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BACKGROUND: The lesser grain borer, Rhyzopertha dominica (F.), is a highly destructive pest of stored grain that is strongly resistant to the fumigant phosphine (PH3). Phosphine resistance is due to genetic variants at the rph2 locus that alter the function of the dihydrolipoamide dehydrogenase (DLD) gene. This discovery now enables direct detection of resistance variants at the rph2 locus in field populations. RESULTS: A genotype assay was developed for direct detection of changes in distribution and frequency of a phosphine resistance allele in field populations of R. dominica. Beetles were collected from ten farms in south-east Queensland in 2006 and resampled in 2011. Resistance allele frequency increased in the period from 2006 to 2011 on organic farms with no history of phosphine use, implying that migration of phosphine-resistant R. dominica had occurred from nearby storages. CONCLUSION: Increasing resistance allele frequencies on organic farms suggest local movement of beetles and dispersal of insects from areas where phosphine has been used. This research also highlighted for the first time the utility of a genetic DNA marker in accurate and rapid determination of the distribution of phosphine-resistant insects in the grain value chain. Extending this research over larger landscapes would help in identifying resistance problems and enable timely pest management decisions. © 2013 Society of Chemical Industry © 2013 Society of Chemical Industry 69 6 June 2013 10.1002/ps.3514 Rapid Report Rapid Report © 2013 Society of Chemical Industry.

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Naked oat (Avena sativa f.sp. nuda L.) is the highest quality cereal in northern growing conditions. However the cultivation area of naked oat is remarkably small. Major challenges for naked oat production are to observe its nakedness. The caryopsis of naked oat is sensitive to mechanical damage at harvest, especially at high grain moisture content. The greater the grain moisture content of naked oat at harvest, the more loses of germination capacity was caused by threshing. For producing high quality naked oat seed, it is recommended that harvesting be done at as low grain moisture content as possible. However, if this is not possible, better germination can be ensure with gentle harvest by reducing the cylinder speed. In spite of conventional oat s excellent fat and amino acid composition in animal feed use, as far as nutritional value is concerned, the total energy yield of oat is weaker than other cereals because of the hulls. Also with naked oat the dehulling is not complete, while hull content on different cultivars mostly varied between one to six percent. In addition to genotype, environmental conditions markedly control the expression of nakedness. Thresher settings had only limited effects on hull content. The function of hulls is to protect the groat, but this was confirmed only for Finnish, small grain, cultivar Lisbeth. The oat kernel is generally covered with fine silky hairs termed trichomes. The trichomes of naked oat are partly lost during threshing and handling of grains. Trichomes can cause itchiness in those handling the grains and also accumulate and form fine dust and can block-up machinery. The cultivars differed considerably in pubescence. Some thresher settings, including increased cylinder speed, slightly increased grain polishing such that grains had some areas completely free of trichomes. Adjusting thresher settings was generally not an efficient means of solving the problems associated with naked oat trichomes. The main differences in cultivation costs between naked and conventional oat lie in the amount of seeds required and the drying costs. The main differences affecting the economic result lie in market prices, yield level and feed value. The results indicate that naked oat is financially more profitable than conventional oat, when the crop is sold at a specific price at all yield levels and when the crop is used as feed at highest yield level. At lower yield levels, conventional oat is, in spite of its lower feed value, the more profitable option for feed use. Dehulled oat did not achieve the same economic result as naked oat, as the cost of dehulling, including the hull waste, was considerable. According to this study naked oat can be cultivated successfully under northern conditions, when taking into consideration the soft, naked grain through cultivation chain.

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Spring barley is the most important crop in Finland based on cultivated land area. Net blotch, a disease caused by Pyrenophora teres Drech., is the most damaging disease of barley in Finland. The pressure to improve the economics and efficiency of agriculture has increased the need for more efficient plant protection methods. Development of durable host-plant resistance to net blotch is a promising possibility. However, deployment of disease resistant crops could initiate selection pressure on the pathogen (P. teres) population. The aim of this study was to understand the population biology of P. teres and to estimate the evolutionary potential of P. teres under selective pressure following deployment of resistance genes and application of fungicides. The study included mainly Finnish P. teres isolates. Population samples from Russia and Australia were also included. Using AFLP markers substantial genotypic variation in P. teres populations was identified. Differences among isolates were least within Finnish fields and significantly higher in Krasnodar, Russia. Genetic differentiation was identified among populations from northern Europe and from Australia, and between the two forms P. teres f. teres (PTT, net form of net blotch) and P. teres f. maculata (PTM, spot form of net blotch) in Australia. Differentiation among populations was also identified based on virulence between Finnish and Russian populations, and based on prochloraz (fungicide) tolerance in the Häme region in Finland. Surprisingly only PTT was recovered from Finland and Russia although both forms were earlier equally common in Finland. The reason for the shift in occurrence of forms in Finland remained uncertain. Both forms were found within several fields in Australia. Sexual reproduction of P. teres was supported by recover of both mating types in equal ratio in those areas although the prevalence of sexual mating seems to be less in Finland than in Australia. Population from Krasnodar was an exception since only one mating type was found in there. Based on the substantial high genotypic variation in Krasnodar it was suggested go represent an old P. teres population, whereas the Australian samples were suggested to represent newer populations. In conclusion, P. teres populations are differentiated at several levels. Human assistance in dispersal of P. teres on infected barley seed is obvious and decreases the differentiation among populations. This can increase the plant protection problems caused by this pathogen. P. teres is capable of sexual reproduction in several areas but the prevalence varies. Based on these findings it is apparent that P. teres has the potential to pose more serious problems in barley cultivation if plant protection is neglected. Therefore, good agricultural practices, including crop rotation and the use of healthy seed, are recommended.

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Vasikoiden kasvatus yksilökarsinoissa, imemismahdollisuuden puute maitojuoton yhteydessä sekä pienet juomamäärät ovat tekijöitä, jotka mahdollisesti voivat vähentää vasikoiden hyvinvointia. Vasikoiden kasvatukseen etsitäänkin uusia tapoja, joissa eläinten käyttäytymistarpeet ja hyvinvointi otetaan entistä paremmin huomioon. Tässä väitöskirjassa vasikoiden kasvatusta on tarkasteltu sekä tuotannon että vasikoiden käyttäytymisen ja hyvinvoinnin kannalta. Väitöskirja koostuu kolmesta kokeesta, joista ensimmäisessä tutkittiin vasikoiden kasvatusta ryhmäkarsinoissa ulkona tai sisällä ja vasikoiden kasvatusta sisällä ryhmä- tai yksilökarsinoissa. Toisessa kokeessa vasikoiden annettiin imeä emiään rajoitetusti lypsyn jälkeen viiden tai kahdeksan viikon ajan ja kolmannessa selvitettiin vasikoiden veden juontia, kun vasikat saivat juomarehua vapaasti. Lisäksi kokeiden yhdistetystä aineistosta analysoitiin eri rehujen syöntimäärien suhdetta sekä rehujen vaikutusta kasvuun ennen ja jälkeen maidosta vieroituksen. Tutkimuksessa todettiin, että vasikoita voi ryhmässä kasvattaa kylmissä ja vaihtelevissa sääoloissa ulkona, kunhan ne hoidetaan ja ruokitaan erittäin huolellisesti. Kylmällä ilmalla vasikat saattavat kuitenkin syödä väkirehua vähemmän varsinkin, jos ruokailupaikka on ulkona ja makuualue sisällä. Ryhmässä kasvaneet vasikat aloittivat sekä kuivien rehujen syönnin että märehtimisen nuorempina kuin yksilökarsinassa kasvaneet. Ryhmissä esiintyvää käyttäytymisongelmaa, toisten vasikoiden imemistä, voidaan vähentää hoito- ja ruokintamenetelmillä. Annettaessa vasikoiden imeä emiään rajoitetusti lypsyn jälkeen vasikat oppivat imemään emiään hyvin nopeasti. Lypsytyö vaikeutui muutamien lehmien kohdalla, sillä ne pidättivät maitoa lypsettäessä. Saadessaan imeä rajoitetusti vasikat imivät suurehkoja maitomääriä kerrallaan. Vieroittaminen suurilta maitomääriltä viiden viikon iässä oli kuitenkin liian aikaista, koska vasikat eivät vielä syöneet riittävästi kuivia rehuja. Vieroitus emästä niin viiden kuin kahdeksankin viikon iässä aiheutti vasikoissa levottomuutta ja ääntelyn lisääntymistä. Saadessaan hapatettua juomarehua vapaasti vasikat joivat keskimäärin vain vähän vettä, olipa vesilähteenä avoin ämpäri tai vesinippa. Vasikoiden välillä oli suurta vaihtelua veden juontimäärissä. Viikkoa ennen maidosta vieroitusta vasikat joivat 0-3 l vettä päivässä. Vasikat joivat nipasta kerrallaan vähemmän vettä kuin ämpäristä, ja käyttivät enemmän aikaa päivässä veden juomiseen kuin vesiämpäristä juoneet vasikat. Suurin osa vasikoista joi vettä juomanipoista erikoisella tavalla esimerkiksi painamalla nippaa otsalla ja juomalla tippuvaa vettä. Vesinipat voivat olla siis vasikoille joko vaikeita tai epämukavia käyttää. Vasikoiden juoman maitomäärän lisääntyessä kasvu lisääntyy selvästi. Runsas maidon juominen vähentää kuitenkin kuivien rehujen syöntiä ja vieroitusvaiheessa kasvu voi hidastua. Vasikat olisikin tärkeää vieroittaa vähitellen, ettei muutoksia kasvuun tulisi. Syönti- ja kasvutulokset eivät aina anna oikeaa kuvaa kasvatusmenetelmien eroista eläinten hyvinvoinnin kannalta. Käyttäytyminen on herkkä hyvinvoinnin mittari ja se tulisikin aina huomioida eri kasvatusmenetelmiä arvioitaessa. .

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The sustainability of food production has increasingly attracted the attention of consumers, farmers, food and retailing companies, and politicians. One manifestation of such attention is the growing interest in organic foods. Organic agriculture has the potential to enhance the ecological modernisation of food production by implementing the organic method as a preventative innovation that simultaneously produces environmental and economic benefits. However, in addition to the challenges to organic farming, the small market share of organic products in many countries today and Finland in particular risks undermining the achievement of such benefits. The problems identified as hindrances to the increased consumption of organic food are the poor availability, limited variety and high prices of organic products, the complicated buying decisions and the difficulties in delivering the intangible value of organic foods. Small volumes and sporadic markets, high costs, lack of market information, as well as poor supply reliability are obstacles to increasing the volume of organic production and processing. These problems shift the focus from a single actor to the entire supply chain and require solutions that involve more interaction among the actors within the organic chain. As an entity, the organic food chain has received very little scholarly attention. Researchers have mainly approached the organic chain from the perspective of a single actor, or they have described its structure rather than the interaction between the actors. Consequently, interaction among the primary actors in organic chains, i.e. farmers, manufacturers, retailers and consumers, has largely gone unexamined. The purpose of this study is to shed light on the interaction of the primary actors within a whole organic chain in relation to the ecological modernisation of food production. This information is organised into a conceptual framework to help illuminate this complex field. This thesis integrates the theories and concepts of three approaches: food system studies, supply chain management and ecological modernisation. Through a case study, a conceptual system framework will be developed and applied to a real life-situation. The thesis is supported by research published in four articles. All examine the same organic chains through case studies, but each approaches the problem from a different, complementary perspective. The findings indicated that regardless of the coherent values emphasising responsibility, the organic chains were loosely integrated to operate as a system. The focus was on product flow, leaving other aspects of value creation largely aside. Communication with consumers was rare, and none of the actors had taken a leading role in enhancing the market for organic products. Such a situation presents unsuitable conditions for ecological modernisation of food production through organic food and calls for contributions from stakeholders other than those directly involved in the product chain. The findings inspired a revision of the original conceptual framework. The revised framework, the three-layer framework , distinguishes the different layers of interaction. By gradually enlarging the chain orientation the different but interrelated layers become visible. A framework is thus provided for further research and for understanding practical implications of the performance of organic food chains. The revised framework provides both an ideal model for organic chains in relation to ecological modernisation and demonstrates a situation consistent with the empirical evidence.

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Interference fits are used extensively in aircraft structural joints because of their improved fatigue performance. Recent advances in analysis of these joints have increased understanding of the nonlinear load-contact and load-interfacial slip variations in these joints. Experimental work in these problems is lacking due to difficulties in determining partial contact and partial slip along the pin-hole interface. In this paper, an experimental procedure is enumerated for determining load-contact relations in interference/clearance fits, using photoelastic models and applying a technique for detecting progress of separation/contact up to predetermined locations. The study incorporates a detailed procedure for model making, controlling interference, locating break of contact up to known locations around the interface, estimating optically the degree of interference, determining interfacial friction and evaluating stresses in the sheet. Experiments, simulating joints in large sheets, were carried out under both pin and plate loads. The present studies provide load-separation behavior in interference joint with finite interfacial friction.

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Bellyache bush (Jatropha gossypiifolia L.) is an invasive weed that poses economic and environmental problems in northern Australia. Competition between pasture and bellyache bush was examined in North Queensland using combinations of five pasture treatments (uncut (control); cut as low, medium, and high pasture; and no pasture) and four bellyache bush densities (0, 2, 6 and 12plantsm(-2)) in a buffel grass (Cenchrus ciliaris L.) dominated pasture. The pasture treatments were applied approximately once per year but no treatments were applied directly to the bellyache bush plants. Measurements of bellyache bush flowering, seed formation, and mortality were undertaken over a 9-year period, along with monitoring the pasture basal cover and plant species diversity. Maximum flowering rates of bellyache bush occurred after 9 years (97%) in plots containing no pasture, with the lowest rates of 9% in uncut control plots. Earliest flowering (322 days after planting) and seed formation (411 days) also occurred in plots with no pasture compared with all other pasture treatments (range 1314-1393 days for seed formation to occur). No seeds were produced in uncut plots. At the end of 9 years, mortality rates of bellyache bush plants initially planted averaged 73% for treatments with some pasture compared with 55% under the no-pasture treatment. The percentage of herbaceous plant basal cover in uncut plots was increased 5-fold after 9 years, much greater than the average 2% increase recorded across the low, medium, and high pasture treatments. The number of herbaceous species in uncut plots remained largely unchanged, whereas there was an average reduction of 46% in the cut pasture treatments. Buffel grass remained the species with the greatest basal cover across all cut pasture treatments, followed by sabi grass (Urochloa mosambicensis (Hack.) Dandy) and then red Natal grass (Melinis repens (Willd.) Ziska). These results suggest that grazing strategies that maintain a healthy and competitive pasture layer may contribute to reducing the rate of spread of bellyache bush and complement traditional control techniques such as the use of herbicides.

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Despite compulsory mathematics throughout primary and junior secondary schooling, many schools across Australia continue in their struggle to achieve satisfactory numeracy levels. Numeracy is not a distinct subject in school curriculum, and in fact appears as a general capability in the Australian Curriculum, wherein all teachers across all curriculum areas are responsible for numeracy. This general capability approach confuses what numeracy should look like, especially when compared to the structure of numeracy as defined on standardised national tests. In seeking to define numeracy, schools tend to look at past NAPLAN papers, and in doing so, we do not find examples drawn from the various aspects of school curriculum. What we find are more traditional forms of mathematical worded problems.

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This study analyzes the war-time rations the Finnish soldiers received on the front from 1939 until 1945. The main objective was to determine the contents of the rations and how they affected the soldiers' nutrition and morale. The information concerning food and feeding is mainly based on the official documents found in the Military Archives. Some additional material was from the historical literature, some from memoirs, or from the veterans who personally experienced the front. The documents in the Archives of Military Medicine provided information on the soldiers' deficiencies. During the Winter War, which took place from 30 November 1939 until 13 March 1940, ample food was available. The cold climate caused problems and the fresh food got frozen. However, no severe deficiency cases were reported and the morale was high. By contrast, during the Continuation War, which began in June, 1941 and ended in September, 1944, difficulties were experienced. At the time farming in the country faced serious problems due to the shortage of labour, fuel, etc. Furthermore, importing food was generally not possible. However, importing food mainly from Germany saved the Finns from hunger. In addition, the self activity of the soldiers on the front added somewhat to the food production. But the rations had to be reduced. Their energy values were consequently low, especially for the young men. Food was monotonous and occasionally caused complaints. The main sources of protein, vitamins and minerals were the whole cereal foods. Butter was fortified with vitamin A and vitamin C tablets were also distributed, to compensate for the scant food sources. Only approximately 300 serious deficiency cases required hospital care during the three years time, out of a total of 400 000 soldiers. Feeding the young soldiers during the war (1944 - 1945) in Lapland, which had been destroyed, was problematic but the increased rations also saved them from deficiencies. In spite of the severe difficulties experienced occasionally in feeding the soldiers during the wars, the system worked all the time. The soldiers were fed, the cases of nutritional deficiency and epidemics caused by food were kept very limited and the morale of soldiers remained high.

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Gram-negative bacteria are harmful in various surroundings. In the food industy their metabolites are potential cause of spoilage and this group also includes many severe or potential pathogens, such as Salmonella. Due to their ability to produce biofilms Gram-negative bacteria also cause problems in many industrial processes as well as in clinical surroundings. Control of Gram-negative bacteria is hampered by the outer membrane (OM) in the outermost layer of the cells. This layer is an intrinsic barrier for many hydrophobic agents and macromolecules. Permeabilizers are compounds that weaken OM and can thus increase the activity of antimicrobials by facililating entry of hydrophobic compounds and macromolecules into the cell where they can reach their target sites and inhibit or destroy cellular functions. The work described in this thesis shows that lactic acid acts as a permeabilizer and destabilizes the OM of Gram-negative bacteria. In addition, organic acids present in berriers, i.e. malic, sorbic and benzoic acid, were shown to weaken the OM of Gram-negative bacteria. Organic acids can poteniate the antimicrobial activity of other compounds. Microbial colonic degradation products of plant-derived phenolic compounds (3,4-dihydroxyphenylacetic acid, 3-hydroxyphenylacetic acid, 3,4-dihydroxyphenylpropionic acid, 4-hydroxyphenylpropionic acid, 3-phenylpropionic acid and 3-hydroxyphenylpropionic acid) efficiently destabilized OM of Salmonella. The studies increase our understanding of the mechanism of action of the classical chelator, ethylenediaminetetra-acetic acid (EDTA). In addition, the results indicate that the biocidic activity of benzalkonium chloride against Pseudomonas can be increased by combined use with polyethylenimine (PEI). In addition to PEI, several other potential permeabilizers, such as succimer, were shown to destabilize the OM of Gram-negative bacteria. Furthermore, combination of the results obtained from various permeability assays (e.g. uptake of a hydrophobic probe, sensitization to hydrophobic antibiotics and detergents, release of lipopolysaccharide (LPS) and LPS-specific fatty acids) with atomic force microscopy (AFM) image results increases our knowledge of the action of permeabilizers.

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The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

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In plotting the variation of frequencies with geometric parameters such as side ratio, skew angle, thickness taper, etc. in detailed studies of the vibration characteristics of plates, situations are encountered such as crossing of the frequency curves or the tendency of these curves to come close together and veer away from each other. These have been generally referred to as “frequency crossings” and “transitions” respectively. The latter may preferably be referred to as “quasi-degeneracies”. In the literature there appears to be some ambiguity in the analysis and interpretation of these features. In this paper, a clarification of some of these questions as regards rectangular and skew plates is presented by making use of concepts from physics dealing with molecular vibrations.

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Phosphorus is a nutrient needed in crop production. While boosting crop yields it may also accelerate eutrophication in the surface waters receiving the phosphorus runoff. The privately optimal level of phosphorus use is determined by the input and output prices, and the crop response to phosphorus. Socially optimal use also takes into account the impact of phosphorus runoff on water quality. Increased eutrophication decreases the economic value of surface waters by Deteriorating fish stocks, curtailing the potential for recreational activities and by increasing the probabilities of mass algae blooms. In this dissertation, the optimal use of phosphorus is modelled as a dynamic optimization problem. The potentially plant available phosphorus accumulated in soil is treated as a dynamic state variable, the control variable being the annual phosphorus fertilization. For crop response to phosphorus, the state variable is more important than the annual fertilization. The level of this state variable is also a key determinant of the runoff of dissolved, reactive phosphorus. Also the loss of particulate phosphorus due to erosion is considered in the thesis, as well as its mitigation by constructing vegetative buffers. The dynamic model is applied for crop production on clay soils. At the steady state, the analysis focuses on the effects of prices, damage parameterization, discount rate and soil phosphorus carryover capacity on optimal steady state phosphorus use. The economic instruments needed to sustain the social optimum are also analyzed. According to the results the economic incentives should be conditioned on soil phosphorus values directly, rather than on annual phosphorus applications. The results also emphasize the substantial effects the differences in varying discount rates of the farmer and the social planner have on optimal instruments. The thesis analyzes the optimal soil phosphorus paths from its alternative initial levels. It also examines how erosion susceptibility of a parcel affects these optimal paths. The results underline the significance of the prevailing soil phosphorus status on optimal fertilization levels. With very high initial soil phosphorus levels, both the privately and socially optimal phosphorus application levels are close to zero as the state variable is driven towards its steady state. The soil phosphorus processes are slow. Therefore, depleting high phosphorus soils may take decades. The thesis also presents a methodologically interesting phenomenon in problems of maximizing the flow of discounted payoffs. When both the benefits and damages are related to the same state variable, the steady state solution may have an interesting property, under very general conditions: The tail of the payoffs of the privately optimal path as well as the steady state may provide a higher social welfare than the respective tail of the socially optimal path. The result is formalized and an applied to the created framework of optimal phosphorus use.

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The purpose of this study was to evaluate intensity, productivity and efficiency in agriculture in Finland and show implications for N and P fertiliser management. Environmental concerns relating to agricultural production have been and still are focused on arguments about policies that affect agriculture. These policies constrain production while demand for agricultural products such as food, fibre and energy continuously increase. Therefore the importance of increasing productivity is a great challenge to agriculture. Over the last decades producers have experienced several large changes in the production environment such as the policy reform when Finland joined the EU 1995. Other and market changes occurred with the further EU enlargement with neighbouring countries in 2005 and with the decoupling of supports over the 2006-2007 period. Decreasing prices a decreased number of farmers and decreased profitability in agricultural production have resulted from these changes and constraints and of technological development. It is known that the accession to the EU 1995 would herald changes in agriculture. Especially of interest was how the sudden changes in prices of commodities on especially those of cereals, decreased by 60%, would influence agricultural production. The knowledge of properties of the production function increased in importance as a consequence of price changes. A research on the economic instruments to regulate productions was carried out and combined with earlier studies in paper V. In paper I the objective was to compare two different technologies, the conventional farming and the organic farming, determine differences in productivity and technical efficiency. In addition input specific or environmental efficiencies were analysed. The heterogeneity of agricultural soils and its implications were analysed in article II. In study III the determinants of technical inefficiency were analysed. The aspects and possible effects of the instability in policies due to a partial decoupling of production factors and products were studied in paper IV. Consequently connection between technical efficiency based on the turnover and the sales return was analysed in this study. Simple economic instruments such as fertiliser taxes have a direct effect on fertiliser consumption and indirectly increase the value of organic fertilisers. However, fertiliser taxes, do not fully address the N and P management problems adequately and are therefore not suitable for nutrient management improvements in general. Productivity of organic farms is lower on average than conventional farms and the difference increases when looking at selling returns only. The organic sector needs more research and development on productivity. Livestock density in organic farming increases productivity, however, there is an upper limit to livestock densities on organic farms and therefore nutrient on organic farms are also limited. Soil factors affects phosphorous and nitrogen efficiency. Soils like sand and silt have lower input specific overall efficiency for nutrients N and P. Special attention is needed for the management on these soils. Clay soils and soils with moderate clay content have higher efficiency. Soil heterogeneity is cause for an unavoidable inefficiency in agriculture.

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The aim of this investigation is to evolve a method of solving two-dimensional unsteady flow problems by the method of characteristics. This involves the reduction of the given system of equations to an equivalent system where only interior derivatives occur on a characteristic surface. From this system, four special bicharacteristic directional derivatives are chosen. A finite difference scheme is prescribed for solving the equations. General rectangular lattices are also considered. As an example, we investigate the propagation of an initial pressure distribution in a medium at rest.