On thek dimensional Piatetski-Shapiro prime number theorem

Thek-dimensional Piatetski-Shapiro prime number problem fork⩾3 is studied. Let π(x ₁ c ₁,⋯,c _k ) denote the number of primesp withp⩽x, , where 1<c ₁<⋯<c _k are fixed constants. It is proved that π(x;c ₁,⋯,c _k ) has an asymptotic formula ifc ₁ ⁻¹ +⋯+c _k ⁻¹ >k−k/(4k ²+2). Project supported by the National Natural Science Foundation of China (Grant No. 19801021) and the Natural Science Foundation of Shandong Province (Grant No.Q98A02110).     

复Fuzzy函数的Buckley导数与Buckley积分

本文对Ｊ．Ｊ．Ｂｕｃｋｌｅｙ在［１］、［２］中给出的实变量复Ｆｕｚｚｙ数值函数的导数与积分加以推广,引出复变量复Ｆｕｚｚｙ数值的导数与积分概念,为研究Ｆｕｚｚｙ复分析打下一定的基础。     

Ternary eutectic growth of Ag-Cu-Sb alloy within ultrasonic field

The liquid to solid transformation of ternary Ag42.4Cu21.6Sb36 eutectic alloy was accomplished in an ultrasonic field with a frequency of 35 kHz, and the growth mechanism of this ternary eutectic was examined. Theoretical calculations predict that the sound intensity in the liquid phase at the solidification interface increases gradually as the interface moves up from the sample bottom to its top. The growth mode of (ε θ Sb) ternary eutectic exhibits a transition of "divorced eutectic- mixture of anomalous and regular structures-regular eutectic" along the sample axis due to the inhomogeneity of sound field distribution. In the top zone with the highest sound intensity, the cavitation effect promotes the three eutectic phases to nucleate independently, while the acoustic streaming efficiently suppresses the coupled growth of eutectic phases. In the meantime, the ultrasonic field accelerates the solute transportation at the solid-liquid interface, which reduces the solute solubility of eutectic phases.     

Electro-hydrodynamic fabrication of ZnO-based dye sensitized solar cells

The electro-hydrodynamic (EHD) technique has been successfully applied for manufacturing ZnO photoanode in dye sensitized solar cells (DSSCs). Porous structure of ZnO film after calcinations was beneficial to the absorption of dye and infiltration of electrolyte. By using ionic liquid as an electrolyte, a high short-circuit photocurrent density of 12.1 mA/cm² was attained and the overall photo-to-electric energy conversion efficiency (η) was 3.4% under an AM-1.5 illumination at 100 mW/cm². At the same time, the influence factors on the solar cell performance, such as the concentrations of polyvinyl alcohol (PVA) during EHD process and light intensity were discussed. PACS 81.07.Bc; 84.60.Jt; 81.15.Rs     

Efficient generation of a photon pair in a bulk periodically poled potassium titanyl phosphate

In this report, we demonstrate the efficient generation of collinearly propagating photon pairs in a bulk periodically poled potassium titanyl phosphate pumped by a cw laser. The detected coincidence counts are more than 7400/s with 3.58 mW pump power in a Hanbury-Brown-Twiss-type experiment. The estimated photon pair production rate is about 0.73 MHz/mW. This is very promising for some applications, such as quantum key distribution, proof of the Bell-inequality, preparation of single photon states in broadband wave packets, Franson-type interference and so on.     

Facile Assembly of Dispersed ZrMCM‐41 Nanoparticles Promoted in‐situ by Zirconium Salt

Mesoporous ZrMCM‐41 nanoparticles were synthesized by a usual way where tetraethyl‐orthosilicate (TEOS) and zirconium nitrate were used as the inorganic precursors. The obtained nanoscale ZrMCM‐41 was characterized by X‐ray diffraction, N₂ physis‐sorption, scanning electron microscopy and transmission electron microscopy. Characterization results revealed that zirconium salt added in the synthesis had a crucial effect on the assembly of nanoscale ZrMCM‐41 with relatively uniform particle size, which was rarely observed in reported studies for ZrMCM‐41 synthesized using the similar method. Meanwhile, the possible mechanism behind the synthesis was discussed based on the character of hydrolysis and condensation of TEOS and the mild acidic environment induced by the hydrolysable zirconium salt under aqueous conditions. Thus obtained nanoscale ZrMCM‐41 with developed pore structures may be advantageous to general applications in catalysis or adsorption host‐guest chemistry in terms of efficient mass transport of guest molecules.     

Polyvinylidene fluoride/polystyrene hybrid fibers with high ionic conductivity and enhanced mechanical strength as lithium-ion battery separators

Journal of Solid State Electrochemistry - Ionic conductivity is an important separator parameter influencing the cycle life and rate capability of lithium-ion batteries (LIBs). To improve the ionic...     

On the conformal mappings in the unit disk fixing arbitrarily many boundary points

In this paper, we give a method of constructing conformal mappings defined in the unit disk which can fix arbitrarily many points on the unit circle.