L p -dual Quermassintegral sums

In this paper, we first introduce a concept of L _p -dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L _p -dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L _p -Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

In situ observation of NaBi(WO4)2 dendrite growth and the study on microstructure of solidification

The dendrite growth process of transparent NaBi(WO₄)₂ with small prandtl and high melting point was studied by using the in-situ observation system. According to the dynamic images and detailed information, there are two kinds of restriction effect on the dendrite growth, the competition between arms and branches and the convection in the melt. The dendrite growth rate was time dependent, and the rate of arm growth reached the maximum 5.8 mm/s in the diffusive-advective region and rapidly decreased in the diffusive-convective region. The growth rate of branch had the same change trends as the arm’s. Based on the EPMA-EDS data of solidification structure of quenched NaBi(WO₄)₂ melt, it was found that there were component differences from stoichiometric concentration in the melt near the interface during the growth process. Supported by the National Natural Science Foundation of China (Grant No. 50331040) and the Innovation Funds from Shanghai Institute of Ceramics, Chinese Academy of Sciences (Grant No. SCX0623)     

Photoluminescence properties of the composite of porous alumina and poly (2,5-dibutoxy-1,4 phenylenevinylene)

The spin coating method was used to assemble polymer (Poly (2,5-dibutoxy-1,4-phenylenevinylene)) (DBO-PPV) into the pores of porous alumina which was prepared by anodization. Four peaks in the photoluminescence (PL) spectra of the composite, with contributions from the DBO-PPV and porous alumina, were found. It was also found that the light emitting from the porous alumina could excite the photoluminescence of DBO-PPV. The nanometer effect of the porous alumina can lead to a blue shift of 90 nm of the PL peaks of DBO-PPV.     

Using Inquiry to Improve Pedagogy through K‐12/University Partnerships

This article focuses on the impact a collaborative project between university graduate fellows and K‐12 classroom teachers had on improved pedagogy in the classroom and in the future at the university. Nine teams participated in a yearlong professional development project to improve pedagogy and communication skills of the participants. This study shows that the participants, the fellows and the K‐12 teacher partners, made changes in planning, implementation, and even motivation for using inquiry‐based methods in their classroom. External observations of the teams further support the individuals' claims of improved pedagogy using inquiry and impact on student conceptual understanding. The Horizon Classroom Observation instrument was used for these observations. The teams showed an overall increase in scores, as well as overall effective and exemplarily implementation of their planning. The program design, the implementation, and the results of this three‐year study will be elaborated in this article.     

Christoffel functions and mean convergence for Lagrange interpolation for exponential weights

For exponential weights, a necessary condition of weighted mean convergence for Lagrange interpolation is given.     

Examples of non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property

In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces.     

寡头垄断市场排污收费的政府调控模型

基于完全信息博弈理论,阐述了寡头垄断市场的排污收费古诺模型.建立了具有政府宏观调控机制的博弈模型,并对调控效果进行了分析.     

目标函数扰动的集值优化问题的稳定性

本文研究了由目标函数扰动的集值优化问题的有效点集所定义的集值映射的半连续性.讨论了目标函数扰动的集值优化问题在上半连续意义下的稳定性.特别地,在广义适定性条件下,证明了集值优化问题在上半连续意义下的稳定性.     

Solvothermal synthesis of TiO2: anatase nanocrystals and rutile nanofibres from TiCl4 in acetone

This work reports a new synthetic approach for single‐phase TiO₂ nanomaterials by solvothermal treatment of titanium tetrachloride in acetone at 80–110 °C. Small, uniform, and yet size‐tunable (5–10 nm) anatase titania nanocrystallites were obtained using a low concentration of TiCl₄ in acetone (i.e., at molar ratios of TiCl₄/acetone ≤ 1:15) in the temperature range of 80–110 °C, while rutile nanofibers were synthesized using a high concentration of TiCl₄ (e.g., TiCl₄/acetone = 1:10) at 110 °C. Copyright © 2007 John Wiley & Sons, Ltd.     

掺铒光纤放大器中上转换过程的影响

掺杂浓度的提高影响了掺铒光纤放大器(EDFA)的性能,对经典Giles模型提出了新的要求。首先研究了高掺杂下铒离子距离较小引起的上转换过程的机理,通过优化速率方程模型分析了上转换过程对EDFA的影响,得出了在泵浦光和信号光远远大于ASE光的假设下泵浦光和信号光沿光纤长度变化的近似表达式,并将该近似分析解与解析解进行了比较。仿真结果表明上转换过程会降低随光纤传输的信号光和泵浦光,影响EDFA的放大性能,并得出了当掺铒浓度大于2.95×1025m-3时,上转换过程的影响不能忽略的结论。