We study the problem of removing an element from an additive basis in a general abelian group. We introduce analogues of the classical functions X,S and E (defined in the case of N) and obtain bounds on them. Our estimates on the functions SG and EG are valid for general abelian groups G while in the case of XG we show that distinct types of behaviours may occur depending on G.

2008;21(2) S Afr J Clin Nutr a Mushaphi LF, RD, BSc Diet, M(Nut), a Mbhenyane XG, RD, MScDiet, PhD(Nut), b Khoza LB, RN, M(Cur), D Litt et Phil, c Amey AKA, MA, PhD a Department of Nutrition, University of Venda , b Department of Advanced Nursing Science, University of Venda, c Department of Statistics, University of Venda Correspondence to: Ms Lindelani Mushaphi, e-mail: Lindelani.Mushaphi@uni...

Let G be a finite group, and let XG = {x = (x(s,t)) ∈ GZ 2 | x(s,t) = x(s,t−1) · x(s+1,t−1) for all (s, t) ∈ Z}. The compact zero–dimensional set XG carries a natural shift Z2–action σG and the pair ΣG = ( XG, σ G ) is a two–dimensional topological Markov shift. Using recent work by Crandall, Dilcher and Pomerance on the Fermat quotient, we show the following: if G is abelian, and the order of ...

In order to modify the xanthan gum (XG) polysaccharide and to develop the hydrogels meant for the drug delivery, we have prepared XG-g-poly [HEMA-co-AA] superporous hydrogel (SPH) through chemical cross-linking by graft copolymerization of 2-hydroxyethyl methacrylate (HEMA) and acrylic acid (AA) on to XG via redox initiator system of ammonium persulfate (APS) and N, N, N’, N’tetramethylethylene...

The building of civil engineering structures on some soils requires their stabilisation. Although Portland cement is the most used substance to stabilise soils, it associated with a lot environmental concerns. Therefore, very pertinent study more sustainable alternative methodologies replace use cement. Thus, this work analyses ability xanthan-like biopolymer, produced by Stenotrophomonas malto...

Plant xyloglucan endotransglycosylase (XET, EC 2.4.1.207) degrades its substrate by a transglycosylation mechanism while endo-cleaving xyloglucan (XG) molecules at their beta-1,4-linked polyglucosyl main chain and transferring the newly generated reducing chain ends to hydroxyls at C-4 of non-reducing glucosyl ends of the main chains of other XG molecules or of low-Mr XG-fragments (OS). Kinetic...

Hereditary hydrocephalus (Bickers and Adams, 1949) is now known, at least in some families, to be an X-borne condition (Edwards, 1961). A few families with the X-borne type of hydrocephalus have been tested for the Xg blood groups but with no hint of linkage between their two loci (Edwards, 1968; Jabbour, 1968). In a kindred recently reported by Fried (1972) a single X-bome gene has apparently ...

Dogs were bled to a mean arterial pressure of 40 mm. Hg until 10 per cent of the shed blood had automatically reinfused from an elevated reservoir. The remaining blood was then rapidly infused intravenously. The procedure was fatal to all 13 dogs. Arterial blood epinephrine levels were followed during the time of hemorrhage and the posthemorrhagic survival period in 9 of these animals. Arterial...

For each open subgroup G of GL2(Ẑ) containing −I with full determinant, let XG/Q denote the modular curve that loosely parametrizes elliptic curves whose Galois representation, which arises from the Galois action on its torsion points, has image contained in G. Up to conjugacy, we determine a complete list of the 248 such groups G of prime power level for which XG(Q) is infinite. For each G, we...

Ginosar and the first author reduced the surjectivity of the norm map NG for a group G to the surjectivity of the norm maps for its elementary abelian subgroups; more precisely, they proved that NG : R → R G is surjective if and only if NU : R → R U is surjective for every elementary abelian subgroup U of G (see [2, Theorem 1]). The R -linearity of NU implies that it is surjective if and only t...