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In a recent paper, Wang [1981] introduces a p-adic algorithm for the construction of partial fraction decompositions. This differs from the usual p-adic algorithms for factorisation or the computation of greatest common divisors ([Wang, 1978], [Wang, 1980], [Moore & Norman, 1981]) in that the p-adic image is used to reconstruct rational numbers, rather than integers.

Biodiesel is a fuel comprising mono-alkyl esters of medium to long-chain fatty acids derived from vegetable oils or animal fats. Typically, engines operated on soybeanbased biodiesel exhibit higher emissions of oxides of nitrogen (NOx) compared with petroleum diesel. The increase in NOx emissions might be an inherent characteristic of soybean oil's polyunsaturation, because the level of saturation is known to affect the biodiesel's cetane number, which can affect NOx. A feedstock that is mostly monounsaturated (i.e. oleate) helps to balance the tradeoff between cold flow and oxidative stability. Genetic modification has produced a soybean event, designated 335-13, with a fatty acid profile high in oleic acid ([85%) and with reduced palmitic acid (\4%). This high-oleic soybean oil was converted to biodiesel and run in a John Deere 4045T 4.5-L four-stroke, four-cylinder, turbocharged direct-injection diesel engine. The exhaust emissions were compared with those from conventional soybean oil biodiesel and commercial No. 2 diesel fuel. There was a significant reduction in NOx emissions (a = 0.05) using the high-oleic soybean biodiesel compared with regular soybean oil biodiesel. No significant differences were found between the regular and high-oleic biodiesel for unburned hydrocarbon and smoke emissions.

Biodiesel is an alternative fuel for diesel engines that consists of the monoalkyl esters of vegetable oils or animal fats. Currently, most biodiesel consists of methyl esters, which have poor cold-flow properties. Methyl esters of soybean oil will crystallize and plug fuel filters and lines at about 0°C. However, isopropyl esters have better cold-flow properties than methyl esters. This paper describes the production of isopropyl esters and their evaluation in a diesel engine. The effects of the alcohol amount, the catalyst amount, and two different catalysts on producing quality biodiesel were studied. Both sodium isopropoxide and potassium isopropoxide were found to be suitable for use in the transesterification process. A 20:1 alcohol/TG molar ratio and a catalyst amount equal to 1% by weight (based on the TG amount) of sodium metal was the most cost-effective way to produce biodiesel fuel. The emissions from a diesel engine running on isopropyl esters made from soybean oil and yellow grease were investigated by comparing them with No. 2 diesel fuel and methyl esters. For nitrogen oxide emission, the difference between the biodiesel produced from soybean oil and yellow grease was greater than the difference between the methyl and isopropyl esters of both feedstocks. The other emissions from using isopropyl esters were about 50% lower in hydrocarbons, 10-20% lower in carbon monoxide, and 40% lower in smoke number when compared with No. 2 diesel fuel.Paper no. J11013 in JAOCS 82, 845-849 (November 2005).Vegetable oils have been investigated as alternative diesel fuels for many years (1). This research has shown that long-term use of vegetable oils can lead to injector coking, thickening of the crankcase oil, and the formation of in-cylinder deposits, leading to piston ring sticking (2-5). Therefore, vegetable oils are not recommended for use in diesel engines. By transesterifying the vegetable oils, the mono alkyl esters of the FA present in the vegetable oil can be obtained. These esters are commonly referred to as biodiesel. Biodiesel is an alternative fuel that is renewable in the sense that its primary feedstock has a sustainable source. In addition to vegetable oil, some other less expensive feedstocks that can be converted to biodiesel are restaurant waste grease and animal fat.The emissions produced from biodiesel are generally lower than those of petroleum-based diesel fuel. Particulate emissions, soot, unburned hydrocarbons (HC), and carbon monoxide (CO) are lower since biodiesel is an oxygenated fuel. However, emissions of nitrogen oxides (NO x ) are higher (6,7). The cause of the rise in NO x is unclear and is being studied (8-12).One particular problem with biodiesel is its cold-flow properties. At low temperatures, crystallization can occur, which leads to plugging of the fuel filters and lines. Neat biodiesel made with methanol and soybean oil has a pour point (i.e., the lowest temperature at which the fuel is pourable) of −3°C (13). Typically in the United States, biodiesel is blended with diesel...

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