If we fix an integer a not equal to -1 and which is not a perfect square, we are interested in estimating the quantity N_{a}(x) representing the number of prime integers p up to x such that a is a generator of the cyclic group (Z/pZ)*. We will first show how to obtain an aymptotic formula for N_{a}(x) under the assumption of the generalized Riemann hypothesis. We then investigate the average behaviour of N_{a}(x) and we provide an unconditional result. Finally, we discuss how to generalize the problem over (Z/mZ)*, where m > 0 is not necessarily a prime integer. We present an average result in this setting and prove the existence of oscillation.

Large software systems are composed of various different run-time components, partner applications and, processes. When such systems operate they are monitored so that audits can be performed once a failure occurs or when maintenance operations are performed. However, log files are usually sizeable, and require filtering and reduction to be processed efficiently. Furthermore, there is no apparent correspondence of how logged events relate to particular use cases the system may be performing. In this thesis, we have developed a framework that is based on heuristic clustering algorithms to achieve log filtering, log reduction and, log interpretation. More specifically we define the concept of the Event Dependency Graph, and we present event filtering and use case identification techniques, that are based on event clustering. The clustering process groups together all events that relate to a collection of initial significant events that relate to a use case. We refer to these significant events as beacon events. Beacon events can be identified automatically or semiautomatically by examining log event types or event names against event types or event names in the corresponding specification of a use case being considered (e.g. events in sequence diagrams). Furthermore, the user can select other or additional initial clustering conditions based on his or her domain knowledge of the system. The clustering technique can be used in two possible ways. The first is for large logs to be reduced or sliced, with respect to a particular use case so that, operators can better focus their attention to specific events that relate to specific operations. The second is for the determination of active use cases where operators select particular seed events of interest and then examine the resulting reduced logs against events or event types stemming from different alternative known use cases being considered, in order to identify the best match and consequently provide insights on which of these alternative use cases may be running at any given time. The approach has shown very promising results towards the identification of executing use cases among various alternative ones in various runs of the Session Initiation Protocol.

Plant growth-promoting rhizobacteria (PGPR) are free-living, soil-borne bacteria that colonize the rhizosphere and, when applied to crops, enhance the growth of plants. Plant growth-promoting rhizobacteria may enhance plant growth either by direct or indirect mechanisms. The direct mechanisms of action include nitrogen fixation,production of phytohormones and lowering of ethylene concentrations. The objective of this study was to determine whether Pseudomonas putida strain 6-8 isolated from the rhizosphere of legume crops grown in Saskatchewan fields was able to promote the growth of canola cv. Smart and lentil cv. Milestone plants by direct mechanisms. Initial studies determined the effect of strain 6-8 and other known phytohormoneproducing PGPR strains on the growth of canola and lentil plants both in gnotobiotic and growth chamber conditions. Variations in the results were observed, as there were significant differences among trials. Strain 6-8 enhanced the growth of canola cv. Smart in growth pouches but not in pots in growth chamber studies. In the case of lentil cv.Milestone, strain 6-8 had no significant effect in growth pouches, but it significantly increased root dry weight, shoot dry weight and root surface area in pots in growth chamber studies. A similar effect was observed with wild-type strains GR12-2 and G20- 18. Strain GR12-2 was consistent in promoting the growth of lentil cv. Milestone both in growth pouches and in pots in growth chambers when compared to other strains and the control. The ability of the PGPR strains to produce auxin and cytokinin phytohomones in pure culture and in the canola rhizosphere was tested using the enzyme linked immunosorbent assay (ELISA). All the PGPR strains produced indole compounds and the concentration of the indoles produced increased with increasing concentrations of the precursor tryptophan. There were no significant differences among PGPR strains in production of indole-3-acetic acid (IAA) when assayed using ELISA. The concentrations of IAA secreted by PGPR strains were extremely low (0.19 µg/ml 9.80 µg/ml). Strain 6-8 produced the cytokinins, isopentenyl adenosine (IPA), zeatin riboside (ZR) and dihydroxyzeatin riboside (DHZR) in pure culture. Indole-3-acetic acid was detected in supernatants obtained from canola growth pouches inoculated with PGPR strains, but there were no significant differences in the concentrations of IAA secreted among PGPR strains. Significantly higher concentrations of IPA and ZR were observed in the rhizosphere of canola inoculated with strain 6-8 than in the non-inoculated control. Strain 6-8 produced siderophores, solubilized inorganic phosphate and used 1-aminocyclopropane-1-carboxylic acid (ACC), the precursor of ethylene, as sole nitrogen source. These traits are considered to be alternative mechanisms for direct plant growth promotion. A qualitative and quantitative study of root colonization by strain 6-8 was conducted by tagging the strain with green fluorescent protein in conjunction with confocal laser scanning microscopy and by conventional plating. The populations of strain 6-8 were higher on canola roots than on lentil roots by conventional plating. Similar results were also observed in confocal laser scanning microscopy (CLSM) studies after 5, 7 and 9 days for canola and 3, 6 and 9 days for lentil. Pseudomonas putida strain 6-8 produced cytokinins and also possessed other direct growth promoting characteristics. The ability of strain 6-8 to promote the growth of canola cv. Smart in growth pouches and lentil cv. Milestone in growth chamber studies may be related to these direct growth promoting characteristics. Strain 6-8 may have potential for development as a plant growth-promoting rhizobacterial inoculant.

This paper investigates the purchasing power parity (PPP) hypothesis using panel data. Under PPP the real exchange rate is stationary around a constant mean. Recent panel data unit root tests are employed to test the PPP proposition where, under the conventional null hypothesis of a unit root, the real exchange rate is not stationary and PPP does not hold. In this case, as the time period t + n approaches infinity, its variance relative to period t will also approach infinity. The usual alternative in unit root tests is stationarity around a constant mean or a linear trend. The paper brings innovation into the PPP and panel unit root testing literature by allowing for possible nonlinear deterministic trends in the alternative hypothesis (as advanced by Cushman (2004)). If the null hypothesis is rejected in favour of the alternative of a non-linear trend, PPP still does not hold, but does at least revert back to a meaningful, stable long-run equilibrium. Given this non-linear trend, the variance of the real exchange rate as t + n approaches infinity, conditional on that trend, remains finite. Overall, evidence for stationarity in exchange rates is found in four out of six panels under consideration, including both support for stationary processes with no trend or a linear trend as well as for processes following a non-linear deterministic trend, in particular at time orders 5 and 6. The rejections are, in fact, most consistent at the nonlinear orders. Given nonlinear trends, PPP as usually defined does not hold, despite the rejection of unit roots. It is also found that stronger evidence for stable long-run equilibria in real exchange rates appears when the German Deutschmark is chosen as a base currency instead of the US Dollar. Finally, it appears that a very recent panel unit root test that takes account of cross-sectional dependencies delivers more consistent and sensible results.

<i>Pseudomonas fluorescens</i> BRG100 produces secondary metabolites with herbicidal activity to the grass weeds wild oat, Avena fatua, and green foxtail, Setaria viridis. The green fluorescence protein (gfp) gene was introduced into P. fluorescens BRG100 from Escherichia coli S17-1¥ë via a Tn5 mini transposon suicide vector system. Colony morphology, growth rate in liquid media, weed biocontrol efficacy (plant growth pouch), carbon utilization (Biolog GN) and root colonization of green foxtail by several P. fluorescens BRG100gfp transformants were determined to be the same as the wild type. <i>Pseudomonas fluorescens</i> BRGgfp-15 was found to be most similar to the wild-type in all of the above characteristics and was thus used in subsequent experiments. Note: all strains of Pseudomonas fluorescens will be referred to by only their strain throughout (ie. BRGgfp-15 and BRG100). <p>It was determined by population dynamics per section of root with spiral plating on culture medium, epi-fluorescence and confocal microscopy that BRGgfp-15 colonized all areas of the root, but showed a preference for the proximal 1/3 section and the seed. In the proximal section the mean number of viable cells per gram dry weight was log109.06 and log109.31, when applied as liquid inoculum and as the pesta granular formulation, respectively. With liquid inoculum there was only log107.53 viable cells/g in the middle 1/3 section and log107.01 viable cells/g in the distal 1/3 section. The number of viable cells/g with pesta granules was log107.61 and log107.34, for the middle and distal sections, respectively. The root hairs, root tip, and ventral portion of the seed were all areas of heavy colonization relative to the other areas of the root. <p>Survival of BRGgfp-15 in the pesta formulation was examined in 2 soil types, clay and clay loam, in a thermogradient plate apparatus by a factorial randomized design complete block experiment. The experiment included: 3-12 hour diurnal temperature regimes: 5-15¨¬C, 15-25¨¬C, and 25-35¨¬C and 3 moisture levels: 25, 50 and 75% of soil moisture holding capacity. Sampling was carried out after 0, 14, 28 and 42 days. The highest numbers of viable BRGgfp-15 cells/g were found in the pesta granules in soil subjected to the lowest diurnal temperature regime and moisture content. The lowest numbers of viable cells/g were found in the pesta granules incubated in the highest diurnal temperature and moisture. This suggests lower soil temperature and moisture enhances survival of BRGgfp-15 in pesta and/ or higher soil temperature and moisture enhances the release and dissemination of BRGgfp-15 from pesta granules. When subjected to a 5-15¨¬C-temperature regime the number of viable cells/g was log109.80. When subjected to 15-25¨¬C the viable cells/g was log108.96 and with 25-35¨¬C it was log107.33. The mean number of viable cells/g was log109.36, log108.86, and log107.87, for 25, 50, and 75% soil moisture holding capacity, respectively. There was also a significantly higher number of viable cells/g in the clay soil collected from Saskatoon, log109.00, as compared to the clay loam soil collected from Scott, which was log108.40. <p>These results suggest that Pseudomonas fluorescens BRG100 has considerable potential as a bioherbicide because of its successful root colonization of green foxtail and wheat. <i>Pseudomonas fluorescens</i> BRGgfp-15 survived well under various environmental conditions when formulated into pesta granules, proving the pesta formulation was an excellent formulation. In addition, gfp was shown to be an excellent conservative marker for monitoring the root colonization and survival of <i>P. fluorescens</i> BRG100.

Root symbioses with dark septate endophytic fungi (DSE) and arbuscular mycorrhizal fungi (AMF) provide plant tolerance to environmental stresses. This research answers several fundamental questions about the occurrence of these fungi in roots of prairie grasses. Traditional methods and current molecular techniques were combined in order to: 1) define the role and specificity of DSE in plant tolerance to drought; 2) assess the level of host specificity in DSE; 3) document AMF biodiversity and pattern of root colonization at different soil depths; 4) define the influence of soil depth and plant species on the distribution of DSE and AMF in roots and; 5) reveal how DSE and AMF interact in plant roots.<p> Under controlled conditions, DSE isolates showed host preference in colonizing roots and promoting plant growth. They colonized with more intensity the plant species from which they were isolated [Agropyron cristatum L. or Psathyrostachys juncea (Fisch) Nevski subsp. Juncea (Syn: Elymus junceus Fisch)]. Inoculation with five DSE isolates resulted in growth stimulation of the C3 grasses A. cristatum and P. juncea, and growth depression of the C4 grass Bouteloua gracillis (Willd. ex Kunth) Lag. ex Griffiths, under water stress. Plant C concentration suggested that DSE inoculation may have resulted in net C drain from B. gracillis.<p. In the field, soil depth influenced root colonization in A. cristatum, Panicum virgatum L., Nassella viridula Trin and Pascopyrum smithii (Rydb.) A. Löve., while AMF diversity was influenced by the interaction between soil depth and host plant species. Molecular analysis of roots serially sampled during one growing season from the A and B soil horizons, in stands of these grasses, revealed spatial and temporal changes in DSE and AMF community composition, and a significant correlation in DSE and AMF community structure.<p> These results suggest that DSE and AMF are adapted to specific environmental conditions and that root occupation by these fungi is a dynamic phenomenon. It is proposed that temporal variation in root occupation by DSE and AMF impacts plant and ecosystem processes at different times during the growing season.

Short rotation woody crops have gained global interest as an alternative energy source to fossil fuels. The availability of this resource is, however, dependent on successful research trials and the identification and quantification of the environmental controls on rapid growth. Knowledge of willow root dynamics is required to determine belowground and aboveground growth relationships, and to provide valuable inputs for the development of a willow carbon model. The objectives of this study were to 1) determine fine root turnover, biomass, and productivity of six willow clones over two growing seasons at four locations in Saskatchewan using the minirhizotron method; 2) determine fine root biomass and fine root carbon sequestration of six willow clones over one growing season at four locations in Saskatchewan using the soil coring method; and 3) determine lateral coarse root structure of six willow clones at two locations in Saskatchewan.<p> Monthly fine root biomass and production was estimated for six willow clones in Saskatoon, Saskatchewan using repeated minirhizotron observations from May to September of 2008 and 2009. Fine root biomass increased from 0.78 Mg ha-1 in May 2008 to 25.75 Mg ha-1 in September 2009. Significant differences were seen between months throughout each growing season, but not between the clones. Mean monthly productivity reached its peak of 8.00 Mg ha-1 in July 2009. Mean turnover for all the clones was 0.96 yr-1 and mean longevity was 1.04 yr-1. The high fine root biomass estimates determined by the minirhizotron method in Saskatoon suggest that this method is not suitable for use in a Vertisolic soil. There was no significant effect of clone on fine root productivity, biomass, turnover or longevity (P < 0.05).<p> Fine root biomass estimates from the soil cores were lower than those from the minirhizotron method. The mean fine root biomass value in Saskatoon for September 2008 was 0.298 Mg ha-1. Mean fine root biomass at each site from September 2007 to September 2008 ranged from 0.022 Mg ha-1 to 0.915 Mg ha-1. Mean root carbon content ranged from 0.010 to 0.426 Mg C ha-1. Fine root biomass and root carbon content were significantly different between each site, with the exception of Saskatoon and Estevan (P < 0.05). Differences in fine root estimates between the sites are suggested to be a function of the soil texture and moisture accessibility at each site. This research indicates that willow roots in Saskatchewan find initial establishment difficult in low moisture, fine textured soils. Also, approximately 44.6 % of fine root biomass is comprised of C, and decomposes to form soil organic matter. Therefore, fine roots have potential to store substantial amounts of carbon if growing conditions are suitable.

Purchasing power parity (PPP) is considered as an important theory of explaining how exchange rate varies in the long run. Most of empirical studies in the past adapted linear cointegration method to test the purchasing power parity. However, there are papers point out that exchange rate exists non-linear cointegration and unexplainable bias might exist in testing the purchase power parity theory while using linear cointegration test. The methodology of this study is based on an application of ESTR ECM proposed by Kapetaniosetet al. to enhance the inadequate of linear cointegration test. We analyze the dynamic adjusting behavior of short-term nominal exchange rate with ESTR ECM model while the non-linear cointegratoin exists. The empirical result indicates that the purchase power parity between Taiwan and its major trading countries is confirmed. Among the trading countries, American, Japan and Hong Kong are suitable for using linear error correction model and non-linear error correction model for Singapore and Korea.

This paper applies both the Engle-Granger and Johansen cointegration test procedures to determine the existence of market linkage among high-valued ( Scomberomorus commerson, milkfish ) and low-valued (cod, Taiwan Tilapia ) fish species using monthly average wholesale price data recorded on the Taipei fisheries wholesale market. If the markets for high-valued and low-valued species are linked, say through commodities arbitrage, individual fish prices cannot diverge ¡§too far¡¨ from other fish prices before market forces to operate to restore equilibrium. From the empirical results, it indicates the existence of only one cointegrating vector involving the prices of these species in Taipei fisheries wholesale market, and that a long-run and stable substitute relationship may exist for the Scomberomorus commerson and other low-valued and high-valued species.

In the early years of human society, all natural resources such as agriculture, animals, forestry, and fisheries were considered to be public property and the treasure belonged to all people. One branch of these natural resources threatened by over-development is straddling and highly migratory fish species, like tuna, which cannot be protected by a single government. While discussing fishery management, we review the change in tuna catches of thirteen countries in Western and Central Pacific Fisheries Commission (WCPFC), as it represents the impacts from different policies and events during a specific period of time. We reference the method applied in economics science by testing for the existence of stochastic convergence and addressing these break points, which are the important targets due to external shocks or internal influence. The characteristic of the method is in testing both time series and panel data by following the traditional unit root tests methods and unit root tests while considering structural breaks. We are able to conclude in preliminary estimates that some serious historical fishery events happened at the break point time, and if we take these structural breaks into consideration, then the growth of tuna catches will be stationary. In other words, if shocks to relative tuna catches are temporary, then the series stochastically converges, meaning that the manager does not need to intervene in the development of tuna fishery, because temporary shocks do not affect the stationarity of tuna catches¡¦ levels. Once the structural breaks occurred in the past, it is not necessary for these government and international organizations to change fishery policies in order to respond to the breaks. They should realize the meaning of the stationary panel instead of enacting an over-intervening policy based on temporary shocks.