Gowers norms and pseudorandom measures of subsets

Let $A \subset {{\Bbb Z}_N}$, and ${f_A}(s) = \left\{ {\begin{array}{*{20}{l}}{1 - \frac{{|A|}}{N},}&{{\rm{for}}\;s \in A,}\\{ - \frac{{|A|}}{N},}&{{\rm{for}}\;s \notin A.}\end{array}} \right.$ We define the pseudorandom measure of order k of the subset A as follows, P_k(A, N) = $\begin{array}{*{20}{c}}{\max }\\D\end{array}$|$\mathop \Sigma \limits_{n \in {\mathbb{Z}_N}}$f_A(n + c₁)f_A(n + c₂) … f_A(n + c_k)|, where the maximum is taken over all D = (c₁, c₂, . . . , c_k) ∈ ${\mathbb{Z}^k}$ with 0 ≤ c₁ < c₂ < … < c_k ≤ N - 1. The subset A ⊂ ${{\mathbb{Z}_N}}$ is considered as a pseudorandom subset of degree k if P_k(A, N) is “small” in terms of N. We establish a link between the Gowers norm and our pseudorandom measure, and show that “good” pseudorandom subsets must have “small” Gowers norm. We give an example to suggest that subsets with “small” Gowers norm may have large pseudorandom measure. Finally, we prove that the pseudorandom subset of degree L(k) contains an arithmetic progression of length k, where L(k) = 2·lcm(2, 4, . . . , 2|$\frac{k}{2}$|), for k ≥ 4, and lcm(a₁, a₂, . . . , a_l) denotes the least common multiple of a₁, a₂, . . . , a_l.     

两个级联型三能级原子受激辐射的非线性性质

本文研究了两个级联型三能级原子同单模腔场的非线性相互作用,研究表明:在激发场场强达到一定阈值以后,两个原子的合作辐射效应变成同步辐射,即多原子系统在一定阈值条件下可以有组织成相当于一个大原子的系统,而产生同步有序辐射。同时,由于这种同步辐射效应,两原子系统的受激辐射的二阶相干度相对于单原子系统的要大,即聚束效应强而反聚束效应弱。另外,两原子系统由于多光子过程的加强而有更深的压缩效应,此时要求的激发场场强也比单原子系统的要强。     

乙基苯基二氯化锡与2－羟基萘醛缩对甲氧基苯胺Schiff碱1∶1配合物的合成和晶体结构

乙基苯基二氯化锡与２－羟基萘醛缩对甲氧基苯胺Ｓｃｈｉｆｆ碱１∶１配合物的合成和晶体结构刘宝殿，包明，孙振刚，贺庆林，邢彦，贾恒庆，林永华（东北师范大学化学系，长春，１３００２４）（中国科学院长春应用化学研究所，长春）关键词乙基苯基二氯化锡，Ｓｃｈｉｆ...     

稀土磷酸盐发光材料的微波合成

稀土磷酸盐发光材料的微波合成徐文国，田一光，刘淼，刘海堂，方光华，庞文琴（吉林大学化学系，环境科学系，长春，１３００２３）关键词微波合成，稀土磷酸盐，微晶玻璃，玻璃态，发光材料稀土磷酸盐发光材料的研究是当前材料科学的热门研究课题。它们一般通过高温固相...     

Carbon Nanotubes Grown on Sepiolite as Catalyst Carrier

Multi-walled carbon nanotubes were synthesized by the catalytic decomposition of acetylene at 750℃ over sepiolite powder,which was treated with aqueous cobalt nitrate. It is expected that the composite with high specific area will have high capacity of hydrogen storage.     

Effect of Low Energy Electron Exposure on Ion Scattering Spectroscopy

The effect of low energy electron (LEE) exposure on ISS, including on the sputter peak and scatter peak as well as on ion neutralization, has been investigated for different samples. Some new results are discussed.     

Electrooxidation Mechanism of Methanol at Pt-Ru Catalyst Modified GC Electrode in Electrolytes with Different pH Using Electrochemical and SERS Techniques

The electrochemical and in-situ surface-enhanced Raman spectroscopy （SERS） techniques were used to investigate the electrooxidation behavior of methanol in acidic, neutral and alkaline media at a Pt-Ru nanoparticle modified glassy carbon （Pt-Ru/GC） electrode. The results showed that methanol could be dissociated spontaneously at the Pt-Ru/GC electrode to produce a strongly adsorbed intermediate, CO. It was found that CO could be oxidized more easily in the alkaline medium than in the acidic and neutral media. The peak potential of methanol oxidation was shifted from 0.663 and 0.708 V in the acidic and neutral media to -0.030 V in the alkaline medium, which is due to that the adsorption strength of CO on the Pt surface in the alkaline medium is weaker than that in the acidic and neutral media. The final product of the methanol oxidation is CO2. However, in the alkaline medium, CO2 produced would form CO3^2- and HCO3^- resulting in the decrease in the alkaline concentration and then in the decrease in the performance of DMFC. Therefore, the performance of the alkaline DMFC is not Stable.     

毛细管电泳在火炸药分析中的应用

综述了近年来毛细管电泳在火炸药领域的应用现状，包括各种分离模式、检测器以及毛细管电泳芯片的应用，并对该技术在火炸药分析中的应用前景作了展望，提出了新的发展方向。引用文献45篇。     

乙烯系单体自由基聚合的阻聚效应──XIX．取代哌啶羟胺和二叔丁基羟胺及其稳定自由基对苯乙烯－丙烯腈共聚合的影响

研究了二叔丁基羟胺（ＤＴＢＨＡ），二叔丁基氮氧自由基（ＤＴＢＮＯ·），２，２，６，６－四甲基－４－羟基哌啶羟胺（ＴＭＨＰＨＡ）和２，２，６，６－四甲基－４－羟基哌啶－１－氧自由基（ＴＭＨＰＯ·）对过氧化苯甲酰（ＢＰＯ）６０℃引发的苯乙烯（Ｍ１）－丙烯腈（Ｍ２）共聚合的阻聚行为．结果表明，这些阻聚剂对Ｓｔ－ＡＮ共聚均表现良好的阻聚行为，其中氮氧自由基优于相应羟胺．同时观察到Ｓｔ—ＡＮ竞聚率的改变，羟胺使ｒ１有所降低，ｒ２略有增大．但相应的氮氧自由基是相反结果．阻聚剂为２００ｐｐｍ时，共聚物中的恒比共聚点由对照实验的０．６１９变化为０．５３３，０．６４５，０．５８９和０．６９８相对于ＤＴＢＨＡ，ＤＴＢＮＯ·，ＴＭＨＰＨＡ和ＴＭＨＰＯ·．     

Exact quantum mechanical vibration-rotation kinetic energy operator of four-particle system in various coordinates

The vibration-rotational kinetic energy operators of four-particle system in various coordinates are derived using a new and simple angular momentum method. The operators are respectively suitable for studying the systems described by scattering coordinate, valence coordinate, Radau coordinate, Radau/Jacobi and Jacobi/valence hybrid coordinates and so on. Certain properties of these operators and their possible applications are discussed.