19,881 research outputs found

    Code loops in dimension at most 8

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    Code loops are certain Moufang 22-loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups. More precisely, code loops are central extensions of the group of order 22 by an elementary abelian 22-group VV in the variety of loops such that their squaring map, commutator map and associator map are related by combinatorial polarization and the associator map is a trilinear alternating form. Using existing classifications of trilinear alternating forms over the field of 22 elements, we enumerate code loops of dimension d=dim(V)ā‰¤8d=\mathrm{dim}(V)\le 8 (equivalently, of order 2d+1ā‰¤5122^{d+1}\le 512) up to isomorphism. There are 767767 code loops of order 128128, and 8082680826 of order 256256, and 937791557937791557 of order 512512

    The Eighteenth Century

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    This chapter has three sections: 1. General and Prose; 2. The Novel; 3. Poetry. Section 1 is by Eliza Oā€™Brien; section 2 is by Elles Smallegoor and Sandro Jung; section 3 is by David E. Shuttleton

    Cost-effectiveness acceptability curves - facts, fallacies and frequently asked questions

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    Cost-effectiveness acceptability curves (CEACs) have been widely adopted as a method to quantify and graphically represent uncertainty in economic evaluation studies of health-care technologies. However, there remain some common fallacies regarding the nature and shape of CEACs that largely result from the textbook illustration of the CEAC. This textbook CEAC shows a smooth curve starting at probability 0, with an asymptote to 1 for higher money values of the health outcome (). But this familiar ogive shape which makes the textbook CEAC look like a cumulative distribution function is just one special case of the CEAC. The reality is that the CEAC can take many shapes and turns because it is a graphic transformation from the cost-effectiveness plane, where the joint density of incremental costs and effects may straddle quadrants with attendant discontinuities and asymptotes. In fact CEACs: (i) do not have to cut the y-axis at 0; (ii) do not have to asymptote to 1; (iii) are not always monotonically increasing in ; and (iv) do not represent cumulative distribution functions (cdfs). Within this paper we present a gallery of CEACs in order to identify the fallacies and illustrate the facts surrounding the CEAC. The aim of the paper is to serve as a reference tool to accompany the increased use of CEACs within major medical journals

    Recognition of finite exceptional groups of Lie type

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    Let qq be a prime power and let GG be an absolutely irreducible subgroup of GLd(F)GL_d(F), where FF is a finite field of the same characteristic as \F_q, the field of qq elements. Assume that Gā‰…G(q)G \cong G(q), a quasisimple group of exceptional Lie type over \F_q which is neither a Suzuki nor a Ree group. We present a Las Vegas algorithm that constructs an isomorphism from GG to the standard copy of G(q)G(q). If Gā‰…Ģø3D4(q)G \not\cong {}^3 D_4(q) with qq even, then the algorithm runs in polynomial time, subject to the existence of a discrete log oracle

    Evaluation of on-farm labour saving strategies for optimisation of herd size that could be managed by one operator

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    End of project reportAlternative milking frequencies Once a day (OAD) milking throughout lactation of a herd (over 2 years, incorporating 24% heifers) resulted in loss in milk solids (MS) production of 17% per cow. Milking cows OAD in their 1st lactation does not adversely impact on milk production in the second lactation, when changed to twice a day (TAD) milking but may lead to a higher mastitis incidence. Changeover in milking frequency in mid lactation resulted in a similar yield of MS per cow for TAD milking for the full lactation (474 kg) and the TAD OAD group (TAD for the first 110 days and OAD for the remainder of the lactation) (469 kg). Thirteen times weekly milking in late lactation (omitting the Sunday evening milking) compared to twice daily milking every day had no effect on milk yield or composition and maximum SCC observed during the trial was 270x103 cells/ml. Once daily milking did not adversely affect the processability of milk. Once daily milking did not significantly increase milk SCC levels. Alternative calf rearing systems The improved efficiency increased herd size may be due to less use of buckets for calf feeding together with more frequent use of teat feeding from a container, automatic feeders and ad libitum feeding A study on OAD calf feeding (whole milk) demonstrated that calves can be reared with a OAD milk feeding system and weaned early (42 days) without adversely affecting performance There was no difference in the live-weight gain of calves on once daily feeding, twice daily feeding or once daily feeding going outdoors after 28 days Calf liveweight gain was greater with once daily feeding with milk replacer compared to once daily feeding with whole milk or once daily feeding with milk replacer going outdoors after 28 days Economic analysis of alternative milking systems When deciding on the type, size and level of technology in the milking parlour, the trade-off between labour requirement and cost and the initial capital investment requirement should be key in making the decision

    Reliability and reproducibility of Atlas information

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    We discuss the reliability and reproducibility of much of the information contained in the Atlas of Finite Groups
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