性能的影响.结果表明:反应前驱物中氨水浓度在0.4～1.0mol/L范围内,可以在衬底上形成均匀致密的CdS纳米晶颗粒薄膜.随着氨水浓度的增加,CdS纳米晶的平均晶粒尺寸逐渐减少,S/Cd原子比逐渐增加,由富Cd型转变为富S型,禁带宽度逐渐增加.在500～1000 nm波段内,折射率的平均值为1.75;消光系数k小于0.07.     

Quadratic perturbations of a quadratic reversible center of genus one

In this paper, we study a reversible and non-Hamitonian system with a period annulus bounded by a hemicycle in the Poincaré disk. It is proved that the cyclicity of the period annulus under quadratic perturbations is equal to two. This verifies some results of the conjecture given by Gautier et al.     

On the Diophantine Equation x2 - kxy ＋ y2 ＋ 1x = 0

Let l be a given nonzero integer.The authors give an explicit characterization of the positive integer k that makes the Diophantine equation x2-kxy+y2+lx=0 have infinitely many positive integer solutions(x,y).     

Effect of KOH molarity and annealing temperature on ZnO nanostructure properties

In this work, ZnO nanorods (NRs) were fabricated using a low cost chemical bath deposition (CBD) method. The effect of the potassium hydroxide concentration on the fabricated ZnO nanostructures was studied in depth. The optical, structure, and surface morphology properties of the fabricated ZnO nanostructures were investigated using Uv-vis spectroscopy, XRD, and SEM. The results indicate that the formation of hexagonally structured ZnO nanorods with different lengths and diameters was dependent on the KOH concentration. The sample prepared with 2 M of KOH was the best one for optoelectronic applications, since it has the smallest diameters. This sample was annealed at different temperatures (473 K–1073 K). Positron Annihilation Lifetime Spectroscopy was used to determine the defects in the ZnO nanorods. The results show that the positron mean lifetime (τ_m) decreased as the annealing temperature increased, which means that the overall defects in the ZnO nanorods decreased with increasing temperature. Consequently, higher performance semiconductor devices based on ZnO nanorods could be fabricated after high annealing of the ZnO nanorods.     

Effect of quadratic pressure gradient term on a one-dimensional moving boundary problem based on modified Darcy’s law

A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy’s flow problem, the exact analytical solution for the case of Darcy’s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem.     

Annealing effect on the structural and optical properties of a Cd1−xZnxS thin film for photovoltaic applications

Herein is a report of a study on a Cd_1−xZn_xS thin film grown on an ITO substrate using a chemical bath deposition technique. The as-deposited films were annealed in air at 400 °C for 30 min. The composition, surface morphology and structural properties of the as-deposited and annealed Cd_1−xZn_xS thin films were studied using EDX, SEM and X-ray diffraction techniques. The annealed films have been observed to possess a crystalline nature with a hexagonal structure. The optical absorption spectra were recorded within the range of 350-800 nm. The band gap of the as-deposited thin films varied from 2.46 to 2.62 eV, whereas in the annealed film these varied from 2.42 to 2.59 eV. The decreased band gap of the films after annealing was due to the improved crystalline nature of the material.     

Physical properties of ZnS thin films prepared by chemical bath deposition

Zinc sulphide thin films are deposited on SnO₂/glass using the chemical bath deposition technique. X-ray diffraction and atomic force microscopy are used to characterize the structure of the films; the surface composition of the films is studied by Auger electrons spectroscopy, the work function and the photovoltage are investigated by the Kelvin method. Using these techniques, we specify the effect of pH solution and heat treatment in vacuum at 500 °C. The cubic structure corresponding to the (1 1 1) planes of β-ZnS is obtained for pH equal to 10. The work function (Φ_material − Φ_probe) for ZnS deposited at pH 10 is equal to −152 meV. Annealing at 500 °C increases Φ_m (by about 43 meV) and induces the formation of a negative surface barrier. In all cases, Auger spectra indicate that the surface composition of zinc sulphide thin films exhibits the presence of the constituent elements Zn and S as well as C and O as impurity elements.     

On the Uniqueness for the Spatially Homogeneous Boltzmann Equation with a Strong Angular Singularity

We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local (in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedness result is shown for all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying to a strong angular singularity, except in the special case of Maxwell molecules. Our proof relies on the ideas of Tanaka (Z. Wahrscheinlichkeitstheor. Verwandte. Geb. 46(1):67–105, [1978]) we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to couple two such processes started with two different initial conditions, in such a way that they almost surely remain close to each other.     

Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath

We study a scheme of thermal management where a three-qubit system assisted with a coherent auxiliary bath (CAB) is employed to implement heat management on a target thermal bath (TTB). We consider the CAB/TTB being ensemble of coherent/thermal two-level atoms (TLAs), and within the framework of collision model investigate the characteristics of steady heat current (also called target heat current (THC)) between the system and the TTB. It demonstrates that with the help of the quantum coherence of ancillae the magnitude and direction of heat current can be controlled only by adjusting the coupling strength of system-CAB. Meanwhile, we also show that the influences of quantum coherence of ancillae on the heat current strongly depend on the coupling strength of system—CAB, and the THC becomes positively/negatively correlated with the coherence magnitude of ancillae when the coupling strength below/over some critical value. Besides, the system with the CAB could serve as a multifunctional device integrating the thermal functions of heat amplifier, suppressor, switcher and refrigerator, while with thermal auxiliary bath it can only work as a thermal suppressor. Our work provides a new perspective for the design of multifunctional thermal device utilizing the resource of quantum coherence from the CAB.