Classification of finite congruence-simple semirings with zero

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We also investigate those subsemirings further, addressing e.g. the question of isomorphy.Comment: 16 page

On the rank of semimodules over semirings

In this paper we investigate conditions on a semiring $S$ such that there are semimodules over $S$ with bases of different length. This includes and generalizes corresponding results on rings, in particular one due to P. Dubreil

Dicarboxylic acids, short-chained – Determination of oxalic acid, malonic acid, succinic acid, glutaric acid and adipic acid in the workplace air using ion chromatography (IC)

The analytical method described here permits the determination of five linear chain aliphatic dicarboxylic acids with 2 to 6 carbon atoms and terminal carboxy groups occurring as inhalable particles in workplace air. The concentration range covers one tenth up to twice the currently valid Occupational Exposure Limit Value (OELV) in Germany, which is 1 mg/m3 for oxalic acid and 2 mg/m3 for succinic, glutaric and adipic acid (inhalable fraction). The peak limitation with an excursion factor of 2 can also be checked. At the moment, there is no OELV for malonic acid, so the same concentration range has been considered as for oxalic acid. Sampling is performed using a flow-regulated pump to draw a defined volume of air through a glass fibre filter, which is alkaline-impregnated with sodium carbonate and inserted in a GSP sampling system. The volumetric flow rate is 10 l/min. For sampling, 2 hours or 15 minutes can be used. The collected dicarboxylic acid deposited on the filter is extracted by means of an aqueous sodium carbonate/sodium hydroxide solution and analysed by means of ion chromatography using a conductivity detector. Quantitative determination is based on multiple-point calibrations with external standards. For an air sample volume of 1200 litres, the relative limit of quantification (LOQ) is in the range from 0.0002 mg/m3 for oxalic acid and 0.0009 mg/m3 for succinic acid. With LOQs less than 0.0076 mg/m3, the measurement of the short-term exposure limit (STEL) is also enabled with an air sample volume of 150 litres. The recoveries of the five dicarboxylic acids range from 96% to 110% and the expanded uncertainty is less than 29%

Simulations of Weighted Tree Automata

Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noetherian semirings, semiring of natural numbers) that all equivalent wta M and N can be joined by a finite chain of simulations. More precisely, in all mentioned cases there exists a single wta that simulates both M and N. Those results immediately yield decidability of equivalence provided that the semiring is finitely (and effectively) presented.Comment: 17 pages, 2 figure