A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Uniformisierbarkeit in Familien von abelschen t-Moduln höheren Ranges

Diese Arbeit beschäftigt sich mit der Frage, wie sich in einer Familie von abelschen t-Moduln die Teilfamilie der uniformisierbaren t-Moduln beschreiben lässt. Abelsche t-Moduln sind höherdimensionale Verallgemeinerungen von Drinfeld-Moduln über algebraischen Funktionenkörpern. Bekanntermaßen lassen sich Drinfeld-Moduln in allgemeiner Charakteristik durch analytische Tori parametrisieren. Diese Tatsache überträgt sich allerdings nur auf manche t-Moduln, die man als uniformisierbar bezeichnet. Die Situation hat eine gewisse Analogie zur Theorie von elliptischen Kurven, Tori und abelschen Varietäten über den komplexen Zahlen. Um zu entscheiden, ob ein t-Modul in diesem Sinne uniformisierbar ist, wendet man ein Kriterium von Anderson an, das die rigide analytische Trivialität der zugehörigen t-Motive zum Inhalt hat. Wir wenden dieses Kriterium auf eine Familie von zweidimensionalen t-Moduln vom Rang vier an, die von Koeffizienten a,b,c,d abhängen, und gelangen dabei zur äquivalenten Fragestellung nach der Konvergenz von gewissen rekursiv definierten Folgen. Das Konvergenzverhalten dieser Folgen lässt sich mit Hilfe von Newtonpolygonen gut untersuchen. Schließlich erhält man durch dieses Vorgehen einfach formulierte Bedingungen an die Koeffizienten a,b,c,d, die einerseits die Uniformisierbarkeit garantieren oder andererseits diese ausschließen.

Successful rescue and field establishment of native banana varieties severely affected by rhizome rot

Rhizome rot disease caused by Erwinia spp. is emerging as a major problem in banana nurseries and young plantations worldwide. Management of the disease is possible only in the initial stages of development. Currently no method is available for rescuing plant material already infected with this pathogen. A total of 95 Nanjanagud Rasabale and 212 Elakki Bale suckers were collected from different growing regions of Karnataka, India. During nursery maintenance of these lines, severe Erwinia infection was noticed. We present a method to rescue infected plants and establish them under field conditions. Differences were noticed in infection severity amongst the varieties and their accessions. Field data revealed good establishment and growth of most rescued plants under field conditions. The discussed rescue protocol coupled with good field management practices resulted in 89.19 and 82.59 percent field establishment of previously infected var. Nanjanagud Rasabale and var. Elakki Bale plants, respectively.

Farmers’ desired traits and selection criteria for maize varieties and their implications for maize breeding: A case study from KwaZulu-Natal Province, South Africa

Adoption of hybrids and improved varieties has remained low in the smallholder farming sector of South Africa, despite maize being the staple food crop for the majority of households. The objective of this study was to establish preferred maize characteristics by farmers which can be used as selection criteria by maize breeders in crop improvement. Data were collected from three villages of a selected smallholder farming area in South Africa using a survey covering 300 households and participatory rural appraisal methodology. Results indicated a limited selection of maize varieties grown by farmers in the area compared to other communities in Africa. More than 97% of the farmers grew a local landrace called Natal-8-row or IsiZulu. Hybrids and improved open pollinated varieties were planted by less than 40% of the farmers. The Natal-8-row landrace had characteristics similar to landraces from eastern and southern Africa and closely resembled Hickory King, a landrace still popular in Southern Africa. The local landrace was preferred for its taste, recycled seed, tolerance to abiotic stresses and yield stability. Preferred characteristics of maize varieties were high yield and prolificacy, disease resistance, early maturity, white grain colour, and drying and shelling qualities. Farmers were willing to grow hybrids if the cost of seed and other inputs were affordable and their preferences were considered. Our results show that breeding opportunities exist for improving the farmers’ local varieties and maize breeders can take advantage of these preferred traits and incorporate them into existing high yielding varieties.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Effects of phosphorus and water stress on shoot and root growth and on mycorrhization of different pearl millet (Pennisetum glaucum (L.) R. Br.) varieties from West Africa

This research work aimed at investigating the physiological mechanisms of tolerance of pearl millet to low soil Phosphorus availability and drought under the Sahelian conditions.

Effects of row spacing on productivity and nodulation of two soybean varieties under hot sub-moist tropical conditions in south-western Ethiopia

The objective of this study was to determine the optimum row spacing to improve the productivity of two soybean (Glycine max L.) varieties under the tropical hot sub-moist agroecological conditions of Ethiopia. A two-year split-plot design experiment was conducted to determine the effect of variety (Awasa-95 [early-maturing], Afgat [medium-maturing]) and row spacing (RS: 20, 25, 30, 35, 40, 45, 50, 55, 60 cm) on the productivity, nodulation and weed infestation of soybean. Seed and total dry matter (TDM) yield per ha and per plant, and weed dry biomass per m^2 were significantly affected by RS. Soybean variety had a significant effect on plant density at harvest and some yield components (plant height, number of seeds/pod, and 1000 seed weight). Generally, seed and TDM yield per ha and per plant were high at 40 cm RS, and weed dry biomass per m^2 was higher for RS >= 40 cm than for narrower RS. However, the results did not demonstrate a consistent pattern along the RS gradient. The medium-maturing variety Afgat experienced higher mortality and ended up with lower final plant density at harvest, but higher plant height, number of seeds per pod and 1000 seed weight than the early-maturing variety Awasa-95. The results indicate that 40 cm RS with 5 cm plant spacing within a row can be used for high productivity and low weed infestation of both soybean varieties in the hot sub-moist tropical environment of south-western Ethiopia.

Image Based Rendering Using Algebraic Techniques

This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection.

Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).

On the Development of Early Algebraic Thinking. 'Sobre el desarrollo del pensamiento algebraico temprano'.

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Perceptions of the impacts of genetically modified cotton varieties: a case study of the cotton industry in Gujarat, India

The paper reports the findings of a study designed to consider the impact of the adoption of Bt cotton on markets, businesses, and institutional arrangements in India. Given that evidence to date suggests that widespread adoption of Bt cotton by farmers is likely to increase production, this study aims to assess possible implications for markets (access to inputs, prices of inputs and outputs, etc.) and local industries and to identify potential winners and losers. The results suggest that there are impacts on the cotton industry following from the release of Bt hybrids, and so far the impacts are most noticeable "upstream" (i.e., the input suppliers), where companies are rapidly moving away from the sale of bollworm insecticide and attempting to sell Bt seeds. Seed companies are looking for partnerships with Monsanto, the owner of the Bt gene. One reason that companies are keen to move away from insecticide is so they can avoid the need for credit supply to their customers. Seed purchase is not normally through credit, whereas insecticide purchase is. Issues for companies "downstream" (gins, textile manufacturers) relate more to the better quality of Bt cotton and the need for adequate segregation of Bt and non-Bt cotton.