数论中切比雪夫不等式的一点补充

利用Wallis不等式,得到素数计算函数的一个下界估计.     

“Can you help me count these pennies?”: Surfacing preschoolers’ understandings of counting

ABSTRACT

Capturing the breadth and variety of children’s understanding is critical if studies of children’s mathematical thinking are to inform policy and practice in early childhood education. This article presents an investigation of young children’s counting. Detailed coding and analyses of assessment interviews with 476 preschoolers revealed understandings that would be overlooked by solely assessing the accuracy of their responses. In particular, many children demonstrated understandings of counting principles on a challenging task that were not captured by other, simpler tasks. We conclude that common approaches to capturing young children’s mathematical understanding are likely underestimating their capabilities. This study contributes to researchers’ understanding of what making sense of counting looks and sounds like for preschool age children (3–5 years), the development and relations among counting principles (one-to-one, cardinal, and patterns of the number sequence), and the affordances of challenging, open-ended tasks. We close by considering the implications of recognizing and building from what children know and can do for researchers, practitioners, and policymakers.     

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.     

高光学质量氮化碳薄膜的制备和表征

氮化碳(graphitic carbon nitride,g-CN)作为一种非金属半导体材料已被广泛应用于多种能源相关领域研究中。目前由于制备高质量g-CN薄膜的困难,大大限制了其在实际器件上的应用。本文中,我们报道了一种可制备高光学质量gCN薄膜的方法:即由三聚氰胺先通过热聚合制备本体g-CN粉末,再由本体g-CN粉末经过气相沉积在ITO导电玻璃或钠钙玻璃基底上制备g-CN薄膜。扫描电子显微镜和原子力显微镜的测量结果表明在ITO玻璃基底上形成的g-CN薄膜形貌结构均一且致密,厚度约为300nm。扫描电镜能量色散能谱和X射线光电子能谱测量结果表明在ITO玻璃基底上制备的g-CN薄膜的化学组成与本体g-CN粉末的化学组成基本一致。同时,我们发现制备的g-CN薄膜和本体g-CN粉末一样在光照射下可以有效降解亚甲基蓝染料。此外,我们还测量了制备的g-CN薄膜的稳态吸收光谱、稳态荧光光谱、荧光寿命和价带谱,并运用吸收光谱和价带谱数据确定了其能带结构。     

紫外单光子成像系统的研究

搭建了紫外单光子成像系统,详细介绍了该系统的组成、工作原理和分辨率性能测试.由汞灯发出的紫外光经过大气散射、多块减光片得到了紫外单光子流.单光子直接打在微通道板上,微通道板产生的倍增电子由楔条形阳极收集,电荷灵敏前置放大器将阳极输出的电荷信号转变为电压信号,主放大器对前放信号进行滤波整形.利用高速数据采集卡连续采集主放大器的输出波形,通过软件对采集波形进行处理,采用图像处理技术得到了紫外单光子10min的计数图像,并对图像进行了畸变校正.此外,通过自己设计的分辨率板,测得该系统的分辨率可达150μm.该系统在极微弱光探测成像,生物发光,空间环境探测等方面具有广泛应用. 关键词： 单光子计数成像 阳极探测器 楔条形阳极 分辨率     

干涉条纹大数计数软件新方法及其实现

提出了一种根据干涉条纹信号过上升沿与下降沿阈值计数的异同及其起始和结束位置幅值判断的软件大数计数新方法,解决了在干涉条纹信号开始和结束位置可能出现±1计数误差的问题,进行了实现新计数方法的干涉测量实验。实验结果表明了该软件大数计数新方法的正确性。     

Fluorescence and Rotational Dynamics of Dityrosine

We have examined the lifetimes and rotational correlation times of dityrosine emission by time-correlated single-photon counting. We first noticed dityrosine fluorescence in samples of tyrosine and tyrosine dipeptides by its characteristic red-shifted emission at 400 to 430 nm. The longer rotational correlation time relative to tyrosine proved that this fluorescence emanated from a distinct species. Comparison with the fluorescence properties of synthesized dityrosine established the identity of the emitting species. Fluorescence intensity decays of dityrosine are generally characterized by two decay components, one with a lifetime in the range of 150 to 800 ps and another between 2.5 and 4.5 ns. We found no evidence for an excited-state reaction, since a rising phase (negative-amplitude component) was not observed. In the pH range from 4 to 10, two ground-state species exist in equilibrium with pK _a 7. Both species exhibit two fluorescence decays. The average fluorescence lifetime increases gradually with pH over the pH range from 4 to 10 and decreases at pH 2. Anisotropy decays were measured for dityrosine and the alanine–dityrosine–alanine and leucine–dityrosine–leucine dipeptides. The rotational correlation times of dityrosine and dityrosine dipeptides increase linearly with van der Waals volumes. The slope indicates a stronger solute–solvent interaction than predicted with stick boundary conditions. It is suggested that these interactions result from the presence of two zwitterionic pairs.     

Eigenvalue Asymptotics of the Stokes Operator for Fractal Domains

The leading asymptotic term for the function that counts theeigenvalues of the Stokes operator is determined for fairlygeneral underlying bounded domains. Moreover, the remainderis estimated in terms of the fractality of the boundary of thedomain. The results obtained resemble corresponding ones forthe Dirichlet Laplacian. 1991 Mathematics Subject Classification:35P20.     

A Number Theoretic Conjecture and the Existence of S–Cyclic Steiner Quadruple Systems

In their survey article on cyclic Steiner Quadruple Systems SQS(v) M. J. Grannel and T. S. Griggs advanced the conjecture (cf. [8, p. 412]) that their necessary condition for the existence of S-cyclic SQS(v) (cf. [7, p. 51]) is also sufficient. Some years prior to that E. Köhler [10] used a graph theoretical method to construct S-cyclic SQS(v). This method was extended in [17]-[20] and eventually used to reduce the conjecture of Grannel and Griggs to a number theoretic claim (cf. also [21], research problem 146). The main purpose of the present paper is to attack this claim. For the long intervals we have to distinguish four cases. The proof of cases I–III can be accomplished by a thorough study of how the multiples of a certain set belonging to the first column of a certain matrix (the elements of which are essentially the vertices of a graph corresponding to SQS(2p)) are distributed over the columns. The proof is by contradiction. Case IV is most difficult to treat and could only be dealt with by very deep lying means. We have to use an asymptotic formula on the number of lattice points (x,y) with xy 1 mod p (we speak of 1-points) in a rectangle and this formula shows that the 1-points are equidistributed. But even so our claim could not be proved for all intervals of admissible length. Intervals [a,b] with for some m and could not be covered. In the last section we discuss some conclusions which would follow from the non-existence of complete intervals.     

Composition operators on Hardy spaces on Lavrentiev domains

For any simply connected domain , we prove that a Littlewood type inequality is necessary for boundedness of composition operators on , , whenever the symbols are finitely-valent. Moreover, the corresponding ``little-oh' condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith (2003). Finally, we show a striking link between the geometry of the underlying domain and the symbol inducing the composition operator in , and in this sense, we relate both facts characterizing bounded and compact composition operators whenever is a Lavrentiev domain.