伽利略的自由落体定律研究——"最美丽"的十大物理实验之一

在伽利略的运动学研究中,自由落体运动是一个重要课题.他敏锐地认识到,通过打开自由落体运动这个缺口,会导致一门新科学的诞生.他在《两门新科学》(即《关于两门新科学的数学证明的对话》)一书中写道:"我的目的,是要阐述一门崭新的科学,它研究的却是非常古老的课题.也许,在自然界中最古老的课题莫过于运动了.     

Solid-state Electrochemistry of Gadolinium Hexacyanoferrate Modified Electrode and Electrocatalytic Properties of Gadolinium Hexacyanoferrate

A new electroactive polynuclear inorganic compound of rare earth metal, gadolinium hexacyanoferrate (GdHCF), was prepared and characterized using the techniques of FTIR spectroscopy, thermogravimetric analysis (TG), UV-Vis spectrometry, X-ray photoelectron spectroscopy (XPS), ICP atomic emission spectroscopy, and EDX. The results of ICP atomic emission spectroscopy, EDX, and TGA indicated that the prepared GdHCF sample had a stoichiometry of NaGdFe(CN)₆·12H₂O (when GdHCF was prepared in NaCl solution). The FTIR spectrum of GdHCF showed that there were two types of water molecules in the structure of GdHCF: one was the interstitial water (5 H₂O), which resulted from the association of water due to H-bonding, and the other was water coordinated with Gd (7 H₂O). The results obtained using XPS showed that the oxidation state of Fe and Gd in the GdHCF sample was +2 and +3, respectively. GdHCF was immobilized on the surface of spectroscopically pure graphite (SG) electrode forming the GdHCF/SG electrode, and the solid-state electrochemistry of the resultant electrode was studied using cyclic voltammetry. The cyclic voltammetric results indicated that the GdHCF/SG electrode exhibited a pair of well-defined and stable redox peaks with the formal potential of E^0′=(197±3) mV. The effects of the concentration of the supporting electrolyte on the electrochemical characteristics of GdHCF were studied, and the results showed that the value of E^0′ increased linearly with the activity of the cationic ion of the supporting electrolyte (lga_Na⁺), with a slope of 54.1 mV, which may become a novel method for determining the activity of Na⁺ in solution. Further experimental results indicated that GdHCF had electrocatalytic activities toward the oxidation of dopamine (DA) and ascorbic acid (AA), and the electrocatalytic current increased linearly with the concentration of DA (or AA) in the range of 1.0–10.0 mmol·L^?1 (for DA) or 0.5–20.0 mmol·L^?1 (for AA).     

A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. In this paper we consider the influence of the refined interfaces on the steady state errors for second‐order three‐point difference approximations of flow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to refinement‐induced errors, it is sufficient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, different to local truncation error, and reflects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth refinement grids and on uniform grids. The conclusion seems to support the numerical findings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181: 280–316) that refinement does not necessarily reduce the numerical error. Copyright © 2005 John Wiley & Sons, Ltd.     

MC模式下顾客需求与厂商供应的纳什均衡

在大规模定制(MC，Mass Customization)模式下，基于市场需求的复杂化，厂商对个性化的顾客需求很难做出及时准确的反应，而且由于其自身生产能力的限制，不可能对所有的个性化用户进行一一地满足，只可能对已经存在的个性化需求，根据自身的生产能力和规模，以利润最大化及顾客对产品的满意度为目标，对个性化需求进行较准确地预测，从而正确指导生产。本通过博弈论的方法，提出了一个基于顾客对产品的满意度及企业的利润的一个非合作博弈模型，并给出求解纳什均衡的方法。     

一个增算子不动点定理及其在Banach 空间非线性方程的应用

给出了Banach空间的一个增算子不动点定理,将这一定理应用到Banach空间的积分-微分方程,给出了一类积分-微分方程的连续可微最大解和连续可微最小解的存在性定理.     

含氟碳菁染料聚集行为的研究

本文对五种不同结构的含氟碳菁染料的甲醇溶液及吸附在碘溴化银T 颗粒表面的聚集行为进行了研究 ,测定了照相性能 ,计算了增感倍率。Dye1 ,Dye2 ,Dye3在甲醇溶液中测得的单分子态吸收曲线 ,当取代基从C2 H5→CH3→无取代基时 ,最大吸收峰对应的波长向短波方向移动 ;乙基取代基的增感染料 (Dye1 )吸附在碘溴化银表面形成的J 聚集态峰值较高 ,对应的增感倍率也高。没有取代基的增感染料 (Dye3)不形成J 聚集 ,增感倍率低 ,有减感作用。Dye4与Dye5相比 ,Dye4具有尖而窄的J 聚集反射光谱 ,增感倍率高。结果表明 :不同结构的增感染料吸附在卤化银颗粒上形成的J 聚集态不同 ,吸收谱带窄的J 聚集态增感染料具有较高的增感倍率。     

Low Cost, High Efficiency, Gain Flattened L Band EDFA Using FBGs as C Band Seed Generators

A low cost, coolerless 980nm diode pumped, gain flattened L band EDFA with fast transient control, high pump efficiency and gain clamping effect was realized by using FBGs as C band seed generators.     

Experimental investigation and theoretical modeling of liquid entrainment in a horizontal tee with a vertical-up branch

This article describes a comprehensive literature review of liquid entrainment in horizontal pipes with vertical-up branches. Deficiencies in the available data and correlations were identified. The Air–water Test Loop for Advanced Thermal–hydraulic Studies (ATLATS) was constructed and entrainment onset and steady-state data were collected for a wide range of flow conditions. Using new insights gained from experimental testing, the authors developed a model for predicting the onset of entrainment and steady-state entrainment rate. Previously published correlations, along with the new model, are compared against all available data. The new model shows very good agreement with the onset data, but is not very good at predicting branch quality at high liquid flow rates.