Fiberings with Fiber RP（κ）

Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP（ξ^κ）] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.     

On Rado's Boundedness Conjecture

We prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We then prove the first nontrivial case of Rado's Boundedness Conjecture: if a₁,a₂, and a₃ are integers, and if for every 24-coloring of the positive integers (or even the nonzero rational numbers) there is a monochromatic solution to the equation a₁x₁+a₂x₂+a₃x₃=0, then for every finite coloring of the positive integers there is a monochromatic solution to a₁x₁+a₂x₂+a₃x₃=0.     

Determination of colloidally-associated polycyclic aromatic hydrocarbons (PAHs) in fresh water using C18 solid phase extraction disks

A new application of reversed-phase octadecyl (C₁₈) solid phase extraction disks has been developed to separate the colloidally-associated polycyclic aromatic hydrocarbons (PAHs) from those that were truly dissolved in the samples of fresh water. A correction for the retention of small amounts of colloidal material on the C₁₈ disks was required, which would have otherwise lead to minor underestimates in the degree of partitioning between the two phases. Using the humic substance Aldrich Humic Acid (AHA) as a model colloid and the 16 PAHs on the US Enrivonmental Protection Agency priority pollutant list, the partitioning coefficients of the PAHs between the colloidal and truly dissolved phases were shown to be proportional to the hydrophobicity of the PAHs, as measured by their octanol water partition coefficients (K_ow). The values for the partition coefficients obtained (cK_doc′) were similar to those previously reported in the literature using alternative methods, confirming that the technique was producing acceptable results. The technique allows the in situ partitioning of PAHs between the truly dissolved and colloidal phases in fresh water bodies to be determined. It will provide an invaluable cross-check of the laboratory-based methods which often require substantial manipulation of the sample and potentially alter the partitioning between the phases.     

A four-parameter partition identity

We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrews in which he considers the generating function for partitions with respect to size, number of odd parts, and number of odd parts of the conjugate. 2000 Mathematics Subject Classification Primary—05A17; Secondary—11P81     

Behaviour of organic pollutants in paper and board samples intended to be in contact with food

This paper deals with the study of volatile compounds present in a set of three paper and board (P&B) samples of different composition, surface treatment, grammage and thickness. The volatile compounds released by the packaging material (P&B) can be trapped on the food and may then affect the safety and health of consumers. To evaluate if the recycled P&B could be used as food packaging material, adsorption studies have been performed with a selection of chemical substances. The adsorption isotherms are provided. Partition coefficients between paper and air have been calculated for a series of volatile compounds used as model compounds to represent different families of contaminants commonly present in P&B. Values from 4 to 3243 were obtained at different temperatures. The analysis of volatile compounds have been carried out by automatic headspace coupled on-line with GC/MS in SIM mode. The results obtained are shown and discussed.     

结合三维静电势参数研究二取代苯的定量结构－疏水性关系

对含有常见取代基的92个二取代苯化合物进行了结构优化和静电势及其导出参数的计算,运用多元线性回归方法对化合物的疏水常数与分子的结构参数进行了关联.结果表明,分子表面负静电势的加和ΣV－S、分子空间内最负的静电势Vmin、表面最大静电势Vs,max以及分子体积V、极性表面积APS和分子的偶极密度μ/V这六个参数,可以很好地用于表达这些化合物疏水性与分子结构间的定量关系,而不用具体考虑分子中极性基团间的相互作用.用建立起来的QSPR(quantitative structure-property relationship)关系式对111个类似化合物的疏水性进行了预测,获得了满意的结果.     

应用反向传播神经网络预测化合物脑血分配系数

选用27种三维结构性质描述符对脑血分配系数预测建立神经网络模型.网络模型选用典型的适合函数逼近的两层结构神经网络对脑血分配系数(lgBB,BB为脑血浓度比)进行预测,计算中采用的模型具有一个双曲正切型激活函数的隐含层和一个线性激活函数的输出层.计算表明,使用小心选择的反向传播神经网络模型对化合物脑血分配系数具有较好的预测能力.     

Vibrational partition functions for H2O derived from perturbation-theory energy levels

Purely vibrational energy levels and partition functions are calculated using three different potential energy surfaces for the H₂O molecule. Results obtained with perturbation-theory, independent-normal-mode (INM), and harmonic approximations are compared with accurate values. For the cases considered here, the expected improvement that perturbation theory provides over the corresponding harmonic treatment is found to be substantial, while the INM approximation leads to results which are worse than the corresponding harmonic ones. In fact, we show that reliable partition functions for these potential surfaces can be obtained when resonance contributions are removed from the perturbation-theory treatment, and we propose a theoretical criterion for deciding when a particular interaction should be treated as resonant.     

Determination of partition behavior of organic surrogates between paperboard packaging materials and air

The suitability of recycled paperboard packaging materials for direct food contact applications is a major area of investigation. Chemical contaminants (surrogates) partitioning between recycled paper packaging and foods may affect the safety and health of the consumer. The partition behavior of all possible organic compounds between cardboards and individual foodstuffs is difficult and too time consuming for being fully investigated. Therefore it may be more efficient to determine these partition coefficients indirectly through experimental determination of the partitioning behavior between cardboard samples and air. In this work, the behavior of organic pollutants present in a set of two paper and board samples intended to be in contact with foods was studied. Adsorption isotherms have been plotted and partition coefficients between paper and air have been calculated as a basis for the estimation of their migration potential into food. Values of partition coefficients (Kpaper/air) from 47 to 1207 were obtained at different temperatures. For the less volatile surrogates such as dibutyl phthalate and methyl stearate higher Kpaper/air values were obtained. The adsorption curves showed that the more volatile substances are partitioning mainly in air phase and increasing the temperature from 70 to 100 degrees C their concentrations in air (Cair) have almost doubled. The analysis of surrogates was performed with a method based on solvent extraction and gas chromatographic-flame ionization detection (GC-FID) quantification.