The Kissing Triangles: The Aesthetics of Mathematical Discovery

Papert's (1978) appeal to reconsider the power and possibilities of the aesthetic in mathematics learning is often ignored in mathematics education research. This paper begins with the premise, put forth by Dewey (1934), that the aesthetic structures many dimensions of inquiry and experience. In the same way that using particular paintings, musical compositions, or even everyday experiences has been instrumental to attempts by philosophers to understand the aesthetic dimensions of meaning and experience in artistic domains, I propose that analysing a particular encounter with mathematics may help reveal the nature and role of the often nebulous responses of elegance, beauty, and `fit' to which mathematicians lay claim in their mathematical activity. To achieve this, I draw on and adapt the defining features of the aesthetic character of experience set forth by the aesthetician Beardsley (1982). This, in turn, sheds light on the role thataesthetics can play in mathematical inquiry and experience, and provides initial categories and conjectures that can be used to investigate the potential roles of aesthetics in mathematics learning contexts.This revised version was published online in September 2005 with corrections to the Cover Date.     

增湿活化反应器内喷水脱硫试验研究

本文介绍在热态脱硫试验台上进行的生石灰和消石灰的喷水活化脱硫试验,研究了Ca/S比、饱和温距、入口烟气SO2浓度、烟气速度及水喷嘴雾化风对脱硫效率和钙利用率的影响规律,对两种脱硫剂的脱硫活性进行了比较,并对喷水增湿提高脱硫效率的机理进行了分析。研究表明,喷水增湿使两种脱硫剂的活性都有明显提高,生石灰具有价格优势。     

双预脉冲驱动X射线激光实验研究

 在“星光-Ⅱ”激光装置上进行了双预脉冲驱动类氖铬X射线激光实验，介绍了实验方法和实验结果，并对结果进行了简短讨论。由于目前“星光”装置输出能量较低，所进行的双预脉冲驱动未能显著提高X射线激光强度，改变预脉冲幅度时X射线激光强度也未有显著变化。利用MED103程序进行了模拟计算，其结果与实验结果一致。     

小长径比垂直管气液两相流动特性分析

实验观察了小长径比垂直上流管内流型及特点,并对管入口处的压力波动特性和系统的压差波动特性进行了试验研究.结果表明:小长径比(L/D)垂直管内流型表现为泡状流、塞状流、乳沫状流、环状流和液束环状流;分别增加管线中的气量、液量,或者同时增加气液流量,均会造成垂直管入口处压力波动的均值和最大压力的增加;压力信号的概率密度(PDF)大部分呈双峰分布,也存在单峰和多峰分布;差压信号的概率密度符合正态分布,其功率谱密度同压力信号相比具有频率波动范围宽、幅值小的特点.     

Short-range order and F ion diffusion inside the Pb1 − xAlxF2 + x solid solution Part II: Al NMR investigation and proposal of clustering process

A ²⁷Al nuclear magnetic resonance (NMR) investigation at room temperature of the Pb_{1 − x}Al_xF_{2 + x} (0 ≤ x ≤ 0.12) solid solution and of the ordered Pb₉Al₂F₂₄ phase is carried out. Two different types of aluminium ions are identified and their ratio is determined as a function of x. A clustering process based on the formation of column clusters, more and more extended when x increases, is proposed on the basis of results issued from the ¹⁹F (Part I) and ²⁷Al NMR investigations.     

Tetraarylester der μ-Imidodiphosphorsäure und ihre Thioderivate — Strukturuntersuchungen

Tetraarylesters of μ-Imido-Diphosphoric Acid and its Thio Derivatives — Structure Investigations New O,O′,O″,O?-tetratolyl- and ditolyl-diphenylesters of the μ-imido-diphosphoric acid and its mono and dithio derivatives were synthesized, compared with the corresponding tetraphenylesters and investigated by ¹H, ¹³C, and ³¹P NMR spectroscopy and X-ray crystal structure analysis. Structures of the O,O′,O″,O?-tetrakis-(2-methyl-phenyl)-μ-imidodiphosphate, 1b , as well as of the corresponding ortho-, meta- and para-tolylesters of the μ-imido-monothiodiphosphoric acid ( 2a , 2b , 2c ) were determined. All the compounds form dimers via N? H…?O hydrogen bonds in the crystal as well as in nonpolar solvents. The distances around the phosphorus atoms rise with decreasing electronegativity of the phosphorus substituents. Signs of the ²J_{P? N? P} coupling constants were determined by ¹³C{¹H, ³¹P} triple resonance experiments for some compounds. These constants become more negative owing to substitution of a phosphoryl by a thiophosphoryl group.     

Calorimetric study on the solubilization of some primary alcohols by reversed AOT micelles

A calorimetric method to evaluate, at the same time, the distribution constant and the standard enthalpy of transfer of a solute partitioned between organic phase and reversed micelles is proposed. The method was applied to the partition of methanol, 1-propanol and 1-pentanol between n-heptane and AOT reversed micelles containing water at 25°C. The results show that the distribution constant decreases as the alcohol alkyl chain length increases and that the solubilization site can change as the water content of reversed AOT micelles increases. In particular, at sufficiently high water content, methanol seems to be preferably solubilized in the aqueous pseudophase whereas 1-pentanol prefers always the palisade layer as site of solubilization.In part from Doctor in Biology thesis of F. Pinio, University of Palermo, Italy.     

Thermal stabilities,electronic properties and structures of metformin-metal complexes

The atomic superposition and electron delocalization molecular orbital (ASED-MO) theory was used to calculate structures and relative stabilities of metformin-metal complexes. The relative stabilities and decomposition pathways were discussed in terms of bond order, binding energy and the nature of charge on the central metal atom. The electronic transitions and their energy gaps were also studied. The optimization of the structures shows that the most stable state is distorted from planarity for Co^II and Ni^II complexes.     

Spectrothermal investigation of the decomposition course of lanthanum acetate hydrate

Thermogravimetry, differential thermal, X-ray diffraction and infrared spectroscopy analyses showed La(CH₃COO)₃·1.5H₂O to decompose completely at 700°C yielding La₂O₃. The results revealed that the compound dehydrates in two steps at 130 and 180°C, and recrystallizes at 210°C. Water thus produced hydrolyzes surface acetates (at 310°C), releasing acetic acid into the gas phase. At 334°C, the anhydrous acetate releases gas phase CH₃COCH₃ to give La₂(CO₃)₃ residue, which decomposes to La₂O₂(CO₃) via the intermediate La₂O(CO₃)₂. On further heating up to 700°C, La₂O₃ is formed. IR spectroscopy of the gaseous products indicated a chemical reactivity at gas/solid interfaces formed throughout the decomposition course. As a result, CH₃COCH₃ was involved in a surface-mediated, bimolecular reaction, releasing CH₄ and C₄H₈ (isobutene) into the gas phase. Non-isothermal kinetic parameters, the rate constantk, frequency factorA, and activation energy ΔE, were calculated on the basis of temperature shifts experienced in the thermal processes encountered, at various heating rates (2–20 deg·min^?1).