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。     

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.     

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).     

Reaction of 3,3-dichloropentane-2,4-dione with aromatic aldehydes under the conditions of Darzens reaction

3,3-Dichloropentane-2,4-dione reacts with aromatic aldehydes under the conditions of Darzens reaction to give 4-acetoxy-4-aryl-3,3-dichlorobutan-2-ones, the products of insertion into the -C-C bond. The reaction of ethyl dichloroacetylacetate with benzaldehyde yields a derivative of tricyclo[5.1.0.0^3,5]octane, rather than 2,6-bis(1-chlorobenzylidene)cyclohexane-1,4-dione, as the by-product.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1294–1298, July, 1995.     

巢湖主要入湖河道磷的污染现状

为了解巢湖主要入湖河道中总磷的污染状况,进行了为期三年每月一次的污染调查,十五里河、南淝河、双桥河,污染较重,超出了(GH281-1999)《地表水环境质量标准》的V娄标准。污染主要来自工业废水、生活污水、和农业面源。认为只有开展农业面源污染治理,城市环境综合整治,城市环境综合整治,加强和削减农业化肥的使用量,使得入湖河道水质变好,巢湖的富营养化才能得到控制。     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.