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The risk posed by the quantity of heavy metal lead present in Ca supplements is of grave concern. Some lead levels have been measured up to the extent of regulatory limit set by the United States. Calcium supplements inevitably get contaminated with lead as both are naturally occurring elements having the same charge density. Therefore, it is imperative to indicate the level of this toxic metal in these supplements in order to create awareness among consumers. The calcium in the supplements is derived from natural as well as synthetic/refined sources (chelated or non-chelated). In this study, a sophisticated analytical technique, atomic absorption spectrometer (both with FAAS and GFAAS modes of atomization), was used for the purpose of analyzing Pb contents in 27 commonly used Ca supplements manufactured by different national and multinational companies. The daily intake of lead through these supplements was calculated. Only 10% of the calcium supplements analyzed met the criteria of acceptable Pb levels (1.5 μg/daily dose) in supplements/consumer products set by the United States. It was also found that Pb intake was highest in chelated calcium supplements whereas lowest through calcium supplements with vitamin D formulation. The Pb concentration in calcium supplements was significantly increased (p < 0.001) according to their composition. In order to validate our results from the study conducted, IAEA-certified reference material (animal bone, H-5) was analyzed for Pb levels. The limit of detection of the method used was 0.05 μg/g and a 95% lead recovery of IAEA-certified reference material (animal bone, H-5).

Let C be a class of algebras of a given fixed type τ . Associated with the type is a first order language L τ . One can then ask the question, when is the class C axiomatisable by sentences of L τ ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a pomonoid S (that is, a monoid S equipped with a partial order compatible with the binary operation). We aim to determine the pomonoids S such that certain categorically defined classes are axiomatisable. The classes we consider are the free S-posets, the projective S-posets and classes arising from flatness properties. Some of these cases have been studied in a recent article by Pervukhin and Stepanova. We present some general strategies to determine axiomatisability, from which their results for the classes of weakly po-flat and po-flat S-posets will follow. We also consider a number of classes not previously examined.

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A monoid S satisfies Condition (A) if every locally cyclic left S-act is cyclic. This condition first arose in Isbell's work on left perfect monoids, that is, monoids such that every left S-act has a projective cover. Isbell showed that S is left perfect if and only if every cyclic left S-act has a projective cover and Condition (A) holds. Fountain built on Isbell's work to show that S is left perfect if and only if it satisfies Condition (A) together with the descending chain condition on principal right ideals, MR. We note that a ring is left perfect (with an analogous definition) if and only if it satisfies MR. The appearance of Condition (A) in this context is, therefore, monoid specific. Condition (A) has a number of alternative characterisations, in particular, it is equivalent to the ascending chain condition on cyclic subacts of any left S-act. In spite of this, it remains somewhat esoteric. The first aim of this paper is to investigate the preservation of Condition (A) under basic semigroup-theoretic constructions. Recently, Khosravi, Ershad and Sedaghatjoo have shown that every left S-act has a strongly flat or Condition (P) cover if and only if every cyclic left S-act has such a cover and Condition (A) holds. Here we find a range of classes of S-acts $\mathcal{C}$ such that every left S-act has a cover from $\mathcal{C}$ if and only if every cyclic left S-act does and Condition (A) holds. In doing so we find a further characterisation of Condition (A) purely in terms of the existence of covers of a certain kind. Finally, we make some observations concerning left perfect monoids and investigate a class of monoids close to being left perfect, which we name left$\mathcal{IP}$a-perfect.