Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

Analysis of shade and temperature effects on assimilate partitioning in the everbearing strawberry 'Everest' as the basis for optimised long-season fruit production

Growth patterns and cropping were evaluated over the season for the everbearing strawberry 'Everest' at a range of temperatures (15-27degreesC) in two light environments (ambient and 50% shade). The highest yield was recorded for unshaded plants grown at 23degreesC, but the optimum temperature for vegetative growth was 15degreesC. With increasing temperature fruit number increased, but fruit weight decreased. Fruit weight was also significantly reduced by shade, and although 'Everest' showed a degree of shade tolerance in vegetative growth, yield was consistently reduced by shade. Shade also reduced the number of crowns developed by the plants over the course of the season, emphasising that crown number was ultimately the limiting factor for yield potential. We conclude that, in contrast to Junebearers which partition more assimilates to fruit at temperatures around 15degreesC (Le Miere et al., 1998), optimised cropping in the everbearer 'Everest' is achieved at the significantly higher temperature of 23degreesC. These findings have significance for commercial production, in which protection tends to reduce light levels but increase average temperature throughout the season.

Photosynthetic activity and early growth of four Cacao genotypes as influenced by different shade regimes under West African dry and wet season conditions

The physiological performance of four cacao clones was examined under three artificial shade regimes over the course of a year in Ghana. Plants under light shade had significantly higher photosynthetic rates in the rainy seasons whereas in the dry season there was a trend of higher photosynthetic rates under heavy shade. The results imply that during the wet seasons light was the main limiting factor to photosynthesis whereas in the dry season vapour pressure deficit was the major factor limiting photosynthesis through stomatal regulation. Leaf area was generally lower under heavier shade but the difference between shade treatments varied between clones. Such differences in leaf area allocation appeared to underlie genotypic differences in final biomass production in response to shade. The results suggest that shade for young cacao should be provided based on the current ambient environment and genotype.

The influence of shade and organic fertilizer treatments on the physiology and establishment of Theobroma cacao clones

Aims: This experiment aimed to determine whether the soil application of organic fertilizers can help the establishment of cacao and whether shade alters its response to fertilizers. Study Design: The 1.6 ha experiment was conducted over a period of one crop year (between April 2007 and March 2008) at the Cocoa Research Institute of Ghana. It involved four cacao genotypes (T 79/501, PA 150, P 30 [POS] and SCA 6), three shade levels (‘light’, ‘medium’ and ‘heavy’) and two fertilizer treatments (‘no fertilizer’, and ‘140 kg/ha of cacao pod husk ash (CPHA) plus poultry manure at 1,800 kg/ha). The experiment was designed as a split-plot with the cacao genotypes as the main plot factor and shade x fertilizer combinations as the sub-plots. Methodology: Gliricidia sepium and plantains (Musa sapientum) were planted in different arrangements to create the three temporary shade regimes for the cacao. Data were collected on temperature and relative humidity of the shade environments, initial soil nutrients, soil moisture, leaf N, P and K+ contents, survival, photo synthesis and growth of test plants. Results: The genotypes P 30 [POS] and SCA 6 showed lower stomatal conductance under non-limiting conditions. In the rainy seasons, plants under light shade had the highest CO2 assimilation rates. However, in the dry season, plants under increased shade recorded greater photosynthetic rates (P = .03). A significant shade x fertilizer interaction (P = .001) on photosynthesis in the dry season showed that heavier shade increases the benefits that young cacao gets from fertilizer application in that season. Conversely, shade should be reduced during the wet seasons to minimize light limitation to assimilation. Conclusion: Under ideal weather conditions young cacao exhibits genetic variability on stomatal conductance. Also, to optimize plant response to fertilizer application shade must be adjusted taking the prevailing weather condition into account.

Food-chain transfer of zinc from contaminated Urtica dioica and Acer pseudoplatanus L. to Microlophium carnosum and Drepanosiphum platanoidis Schrank

This study examines the food-chain transfer of Zn from two plant species, Urtica dioica (stinging nettle) and Acer pseudoplatanus (sycamore maple), into their corresponding aphid species, Microlophium carnosum and Drepanosiphum platanoidis. The plants were grown in a hydroponic system using solutions with increasing concentrations of Zn from 0.02 to 41.9 mg Zn/l. Above-ground tissue concentrations in U. dioica and M. carnosum increased with increasing Zn exposure (p < 0.001). Zn concentrations in A. pseudoplatanus also increased with solution concentration from the control to the 9.8 mg Zn/l solution, above which concentrations remained constant. Zn concentrations in both D. platanoidis and the phloem tissue of A. pseudoplatanus were not affected by the Zn concentration in the watering solution. It appears that A. pseudoplatanus was able to limit Zn transport in the phloem, resulting in constant Zn exposure to the aphids. Zn concentrations in D. platanoidis were around three times those in M. carnosum. Concentrations of Zn in two aphid species are dependant on species and exposure.

The effect of drying and urea treatment on nutritional and anti-nutritional components of browses collected during wet and dry seasons

Fibre, crude protein and tannin concentrations were measured in browse species from the semi-arid region of Northeast Brazil during the dry and wet seasons. The effects of oven-, sun- and shade-drying and of urea treatment were also determined. Crude protein (CP) content varied from 103 to 161 g/kg dry matter (DM) and the browses had similar CP content in the two seasons (during 2002) (102-161 and 107-153 g/kg DM in the wet and dry seasons, respectively). Total tannin concentrations ranged from 13 to 201 g/kg DM amongst the browses and were higher in the dry season. A 30-d treatment with urea reduced extractable tannins significantly (P < 0.05). The urea treatment was also most effective at reducing the in vitro effects of tannins compared to the other drying treatments. This was demonstrated by measuring the effect of polyethylene glycol (PEG) on gas production. Addition of PEG increased gas production of oven- (81.4%), sun- (78.5%) and shade-dried (76.7%) samples much more compared to urea treated samples (10.9%). (c) 2005 Elsevier B.V. All rights reserved.

Farm level tree planting in Pakistan: The role of farmers' perceptions and attitudes

The low proportion of forested land and continuing degradation of existing forest cover are serious threats to the sustainability of forestry in Pakistan. Farm forestry has been identified as a feasible solution, particularly in the plain areas. Applying the Theory of Planned Behaviour in a survey of 124 farmers in Dera Ismail Khan district of Pakistan's North West Frontier Province showed that farmers' willingness to grow trees on their farms is a function of their attitudes towards the advantages and disadvantages of growing trees, their perception of the opinions of salient referents and factors that encourage and discourage farm level tree planting. Farmers viewed farm forestry as economically beneficial and environmentally friendly. Tree planting was perceived as increasing income, providing wood for fuel and furniture, controlling erosion and pollution and providing shade for humans and animals. Farmers saw hindrance in agricultural operations and the harbouring of insects, pests and diseases as negative impacts of tree planting; however, these were outweighed by their perceptions of positive impacts. Tree growing decisions of farmers were influenced by the opinions of family members, owners/tenants, fellow farmers and village elders. The factors that significantly predicted farm level tree planting were availability of barren land, lack of markets, lack of nurseries and damage caused by animals and humans. Farm forestry programmes are more likely to be successful if they acknowledge and address the factors which underlie farmers' reasons for planting or not planting trees.

Persistence of varicella-zoster virus viraemia in patients with herpes zoster.

BACKGROUND: Herpes zoster is caused by the reactivation of varicella-zoster virus from sensory neurons. The commonest complication following zoster is chronic pain termed post herpetic neuralgia. OBJECTIVES: To investigate the dynamics of VZV viraemia and viral load following the resolution of zoster and its relationship to PHN development. STUDY DESIGN: Blood samples were collected at baseline, 1 month, 3 months and 6 month from a prospective study of 63 patients with active zoster. Quantification of VZV DNA in whole blood was performed using a real-time PCR assay. RESULTS: During acute zoster, all patients had detectable VZV DNA in their blood. VZV DNA remained detectable in the blood of 91% of patients at 6 months although levels declined significantly (p<0.0001). A history of prodromal symptoms (p=0.005) and severity of pain at baseline (p=0.038) as well as taking antivirals (p=0.046) and being immunocompromised (p=0.043) were associated, with longer time to recovery from PHN. Viral DNA loads were consistently higher in patients with risk factors for PHN and higher viral DNA loads over time were associated with longer time to recovery (p=0.058 overall and 0.038 in immunocompetent). CONCLUSIONS: Based on these observations we hypothesise that VZV replication persists following acute shingles and that higher viral DNA loads contribute to the risk factors for PHN.

Evaluation of the time resolved fluorescence immunoassay (TRFIA) for the detection of varicella zoster virus (VZV) antibodies following vaccination of healthcare workers

Determination of varicella zoster virus (VZV) immunity in healthcare workers without a history of chickenpox is important for identifying those in need of vOka vaccination. Post immunisation, healthcare workers in the UK who work with high risk patients are tested for seroconversion. To assess the performance of the time-resolved fluorescence immunoassay (TRFIA) for the detection of antibody in vaccinated as well as unvaccinated individuals, a cut-off was first calculated. VZV-IgG specific avidity and titres six weeks after the first dose of vaccine were used to identify subjects with pre-existing immunity among a cohort of 110 healthcare workers. Those with high avidity (≥60%) were considered to have previous immunity to VZV and those with low or equivocal avidity (<60%) were considered naive. The former had antibody levels ≥400mIU/mL and latter had levels <400mIU/mL. Comparison of the baseline values of the naive and immune groups allowed the estimation of a TRFIA cut-off value of >130mIU/mL which best discriminated between the two groups and this was confirmed by ROC analysis. Using this value, the sensitivity and specificity of TRFIA cut-off were 90% (95% CI 79-96), and 78% (95% CI 61-90) respectively in this population. A subset of samples tested by the gold standard Fluorescence Antibody to Membrane Antigen (FAMA) test showed 84% (54/64) agreement with TRFIA.

Long-term acclimation of leaf production, development, longevity and quality following 3 yr exposure to free-air CO2 enrichment during canopy closure in Populus

The effects of elevated CO2 on leaf development in three genotypes of Populus were investigated during canopy closure, following exposure to elevated CO2 over 3 yr using free-air enrichment.• Leaf quality was altered such that nitrogen concentration per unit d. wt (Nmass) declined on average by 22 and 13% for sun and shade leaves, respectively, in elevated CO2. There was little evidence that this was the result of ‘dilution’ following accumulation of nonstructural carbohydrates. Most likely, this was the result of increased leaf thickness. Specific leaf area declined in elevated CO2 on average by 29 and 5% for sun and shade leaves, respectively.• Autumnal senescence was delayed in elevated CO2 with a 10% increase in the number of days at which 50% leaf loss occurred in elevated as compared with ambient CO2.• These data suggest that changes in leaf quality may be predicted following long-term acclimation of fast-growing forest trees to elevated CO2, and that canopy longevity may increase, with important implications for forest productivity.

Chercher pour or chercher après: arguing the case for contact-induced linguistic innovation in different varieties of French

This paper provides evidence for the claim made in Baetens Beardsmore (1971) that the grammatical collocation "chercher après" «to look for», which is very frequent in Brussels French, is the result of transfer from the contact language, Brussels Dutch. A detailed quantitative analysis of this construction in different varieties of French which have more or less contact with a Germanic language was made to investigate the likelihood of influence from the Germanic substrate. The differences between the meaning of "chercher" and "chercher après" are also analysed in some depth, to find out whether or not the particle is redundant. According to Trudgill (2004) redundant constructions are more often found in contact situations involving long-term, stable contact and child bilingualism. The particle "après" was found to add a particular shade of meaning to "chercher", and is thus not redundant. Therefore no evidence could be obtained from the current data for Trudgill’s (2004) claim.

Land-atmosphere energy exchange in Arctic tundra and boreal forest: available data and feedbacks to climate

This paper summarizes and analyses available data on the surface energy balance of Arctic tundra and boreal forest. The complex interactions between ecosystems and their surface energy balance are also examined, including climatically induced shifts in ecosystem type that might amplify or reduce the effects of potential climatic change. High latitudes are characterized by large annual changes in solar input. Albedo decreases strongly from winter, when the surface is snow-covered, to summer, especially in nonforested regions such as Arctic tundra and boreal wetlands. Evapotranspiration (QE) of high-latitude ecosystems is less than from a freely evaporating surface and decreases late in the season, when soil moisture declines, indicating stomatal control over QE, particularly in evergreen forests. Evergreen conifer forests have a canopy conductance half that of deciduous forests and consequently lower QE and higher sensible heat flux (QH). There is a broad overlap in energy partitioning between Arctic and boreal ecosystems, although Arctic ecosystems and light taiga generally have higher ground heat flux because there is less leaf and stem area to shade the ground surface, and the thermal gradient from the surface to permafrost is steeper. Permafrost creates a strong heat sink in summer that reduces surface temperature and therefore heat flux to the atmosphere. Loss of permafrost would therefore amplify climatic warming. If warming caused an increase in productivity and leaf area, or fire caused a shift from evergreen to deciduous forest, this would increase QE and reduce QH. Potential future shifts in vegetation would have varying climate feedbacks, with largest effects caused by shifts from boreal conifer to shrubland or deciduous forest (or vice versa) and from Arctic coastal to wet tundra. An increase of logging activity in the boreal forests appears to reduce QE by roughly 50% with little change in QH, while the ground heat flux is strongly enhanced.