ON THE RATE OF WEIGHTED Lp CONVERGENCE BY THE GRUENWALD INTERPOLATORY OPERATORS

This paper gives the weighted Lp convergence rate estimations of the Gruenwald interpolatory polynomials based on the zeros of Chebyshev polymomials of the first kind,and proves that the order of the estimations is optimal for p≥1.     

Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

On the bounded version of Hilbert's tenth problem

 The paper establishes lower bounds on the provability of 𝒟=NP and the MRDP theorem in weak fragments of arithmetic. The theory I ⁵ E ₁ is shown to be unable to prove 𝒟=NP. This non-provability result is used to show that I ⁵ E ₁ cannot prove the MRDP theorem. On the other hand it is shown that I ¹ E ₁ proves 𝒟 contains all predicates of the form (∀i≤|b|)P(i,x)^Q(i,x) where ^ is =, <, or ≤, and I ⁰ E ₁ proves 𝒟 contains all predicates of the form (∀i≤b)P(i,x)=Q(i,x). Here P and Q are polynomials. A conjecture is made that 𝒟 contains NLOGTIME. However, it is shown that this conjecture would not be sufficient to imply 𝒟=N P. Weak reductions to equality are then considered as a way of showing 𝒟=NP. It is shown that the bit-wise less than predicate, ≤₂, and equality are both co-NLOGTIME complete under FDLOGTIME reductions. This is used to show that if the FDLOGTIME functions are definable in 𝒟 then 𝒟=N P. Received: 13 July 2001 / Revised version: 9 April 2002 / Published online: 19 December 2002 Key words or phrases: Bounded Arithmetic – Bounded Diophantine Complexity     

在PowerPoint演示文稿中轻松插入Flash动画

用PowerPoint制作出的幻灯片简洁明快、条理清晰,而且PowerPoint简单易用,非常适合教师上课使用,成为教师制作多媒体课件的工具之一(在我校大部分教师采用PowerPoint制作多媒体课件).在制作多媒体课件过程中,结合适当的媒体技术(动画、声音、文字)不仅能提高课件的直观生动性,激发学生学习兴趣,同时有助于学生对课堂知识的当堂消化和理解,加深记忆.通过我校开展多媒体教学多年的实践发现:对医科学生的基础课、专业基础课和专业课教学中广泛涉及的机能性、原理性的知识适当采用动画其教学效果是传统教学方法无法比拟的.在众多的动画媒体中(avi、mov、mpg、swf、gif、ram等),Flash动画(swf文件)以其作品容量小(单个swf文件通常不到100 K)、质量高和丰富的交互性,特别是近年推出的Flash5同时能结合视频和音频,成为目前最为流行的二维动画.不仅为网页制作增添了活力,同时也为多媒体制作提供了有效的手段,既精巧又实用,素有"闪客"、"动画精灵"之美誉,越来越受到人们的青睐.如果要把Flash制作好的动画插入到PowerPoint制作的课件中,将会使PowerPoint单调的动画增色不少,使课件更具魅力.为此,我校专门开展了一系列Flash动画制作讲座,广大教师都能结合本专业制作Flash动画.如何将Flash动画加入到PowerPoint中,不少教师都是直接通过"超级连接"导入Flash课件,放映时总会出现讨厌的警告信息和警告声音提示,点击确定后打开Flash课件,有时打开的Flash课件窗口还要重新调整,使用十分不便.如何才能更恰当地引入Flash动画呢?不少杂志刊物和网上发表过类似文章,但大都比较复杂,而且在使用中特别是在PowerPoint中放映Flash动画偶尔会出现这样和那样的问题,这也是我们教学工作中经常遇到的问题,具有一定的普遍性.经过与教师们的众多交流和笔者平时反复摸索,找到了较为简便有效的方法,写出来与大家分享.     

Automorphisms with only infinite orbits on non-algebraic elements

 This paper generalizes results of F. K?rner from [4] where she established the existence of maximal automorphisms (i.e. automorphisms moving all non-algebraic elements). An ω-maximal automorphism is an automorphism whose powers are maximal automorphisms. We prove that any structure has an elementary extension with an ω-maximal automorphism. We also show the existence of ω-maximal automorphisms in all countable arithmetically saturated structures. Further we describe the pairs of tuples (ˉa,ˉb) for which there is an ω-maximal automorphism mapping ˉa to ˉb. Received: 12 December 2001 / Published online: 10 October 2002 Supported by the ``Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture' Mathematics Subject Classification (2000): Primary: 03C50; Secondary: 03C57 Key words or phrases: Automorphism – Recursively saturated structure     

On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

A laser Doppler anemometry technique for Reynolds stresses measurement

A technique is described for the measurement of all components of mean velocity and Reynolds stresses, in a complex turbulent flow where achieving coincidence data acquisition is difficult. The method is based on data recorded using four orientations of the laser probe. It is shown that the measurement errors are not the same for all the components of the Reynolds tensor, but they are sufficiently small to give a good accuracy. An application to a turbomachinery flow is given to illustrate the method.     

Nano-tribological study on a super-hydrophobic film formed on rough aluminium substrates

A novel super-hydrophobic stearic acid (STA) film with a water contact angle of 166^o was prepared by chemical adsorption on aluminum wafer coated with polyethyleneimine (PEI) film. The micro-tribological behavior of the super-hydrophobic STA monolayer was compared with that of the polished and PEI-coated Al surfaces. The effect of relative humidity on the adhesion and friction was investigated as well. It was found that the STA monolayer showed decreased friction, while the adhesive force was greatly decreased by increasing the surface roughness of the Al wafer to reduce the contact area between the atomic force microscope (AFM) tip and the sample surface to be tested. Thus the friction and adhesion of the Al wafer was effectively decreased by generating the STA monolayer, which indicated that it could be feasible and rational to prepare a surface with good adhesion resistance and lubricity by properly controlling the surface morphology and the chemical composition. Both the adhesion and friction decreased as the relative humidity was lowered from 65% to 10%, though the decrease extent became insignificant for the STA monolayer. The project supported by the National Natural Science Foundation of China (50375151, 50323007, 10225209) and the Chinese Academy of Sciences (KJCX-SW-L2)     

Photorefractive Four-Wave Mixing Switches Utilizing Pockels Effect -Longitudinal and Lateral Switches-

We carried out detailed calculations for photorefractive wave-mixing switches based on one of three crystals with high electro-optic coefficients, namely, BaTiO₃, Strontium Barium Niobate (SBN (0.75)), and Potasium Sodium Strontium Barium Niobate (KNSBN). A comparison of results for the three crystals shows that a 0_-cut BaTiO³ crystal is suitable for a longitudinal switch and requires a voltage of about 80 for a 2-mm-thick crystal to induce sufficient phase mismatch. The electrodes must be transparent for the incident and diffracted beams. A 45_-cut SBN (0.75) crystal, however, is suitable for a lateral switch and requires a voltage of about 150 for a 1-mm-wide crystal. The electrodes do not need to be transparent.