Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Extraction of Tschebysheff design data for the low pass dielectric multilayer

The extraction of design data for the lowpass dielectric multilayer according to Tschebysheff performance is described. The extraction proceeds initially by analogy with electric-circuit design, and can then be given numerical refinement which is also described. Agreement with the Tschebysheff desideratum is satisfactory. The multilayers extracted by this procedure are of fractional thickness, symmetric with regard to their central layers.

Using deuterated PAH amendments to validate chemical extraction methods to predict PAH bioavailability in soils

Validating chemical methods to predict bioavailable fractions of polycyclic aromatic hydrocarbons (PAHs) by comparison with accumulation bioassays is problematic. Concentrations accumulated in soil organisms not only depend on the bioavailable fraction but also on contaminant properties. A historically contaminated soil was freshly spiked with deuterated PAHs (dPAHs). dPAHs have a similar fate to their respective undeuterated analogues, so chemical methods that give good indications of bioavailability should extract the fresh more readily available dPAHs and historic more recalcitrant PAHs in similar proportions to those in which they are accumulated in the tissues of test organisms. Cyclodextrin and butanol extractions predicted the bioavailable fraction for earthworms (Eisenia fetida) and plants (Lolium multiflorum) better than the exhaustive extraction. The PAHs accumulated by earthworms had a larger dPAH:PAH ratio than that predicted by chemical methods. The isotope ratio method described here provides an effective way of evaluating other chemical methods to predict bioavailability.

Model inter-comparison between statistical and dynamic model assessments of the long-term stability of blanket peat in Great Britain (1940-2099)

We compared output from 3 dynamic process-based models (DMs: ECOSSE, MILLENNIA and the Durham Carbon Model) and 9 bioclimatic envelope models (BCEMs; including BBOG ensemble and PEATSTASH) ranging from simple threshold to semi-process-based models. Model simulations were run at 4 British peatland sites using historical climate data and climate projections under a medium (A1B) emissions scenario from the 11-RCM (regional climate model) ensemble underpinning UKCP09. The models showed that blanket peatlands are vulnerable to projected climate change; however, predictions varied between models as well as between sites. All BCEMs predicted a shift from presence to absence of a climate associated with blanket peat, where the sites with the lowest total annual precipitation were closest to the presence/absence threshold. DMs showed a more variable response. ECOSSE predicted a decline in net C sink and shift to net C source by the end of this century. The Durham Carbon Model predicted a smaller decline in the net C sink strength, but no shift to net C source. MILLENNIA predicted a slight overall increase in the net C sink. In contrast to the BCEM projections, the DMs predicted that the sites with coolest temperatures and greatest total annual precipitation showed the largest change in carbon sinks. In this model inter-comparison, the greatest variation in model output in response to climate change projections was not between the BCEMs and DMs but between the DMs themselves, because of different approaches to modelling soil organic matter pools and decomposition amongst other processes. The difference in the sign of the response has major implications for future climate feedbacks, climate policy and peatland management. Enhanced data collection, in particular monitoring peatland response to current change, would significantly improve model development and projections of future change.

Assessing the vulnerability of blanket peat to climate change using an ensemble of statistical bioclimatic envelope models

We assessed the vulnerability of blanket peat to climate change in Great Britain using an ensemble of 8 bioclimatic envelope models. We used 4 published models that ranged from simple threshold models, based on total annual precipitation, to Generalised Linear Models (GLMs, based on mean annual temperature). In addition, 4 new models were developed which included measures of water deficit as threshold, classification tree, GLM and generalised additive models (GAM). Models that included measures of both hydrological conditions and maximum temperature provided a better fit to the mapped peat area than models based on hydrological variables alone. Under UKCIP02 projections for high (A1F1) and low (B1) greenhouse gas emission scenarios, 7 out of the 8 models showed a decline in the bioclimatic space associated with blanket peat. Eastern regions (Northumbria, North York Moors, Orkney) were shown to be more vulnerable than higher-altitude, western areas (Highlands, Western Isles and Argyle, Bute and The Trossachs). These results suggest a long-term decline in the distribution of actively growing blanket peat, especially under the high emissions scenario, although it is emphasised that existing peatlands may well persist for decades under a changing climate. Observational data from long-term monitoring and manipulation experiments in combination with process-based models are required to explore the nature and magnitude of climate change impacts on these vulnerable areas more fully.

Keyphrase extraction by synonym analysis of n-grams for e-journals categorisation

Automatic keyword or keyphrase extraction is concerned with assigning keyphrases to documents based on words from within the document. Previous studies have shown that in a significant number of cases author-supplied keywords are not appropriate for the document to which they are attached. This can either be because they represent what the author believes the paper is about not what it actually is, or because they include keyphrases which are more classificatory than explanatory e.g., “University of Poppleton” instead of “Knowledge Discovery in Databases”. Thus, there is a need for a system that can generate appropriate and diverse range of keyphrases that reflect the document. This paper proposes a solution that examines the synonyms of words and phrases in the document to find the underlying themes, and presents these as appropriate keyphrases. The primary method explores taking n-grams of the source document phrases, and examining the synonyms of these, while the secondary considers grouping outputs by their synonyms. The experiments undertaken show the primary method produces good results and that the secondary method produces both good results and potential for future work.

Colon extended physiologically based extraction test (CE-PBET) increases bioaccessibility of soil-bound PAH

Assessment of the risk to human health posed by contaminated land may be seriously overestimated if reliant on total pollutant concentration. In vitro extraction tests, such as the physiologically based extraction test (PBET), imitate the physicochemical conditions of the human gastro-intestinal tract and offer a more practicable alternative for routine testing purposes. However, even though passage through the colon accounts for approximately 80% of the transit time through the human digestive tract and the typical contents of the colon in vivo are a carbohydrate-rich aqueous medium with the potential to promote desorption of organic pollutants, PBET comprises stomach and small intestine compartments only. Through addition of an eight-hour colon compartment to PBET and use of a carbohydrate-rich fed-state medium we demonstrated that colon-extended PBET (CE-PBET) in- creased assessments of soil-bound PAH bioaccessibility by up to 50% in laboratory soils and a factor of 4 in field soils. We attribute this increased bioaccessibility to a combination of the additional extraction time and the presence of carbohydrates in the colon compartment, both of which favor PAH desorption from soil. We propose that future assessments of the bioaccessibility of organic pollutants in soils using physiologically based extraction tests should have a colon compartment as in CE-PBET.

Co-fuelling of peat with meat and bone meal in a pilot scale bubbling bed reactor

Co-combustion performance trials of Meat and Bone Meal (MBM) and peat were conducted using a bubbling fluidized bed (BFB) reactor. In the combustion performance trials the effects of the co-combustion of MBM and peat on flue gas emissions, bed fluidization, ash agglomeration tendency in the bed and the composition and quality of the ash were studied. MBM was mixed with peat at 6 levels between 15% and 100%. Emissions were predominantly below regulatory limits. CO concentrations in the flue gas only exceeded the 100 mg/m3 limit upon combustion of pure MBM. SO2 emissions were found to be over the limit of 50 mg/m3, while in all trials NOx emissions were below the limit of 300 mg/m3. The HCl content of the flue gases was found to vary near the limit of 30 mg/m3. VOCs however were within their limits. The problem of bed agglomeration was avoided when the bed temperature was about 850 °C and only 20% MBM was co-combusted. This study indicates that a pilot scale BFB reactor can, under optimum conditions, be operated within emission limits when MBM is used as a co-fuel with peat. This can provide a basis for further scale-up development work in industrial scale BFB applications

Optimisation of the aqueous extraction conditions of phenols from meadowsweet (Filipendula ulmaria L.) for incorporation into beverages

Meadowsweet was extracted in water at a range of temperatures (60–100 °C), and the total phenols, tannins, quercetin, salicylic acid content and colour were analysed. The extraction of total phenols followed pseudo first-order kinetics, the rate constant (k) increased from 0.09 ± 0.02 min−1 to 0.44 ± 0.09 min−1, as the temperature increased from 60 to 100 °C. An increase in temperature from 60 to 100 °C increased the concentration of total phenols extracted from 39 ± 2 to 63 ± 3 mg g−1 gallic acid equivalents, although it did not significantly affect the proportion of tannin and non-tannin fractions. The extraction of quercetin and salicyclic acid from meadowsweet also followed pseudo first-order kinetics, the rate constant of both compounds increasing with an increase in temperature up until 90 °C. Therefore, the aqueous extraction of meadowsweet at temperatures at or above 90 °C for 15 min yields extracts high in phenols, which may be added to beverages.

Optimisation of the extraction and processing conditions of chamomile (Matricaria chamomilla L.) for incorporation into a beverage

The total phenols, apigenin 7-glucoside, turbidity and colour of extracts from dried chamomile flowers were studied with a view to develop chamomile extracts with potential anti-inflammatory properties for incorporation into beverages. The extraction of all constituents followed pseudo first-order kinetics. In general, the rate constant (k) increased as the temperature increased from 57 to 100 °C. The turbidity only increased significantly between 90 and 100 °C. Therefore, aqueous chamomile extracts had maximum total phenol concentration and minimum turbidity when extracted at 90 °C for 20 min. The effect of drying conditions on chamomile extracted using these conditions was determined. A significant reduction in phenol concentration, from 19.7 ± 0.5 mg/g GAE in fresh chamomile to 13 ± 1 mg/g GAE, was found only in the plant material oven-dried at 80 °C (p ⩽ 0.05). The biggest colour change was between fresh chamomile and that oven-dried at 80 °C, followed by samples air-dried. There was no significant difference in colour of material freeze-dried and oven-dried at 40 °C.

Spatial and temporal modeling of community non-timber forest extraction

This paper examines the interaction of spatial and dynamic aspects of resource extraction from forests by local people. Highly cyclical and varied across space and time, the patterns of resource extraction resulting from the spatial–temporal model bear little resemblance to the patterns drawn from focusing either on spatial or temporal aspects of extraction alone. Ignoring this variability inaccurately depicts villagers’ dependence on different parts of the forest and could result in inappropriate policies. Similarly, the spatial links in extraction decisions imply that policies imposed in one area can have unintended consequences in other areas. Combining the spatial–temporal model with a measure of success in community forest management—the ability to avoid open-access resource degradation—characterizes the impact of incomplete property rights on patterns of resource extraction and stocks.

Synthesis and evaluation of lipophilic BTBP ligands for An/Ln separation in nuclear waste treatment: the effect of alkyl substitution on extraction properties and implications for ligand design

Four new 6,6′-bis(1,2,4-triazin-3-yl)-2,2′-bipyridine (BTBP) ligands, which contain either additional alkyl groups on the pyridine rings or seven-membered aliphatic rings attached to the triazine rings, have been synthesized, and the effects of the additional alkyl substitution in the 4- and 4′-positions of the pyridine rings on their extraction properties with LnIII and AnIII cations in simulated nuclear waste solutions have been studied. The speciation of ligand 13 with some trivalent lanthanide nitrates was elucidated by 1H NMR spectroscopic titrations and ESI-MS. Although 13 formed both 1:1 and 1:2 complexes with LaIII and YIII, only 1:2 complexes were observed with EuIII and CeIII. Quite unexpectedly, both alkyl-substituted ligands 12 and 13 showed lower solubilities in certain diluents than the unsubstituted ligand CyMe4-BTBP. Compared to CyMe4-BTBP, alkyl-substitution was found to decrease the rates of metal-ion extraction of the ligands in both 1-octanol and cyclohexanone. A highly efficient (DAm > 10) and selective (SFAm/Eu > 90) extraction was observed for 12 and 13 in cyclohexanone and for 13 in 1-octanol in the presence of a phase-transfer agent. The implications of these results for the design of improved extractants for radioactive waste treatment are discussed.