Determination of viral load and integration status of HPV 16 in normal and LSIL exfoliated cervical cells

L’intégration du génome du virus papilloma humain (VPH) a été reconnu jusqu’`a récemment comme étant un événnement fréquent mais pourtant tardif dans la progression de la maladie du col de l’utérus. La perspective temporelle vient, pourtant, d’être mise au défi par la détection de formes intégrées de VPH dans les tissus normaux et dans les lésions prénéoplasiques. Notre objectif était de déterminer la charge virale de VPH-16 et son état physique dans une série de 220 échantillons provenant de cols uterins normaux et avec des lésions de bas-grade. La technique quantitative de PCR en temps réel, méthode Taqman, nous a permis de quantifier le nombre de copies des gènes E6, E2, et de la B-globine, permettant ainsi l’évaluation de la charge virale et le ratio de E6/E2 pour chaque spécimen. Le ratio E6/E2 de 1.2 ou plus était suggestif d’intégration. Par la suite, le site d’intégration du VPH dans le génome humain a été déterminé par la téchnique de RS-PCR. La charge virale moyenne était de 57.5±324.6 copies d'ADN par cellule et le ratio E6/E2 a évalué neuf échantillons avec des formes d’HPV intégrées. Ces intégrants ont été amplifiés par RS-PCR, suivi de séquençage, et l’homologie des amplicons a été déterminée par le programme BLAST de NCBI afin d’identifier les jonctions virales-humaines. On a réussi `a identifier les jonctions humaines-virales pour le contrôle positif, c'est-à-dire les cellules SiHa, pourtant nous n’avons pas detecté d’intégration par la technique de RS-PCR dans les échantillons de cellules cervicales exfoliées provenant de tissus normaux et de lésions de bas-grade. Le VPH-16 est rarement intégré dans les spécimens de jeunes patientes.

Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G subset R^2, where the second part consists of three steps: In a first step the unknown potential density is replaced by a linear combination of exponentially decreasing basis functions concentrated near the boundary points. In a second step, integration over the boundary partial G is replaced by integration over the tangents at the boundary points such that even analytical expressions for the potential approximations can be obtained. In a third step, finally, the linear algebraic system is solved to determine an approximate density function and the resulting solution of the Stokes boundary value problem. Even not convergent the method leads to an efficient approximation of the form O(h^2) + epsilon, where epsilon can be chosen arbitrarily small.

Dieselmotor-Kraft-Wärme-Kopplungsanlagen im Kontext der Integration Erneuerbarer Energien in die Energieversorgung

In dieser Arbeit werden die sich abzeichnenden zukünftigen Möglichkeiten, Stärken und Schwächen der Kraft-Wärme-Kopplung (KWK) untersucht. Dies geschieht vor dem Hintergrund des Klimawandels, der Integration steigender Anteile Erneuerbarer Energien in die Stromerzeugung und unter Berücksichtigung der sich damit ergebenden Herausforderungen, eine sichere und nachhaltige Stromversorgung zu gestalten. Der Fokus liegt auf der Dieselmotor-KWK und der Nutzung nachwachsender Kraftstoffe. Es wird davon ausgegangen, dass der Übergang zu einer reinen Stromerzeugung aus Erneuerbaren Energiequellen in Deutschland unter erheblicher Einbindung des hohen Potentials der kostengünstigen, umweltfreundlichen, aber in der Leistung extrem fluktuierenden Windenergie erfolgen wird. Als dezentrales Integrationswerkzeug wurde die Kraft-Wärme-Kopplung mit Dieselmotoren untersucht. Sie entspricht aufgrund ihrer großen Flexibilität und ihrer hohen Wirkungsgrade mit vergleichsweise kleinen Leistungen sehr gut den Anforderungen der gleichzeitigen dezentralen Wärmenutzung. In der Dissertation werden die Randbedingungen der Dieselmotor-KWK untersucht und beschrieben. Darauf aufbauend werden unterschiedliche Modelle der Windintegration durch KWK erarbeitet und in diversen Variationen wird der Ausgleich der Stromerzeugung aus Windenergie durch KWK simuliert. Darüber hinaus werden dezentrale KWK-Anlagen hinsichtlich eines koordinierten gemeinsamen Betriebs und hinsichtlich der optimalen Auslegung für den Windenergieausgleich betrachtet. Es wird für den beschriebenen Kontext der Erneuerbaren Energien und der Kraft-Wärme-Kopplung das Thema „Umweltwirkungen“ diskutiert. Es wird dargelegt, dass die heute verwendeten Ansätze zur Bewertung der KWK zu einer Verzerrung der Ergebnisse führen. Demgegenüber wurde mit der so genannten Outputmethode eine Methode der Ökobilanzierung vorgestellt, die, im Gegensatz zu den anderen Methoden, keine verzerrenden Annahmen in die Wirkungsabschätzung aufnimmt und somit eine eindeutige und rein wissenschaftliche Auswertung bleibt. Hiermit ist die Grundlage für die Bewertung der unterschiedlichen Technologien und Szenarien sowie für die Einordnung der KWK in den Kontext der Energieerzeugung gegeben. Mit der Outputmethode wird u.a. rechnerisch bewiesen, dass die gekoppelte Strom- und Wärmeerzeugung in KWK-Anlagen tatsächlich die optimale Nutzung der regenerativen Kraftstoffe „Biogas“ und „Pflanzenöl“ im Hinblick auf Ressourceneinsatz, Treibhausgaseinsparung und Exergieerzeugung ist. Es wurde darüber hinaus die Frage untersucht woher die für die Stromerzeugung durch Dieselmotor-KWK-Anlagen notwendige Bioenergie genommen werden kann. Es ist erwiesen, dass die in Deutschland nutzbare landwirtschaftliche Fläche nur zur Deckung eines Teils der Stromerzeugung ausreichen würde. Einheimisches Biogas und nachhaltiges importiertes Pflanzenöl, das in hohem Maße auf degradierten Böden angebaut werden sollte, können die notwendige Brennstoffenergie liefern. Um im Ausland ausreichend Pflanzenöl herstellen zu können, wird eine landwirtschaftliche Fläche von 6 bis 12 Mio. ha benötigt. Das Ergebnis ist, dass ein voller Ausgleich von Windenergie-Restlast durch KWK mit Erneuerbaren Energieträgern sinnvoll und machbar ist! Dieses Wind-KWK-DSM-System sollte durch ein Stromnetz ergänzt sein, das Wasserkraftstrom für den Großteil der Regelenergieaufgaben nutzt, und das den großräumigen Ausgleich Erneuerbarer Energien in Europa und den Nachbarregionen ermöglicht.

Development and Integration of Biocontrol Products in Branched Broomrape (Phelipanche ramosa) management in Tomato

Parasitic weeds of the genera Striga, Orobanche, and Phelipanche pose a severe problem for agriculture because they are difficult to control and are highly destructive to several crops. The present work was carried out during the period October, 2009 to February, 2012 to evaluate the potential of arbuscular mycorrhizal fungi (AMF) to suppress P. ramosa on tomatoes and to investigate the effects of air-dried powder and aqueous extracts from Euphorbia hirta on germination and haustorium initiation in Phelipanche ramosa. The work was divided into three parts: a survey of the indigenous mycorrhizal flora in Sudan, second, laboratory and greenhouse experiments (conducted in Germany and Sudan) to construct a base for the third part, which was a field trial in Sudan. A survey was performed in 2009 in the White Nile state, Sudan to assess AMF spore densities and root colonization in nine fields planted with 13 different important agricultural crops. In addition, an attempt was made to study the relationship between soil physico-chemical properties and AMF spore density, colonization rate, species richness and other diversity indices. The mean percentage of AMF colonization was 34%, ranging from 19-50%. The spore densities (expressed as per 100 g dry soil) retrieved from the rhizosphere of different crops were relatively high, varying from 344 to 1222 with a mean of 798. There was no correlation between spore densities in soil and root colonization percentage. A total of 45 morphologically classifiable species representing ten genera of AMF were detected with no correlation between the number of species found in a soil sample and the spore density. The most abundant genus was Glomus (20 species). The AMF diversity expressed by the Shannon–Weaver index was highest in sorghum (H\= 2.27) and Jews mallow (H\= 2.13) and lowest in alfalfa (H\= 1.4). With respect to crop species, the genera Glomus and Entrophospora were encountered in almost all crops, except for Entrophospora in alfalfa. Kuklospora was found only in sugarcane and sorghum. The genus Ambispora was recovered only in mint and okra, while mint and onion were the only species on which no Acaulospora was found. The hierarchical cluster analysis based on the similarity among AMF communities with respect to crop species overall showed that species compositions were relatively similar with the highest dissimilarity of about 25% separating three of the mango samples and the four sorghum samples from all other samples. Laboratory experiments studied the influence of root and stem exudates of three tomato varieties infected by three different Glomus species on germination of P. ramosa. Root exudates were collected 21or 42 days after transplanting (DAT) and stem exudates 42 DAT and tested for their effects on germination of P. ramosa seeds in vitro. The tomato varieties studied did not have an effect on either mycorrhizal colonization or Phelipanche germination. Germination in response to exudates from 42 day old mycorrhizal plants was significantly reduced in comparison to non-mycorrhizal controls. Germination of P. ramosa in response to root exudates from 21 day old plants was consistently higher than for 42 day-old plants (F=121.6; P<.0001). Stem diffusates from non-mycorrhizal plants invariably elicited higher germination than diffusates from the corresponding mycorrhizal ones and differences were mostly statistically significant. A series of laboratory experiments was undertaken to investigate the effects of aqueous extracts from Euphorbia hirta on germination, radicle elongation, and haustorium initiation in P. ramosa. P. ramosa seeds conditioned in water and subsequently treated with diluted E. hirta extract (10-25% v/v) displayed considerable germination (47-62%). Increasing extract concentration to 50% or more reduced germination in response to the synthetic germination stimulants GR24 and Nijmegen-1 in a concentration dependent manner. P. ramosa germlings treated with diluted Euphorbia extract (10-75 % v/v) displayed haustorium initiation comparable to 2, 5-Dimethoxy-p-benzoquinon (DMBQ) at 20 µM. Euphorbia extract applied during conditioning reduced haustorium initiation in a concentration dependent manner. E. hirta extract or air-dried powder, applied to soil, induced considerable P. ramosa germination. Pot experiments were undertaken in a glasshouse at the University of Kassel, Germany, to investigate the effects of P. ramosa seed bank on tomato growth parameters. Different Phelipanche seed banks were established by mixing the parasite seeds (0 - 32 mg) with the potting medium in each pot. P. ramosa reduced all tomato growth parameters measured and the reduction progressively increased with seed bank. Root and total dry matter accumulation per tomato plant were most affected. P. ramosa emergence, number of tubercles, and tubercle dry weight increased with the seed bank and were, invariably, maximal with the highest seed bank. Another objective was to determine if different AM fungi differ in their effects on the colonization of tomatoes with P. ramosa and the performance of P. ramosa after colonization. Three AMF species viz. GIomus intraradices, Glomus mosseae and Glomus Sprint® were used in this study. For the infection, P. ramosa seeds (8 mg) were mixed with the top 5 cm soil in each pot. No mycorrhizal colonization was detected in un-inoculated control plants. P. ramosa infested, mycorrhiza inoculated tomato plants had significantly lower AMF colonization compared to plants not infested with P. ramosa. Inoculation with G. intraradices, G. mosseae and Glomus Sprint® reduced the number of emerged P. ramosa plants by 29.3, 45.3 and 62.7% and the number of tubercles by 22.2, 42 and 56.8%, respectively. Mycorrhizal root colonization was positively correlated with number of branches and total dry matter of tomatoes. Field experiments on tomato undertaken in 2010/12 were only partially successful because of insect infestations which resulted in the complete destruction of the second run of the experiment. The effects of the inoculation with AMF, the addition of 10 t ha-1 filter mud (FM), an organic residues from sugar processing and 36 or 72 kg N ha-1 on the infestation of tomatoes with P. ramosa were assessed. In un-inoculated control plants, AMF colonization ranged between 13.4 to 22.1% with no significant differences among FM and N treatments. Adding AMF or FM resulted in a significant increase of branching in the tomato plants with no additive effects. Dry weights were slightly increased through FM application when no N was applied and significantly at 36 kg N ha-1. There was no effect of FM on the time until the first Phelipanche emerged while AMF and N application interacted. Especially AMF inoculation resulted in a tendency to delayed P. ramosa emergence. The marketable yield was extremely low due to the strong fruit infestation with insects mainly whitefly Bemisia tabaci and tomato leaf miner (Tuta absoluta). Tomatoes inoculated with varied mycorrhiza species displayed different response to the insect infestation, as G. intraradices significantly reduced the infestation, while G. mosseae elicited higher insect infestation. The results of the present thesis indicate that there may be a potential of developing management strategies for P. ramosa targeting the pre-attachment stage namely germination and haustorial initiation using plant extracts. However, ways of practical use need to be developed. If such treatments can be combined with AMF inoculation also needs to be investigated. Overall, it will require a systematic approach to develop management tools that are easily applicable and affordable to Sudanese farmers. It is well-known that proper agronomical practices such as the design of an optimum crop rotation in cropping systems, reduced tillage, promotion of cover crops, the introduction of multi-microbial inoculants, and maintenance of proper phosphorus levels are advantageous if the mycorrhiza protection method is exploited against Phelipanche ramosa infestation. Without the knowledge about the biology of the parasitic weeds by the farmers and basic preventive measures such as hygiene and seed quality control no control strategy will be successful, however.

Vector-Based Integration of Local and Long-Range Information in Visual Cortex

Integration of inputs by cortical neurons provides the basis for the complex information processing performed in the cerebral cortex. Here, we propose a new analytic framework for understanding integration within cortical neuronal receptive fields. Based on the synaptic organization of cortex, we argue that neuronal integration is a systems--level process better studied in terms of local cortical circuitry than at the level of single neurons, and we present a method for constructing self-contained modules which capture (nonlinear) local circuit interactions. In this framework, receptive field elements naturally have dual (rather than the traditional unitary influence since they drive both excitatory and inhibitory cortical neurons. This vector-based analysis, in contrast to scalarsapproaches, greatly simplifies integration by permitting linear summation of inputs from both "classical" and "extraclassical" receptive field regions. We illustrate this by explaining two complex visual cortical phenomena, which are incompatible with scalar notions of neuronal integration.

Inverse effectiveness, multisensory integration, and the bodily self: some statistical considerations

A recent report in Consciousness and Cognition provided evidence from a study of the rubber hand illusion (RHI) that supports the multisensory principle of inverse effectiveness (PoIE). I describe two methods of assessing the principle of inverse effectiveness ('a priori' and 'post-hoc'), and discuss how the post-hoc method is affected by the statistical artefact of,regression towards the mean'. I identify several cases where this artefact may have affected particular conclusions about the PoIE, and relate these to the historical origins of 'regression towards the mean'. Although the conclusions of the recent report may not have been grossly affected, some of the inferential statistics were almost certainly biased by the methods used. I conclude that, unless such artefacts are fully dealt with in the future, and unless the statistical methods for assessing the PoIE evolve, strong evidence in support of the PoIE will remain lacking. (C) 2009 Elsevier Inc. All rights reserved.

A method for estimating the turbulent kinetic energy dissipation rate from a vertically pointing Doppler lidar, and independent evaluation from balloon-borne in situ measurements

A method of estimating dissipation rates from a vertically pointing Doppler lidar with high temporal and spatial resolution has been evaluated by comparison with independent measurements derived from a balloon-borne sonic anemometer. This method utilizes the variance of the mean Doppler velocity from a number of sequential samples and requires an estimate of the horizontal wind speed. The noise contribution to the variance can be estimated from the observed signal-to-noise ratio and removed where appropriate. The relative size of the noise variance to the observed variance provides a measure of the confidence in the retrieval. Comparison with in situ dissipation rates derived from the balloon-borne sonic anemometer reveal that this particular Doppler lidar is capable of retrieving dissipation rates over a range of at least three orders of magnitude. This method is most suitable for retrieval of dissipation rates within the convective well-mixed boundary layer where the scales of motion that the Doppler lidar probes remain well within the inertial subrange. Caution must be applied when estimating dissipation rates in more quiescent conditions. For the particular Doppler lidar described here, the selection of suitably short integration times will permit this method to be applicable in such situations but at the expense of accuracy in the Doppler velocity estimates. The two case studies presented here suggest that, with profiles every 4 s, reliable estimates of ϵ can be derived to within at least an order of magnitude throughout almost all of the lowest 2 km and, in the convective boundary layer, to within 50%. Increasing the integration time for individual profiles to 30 s can improve the accuracy substantially but potentially confines retrievals to within the convective boundary layer. Therefore, optimization of certain instrument parameters may be required for specific implementations.

Building integration photovoltaic module with reference to Ghana: using triple junction amorphous silicon

This paper assesses the potential for using building integrated photovoltaic (BIPV) roof shingles made from triple-junction amorphous silicon (3a-Si) for electrification and as a roofing material in tropical countries, such as Accra, Ghana. A model roof was constructed using triple-junction amorphous (3a-Si) PV on one section and conventional roofing tiles on the other. The performance of the PV module and tiles were measured, over a range of ambient temperatures and solar irradiance. PVSyst (a computer design software) was used to determine the most appropriate angle of tilt. It was observed that 3a-Si performs well in conditions such as Accra, because it is insensitive to high temperatures. Building integration gives security benefits, and reduces construction costs and embodied energy, compared to freestanding PV systems. Again, it serves as a means of protection from salt spray from the oceans and works well even when shaded. However, compared to conventional roofing materials, 3a-Si would increase the indoor temperature by 1-2 °C depending on the surface area of the roof covered with the PV modules. The results presented in this research enhance the understanding of varying factors involved in the selection of an appropriate method of PV installation to offset the short falls of the conventional roofing material in Ghana.

Advances in continuously profiling the thermodynamic state of the boundary layer: integration of measurements and methods

This paper describes advances in ground-based thermodynamic profiling of the lower troposphere through sensor synergy. The well-documented integrated profiling technique (IPT), which uses a microwave profiler, a cloud radar, and a ceilometer to simultaneously retrieve vertical profiles of temperature, humidity, and liquid water content (LWC) of nonprecipitating clouds, is further developed toward an enhanced performance in the boundary layer and lower troposphere. For a more accurate temperature profile, this is accomplished by including an elevation scanning measurement modus of the microwave profiler. Height-dependent RMS accuracies of temperature (humidity) ranging from 0.3 to 0.9 K (0.5–0.8 g m−3) in the boundary layer are derived from retrieval simulations and confirmed experimentally with measurements at distinct heights taken during the 2005 International Lindenberg Campaign for Assessment of Humidity and Cloud Profiling Systems and its Impact on High-Resolution Modeling (LAUNCH) of the German Weather Service. Temperature inversions, especially of the lower boundary layer, are captured in a very satisfactory way by using the elevation scanning mode. To improve the quality of liquid water content measurements in clouds the authors incorporate a sophisticated target classification scheme developed within the European cloud observing network CloudNet. It allows the detailed discrimination between different types of backscatterers detected by cloud radar and ceilometer. Finally, to allow IPT application also to drizzling cases, an LWC profiling method is integrated. This technique classifies the detected hydrometeors into three different size classes using certain thresholds determined by radar reflectivity and/or ceilometer extinction profiles. By inclusion into IPT, the retrieved profiles are made consistent with the measurements of the microwave profiler and an LWC a priori profile. Results of IPT application to 13 days of the LAUNCH campaign are analyzed, and the importance of integrated profiling for model evaluation is underlined.

Integration of a 3D Variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay

This paper describes the implementation of a 3D variational (3D-Var) data assimilation scheme for a morphodynamic model applied to Morecambe Bay, UK. A simple decoupled hydrodynamic and sediment transport model is combined with a data assimilation scheme to investigate the ability of such methods to improve the accuracy of the predicted bathymetry. The inverse forecast error covariance matrix is modelled using a Laplacian approximation which is calibrated for the length scale parameter required. Calibration is also performed for the Soulsby-van Rijn sediment transport equations. The data used for assimilation purposes comprises waterlines derived from SAR imagery covering the entire period of the model run, and swath bathymetry data collected by a ship-borne survey for one date towards the end of the model run. A LiDAR survey of the entire bay carried out in November 2005 is used for validation purposes. The comparison of the predictive ability of the model alone with the model-forecast-assimilation system demonstrates that using data assimilation significantly improves the forecast skill. An investigation of the assimilation of the swath bathymetry as well as the waterlines demonstrates that the overall improvement is initially large, but decreases over time as the bathymetry evolves away from that observed by the survey. The result of combining the calibration runs into a pseudo-ensemble provides a higher skill score than for a single optimized model run. A brief comparison of the Optimal Interpolation assimilation method with the 3D-Var method shows that the two schemes give similar results.

Development and application of a method for the purification of free shigatoxigenic bacteriophage from environmental samples

Shiga toxin producing Escherichia coli (STEC) strains are foodborne pathogens whose ability to produce Shiga toxin (Stx) is due to the integration of Stx-encoding lambdoid bacteriophage (Stx phage). Circulating, infective Stx phages are very difficult to isolate, purify and propagate such that there is no information on their genetic composition and properties. Here we describe a novel approach that exploits the phage's ability to infect their host and form a lysogen, thus enabling purification of Stx phages by a series of sequential lysogen isolation and induction steps. A total of 15 Stx phages were rigorously purified from water samples in this way, classified by TEM and genotyped using a PCR-based multi-loci characterisation system. Each phage possessed only one variant of each target gene type, thus confirming its purity, with 9 of the 15 phages possessing a short tail-spike gene and identified by TEM as Podoviridae. The remaining 6 phages possessed long tails, four of which appeared to be contractile in nature (Myoviridae) and two of which were morphologically very similar to bacteriophage lambda (Siphoviridae).

Choosing the most suitable analogue redesign method for forward-type digital power converters

This work proposes a method to objectively determine the most suitable analogue redesign method for forward type converters under digital voltage mode control. Particular emphasis is placed on determining the method which allows the highest phase margin at the particular switching and crossover frequencies chosen by the designer. It is shown that at high crossover frequencies with respect to switching frequency, controllers designed using backward integration have the largest phase margin; whereas at low crossover frequencies with respect to switching frequency, controllers designed using bilinear integration have the largest phase margins. An accurate model of the power stage is used for simulation, and experimental results from a Buck converter are collected. The performance of the digital controllers is compared to that of the equivalent analogue controller both in simulation and experiment. Excellent correlation between the simulation and experimental results is presented. This work will allow designers to confidently choose the analogue redesign method which yields the greater phase margin for their application.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

Systematic selection of analogue redesign method for forward-type digital power converters

This article proposes a systematic approach to determine the most suitable analogue redesign method to be used for forward-type converters under digital voltage mode control. The focus of the method is to achieve the highest phase margin at the particular switching and crossover frequencies chosen by the designer. It is shown that at high crossover frequencies with respect to switching frequency, controllers designed using backward integration have the largest phase margin; whereas at low crossover frequencies with respect to switching frequency, controllers designed using bilinear integration with pre-warping have the largest phase margins. An algorithm has been developed to determine the frequency of the crossing point where the recommended discretisation method changes. An accurate model of the power stage is used for simulation and experimental results from a Buck converter are collected. The performance of the digital controllers is compared to that of the equivalent analogue controller both in simulation and experiment. Excellent closeness between the simulation and experimental results is presented. This work provides a concrete example to allow academics and engineers to systematically choose a discretisation method.