Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals

We study the approximation of compact linear operators defined over certain weighted tensor product Hilbert spaces. The information complexity is defined as the minimal number of arbitrary linear functionals needed to obtain an $\epsilon$-approximation for the $d$-variate problem which is fully determined in terms of the weights and univariate singular values. Exponential tractability means that the information complexity is bounded by a certain function that depends polynomially on $d$ and logarithmically on ${\epsilon }^{-1}$. The corresponding unweighted problem was studied in Hickernell et al. (2020) with many negative results for exponential tractability. The product weights studied in the present paper change the situation. Depending on the form of polynomial dependence on $d$ and logarithmic dependence on ${\epsilon }^{-1}$, we study exponential strong polynomial, exponential polynomial, exponential quasi-polynomial, and exponential $(s,t)$-weak tractability with $max(s,t)\ge 1$. For all these notions of exponential tractability, we establish necessary and sufficient conditions on weights and univariate singular values for which it is indeed possible to achieve the corresponding notion of exponential tractability. The case of exponential $(s,t)$-weak tractability with $max(s,t)<1$ is left for future study. The paper uses some general results obtained in Hickernell et al. (2020) and Kritzer and Woźniakowski (2019).     

Noise annoyance assessment of various urban road vehicle pass-by noises in isolation and combined with industrial noise: A laboratory study

Noise maps are diagnosis tools which represent the noise exposure situation using the energy-based index L_den (the day–evening–night level). Two major drawbacks may be attributed to noise maps: (1) energy-based indices only account for one acoustical factor (exposure level) that may give rise to annoyance; (2) combined exposures situations are left unframed.     

新加坡初中化学教材栏目设置的特点及思考

以新加坡初中化学G.C.E.‘O’ Level Science Discover Chemistry教材为研究对象,主要从教材中栏目设置情况和具体案例进行分析,总结出该教材具有"信息提示类栏目独具特色,实验探究类栏目强调实际应用,课外资料类栏目突出与时俱进,归纳总结类栏目强化宏微结合,思考练习类栏目注重因材施教"的特点,并对我国初中化学教材的栏目设置提出了几点思考和启示。     

以科技论文为素材的高中化学试题命制策略

命制模拟试题时,教师一般会选择化学科技论文作为试题的背景材料。通过分析近3年江苏高考化学试题,可以看出流程图题考查的基本情况。以江苏某市高考模拟化学卷为例,从4个维度阐述了以科技论文为素材的高中化学试题的命制策略：选择合适的命题背景素材;将文字内容巧妙地转化为工艺流程图;建立背景素材与试题考查之间的联系;精心设计试题设问。根据命题实践提出命制试题的关注点。     

一个无限可微函数类的最优埃尔米特插值CSCD

This paper investigates the optimal Hermite interpolation of a class F_(∞) of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,w)[-1,1],1≤p∞[-1,1]and L_(p,w)[-1,1],1≤p<∞ with w a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation polynomials based on the ze-ros of polynomials with the leading cofficient 1 of the least deviation from zero in L_(∞)[-1,1]and L_(p,w)[-1,1],1≤p<∞are optimal for 1≤p≤∞.We also give the optimal Hermite interpolation nodes when we ask the endpoints to be included in the nodes.     

近红外光谱技术在线监测积雪草药材活性成分的大孔树脂分离纯化过程

利用近红外(NIR)光谱技术研究并建立可在线监测积雪草药材活性成分———羟基积雪草苷和积雪草苷的大孔树脂分离纯化过程的方法。收集积雪草药材提取物的50%乙醇大孔树脂洗脱液,并采集其近红外光谱信息,建立上述收集液中羟基积雪草苷、积雪草苷的高效液相色谱(HPLC)含量测定方法;然后,采用偏最小二乘法(PLS)建立上述收集液的NIR光谱与其中羟基积雪草苷及积雪草苷含量的线性关系。建模过程中,以相关系数(R2)、交叉验证均方根误差(RMSECV)为指标,确定用于建模的最优近红外波段和光谱预处理方法,即羟基积雪草苷和积雪草苷模型的最佳建模波段分别为12 000.8～7 499.8cm-1和12 000.8～9 750.3cm-1;R2分别为96.44和96.07;RMSECV分别为0.084 80和0.000 99。将上述模型用于在线监测积雪草药材提取物大孔树脂分离纯化过程中羟基积雪草苷及积雪草苷的含量,结果表明此模型预测效果良好。该方法快速、简便、准确,可用于生产过程中羟基积雪草苷及积雪草苷的在线检测和质量控制。     

基于集对层次理论的深基坑支护方案综合优选

集对分析是处理不确定性问题的系统理论的新方法,应用集对分析原理、层次分析和集值统计方法,建立了考虑影响因素权重的评价模型,探讨深基坑支护方案评价与优选实用方法.用实例给予了验证.     

Construction of meaning: urban elementary students’ interpretation of geometric puzzles

Mathematical puzzles have long been employed by parents and teachers to augment the standard mathematics curriculum. This paper reports on a study of urban elementary students engaged in the solution of mathematical puzzles. The work confirms that, given the opportunity, these students will construct their own, logically consistent, interpretations of the puzzle clues. In particular, these students used self-generated rules about alignment and orientation to construct meaning in ambiguous clues. Such exercises in logic bring to light the value of student approaches to problem solving, and the possibility of using these approaches as building blocks from which students might construct knowledge in the standard curriculum.     

城市经济可持续发展的综合评价

将多指标可拓综合评价方法应用于城市经济可持续发展水平评价 .分析了城市经济可持续发展水平的影响因素 ,建立了城市经济可持续发展水平评价的物元模型 .将多指标城市经济可持续发展水平的目标评价归结为单目标决策 ,比较简明确切地反映出城市经济可持续发展水平 .