<p>The multidimensional residue theory as well as the theory of integral representations for holomorphic functions is a very powerful tool in complex analysis. The computation of integrals, solving algebraic or differential equations is usually reduced to some residue integral. It is a notable feature of the theory that it is based on few model differential forms. These are the Cauchy kernel and the Bochner-Martinelli kernel. These two model kernels have been the source of other fundamental kernels and residue concepts by means of homological procedures.</p><p>The Cauchy and Bochner-Martinelli forms possess two common properties: firstly, their singular sets are the unions of complex subspaces, and secondly, the top cohomology group of the complement to the singular set is generated by a single element. We shall call such a set an atomic family and the corresponding form the associated residue kernel.</p><p>A large class of atomic families is provided by the construction of toric varieties. The extensively developed techniques of toric geometry have already produced many explicit results in complex analysis. In the thesis, we apply these methods to the following two questions of multidimensional residue theory: simplification of the proof of the Vidras-Yger generalisation of the Jacobi residue formula in the toric setting; and construction of a residue kernel associated with a toric variety and its applications in the theory of residues and integral representations. The central role in our construction is played by the theorem stating that under some assumptions a toric variety admits realisation as a complete intersection of toric hypersurfaces in an ambient toric variety.</p>

The multidimensional residue theory as well as the theory of integral representations for holomorphic functions is a very powerful tool in complex analysis. The computation of integrals, solving algebraic or differential equations is usually reduced to some residue integral. It is a notable feature of the theory that it is based on few model differential forms. These are the Cauchy kernel and the Bochner-Martinelli kernel. These two model kernels have been the source of other fundamental kernels and residue concepts by means of homological procedures. The Cauchy and Bochner-Martinelli forms possess two common properties: firstly, their singular sets are the unions of complex subspaces, and secondly, the top cohomology group of the complement to the singular set is generated by a single element. We shall call such a set an atomic family and the corresponding form the associated residue kernel. A large class of atomic families is provided by the construction of toric varieties. The extensively developed techniques of toric geometry have already produced many explicit results in complex analysis. In the thesis, we apply these methods to the following two questions of multidimensional residue theory: simplification of the proof of the Vidras-Yger generalisation of the Jacobi residue formula in the toric setting; and construction of a residue kernel associated with a toric variety and its applications in the theory of residues and integral representations. The central role in our construction is played by the theorem stating that under some assumptions a toric variety admits realisation as a complete intersection of toric hypersurfaces in an ambient toric variety.

Strip-tillage implements remove the residue from previous crops and form a seedbed ready for planting. An experiment was conducted to evaluate 5 row-cleaning devices. The proportion of residue removed by the implement was used as the performance indicator. Each of the 5 devices was evaluated at 2 speeds and orientations on the implement. The devices were tested in two blocks (fields) of corn residue (one high residue and one medium residue), and one field of wheat residue. An analysis was conducted, using a mixed-effects model, to compare the performance of the cleaners operating in the different conditions. All cleaners performed well, with no statistical difference in mean performance. All row cleaners performed more consistently in wheat residue, compared with performance in corn residue. Numerically, the consistency of the different cleaners was different, with one configuration performing less consistently than the other four. Edge-effects of the outside row unit of the implement had, in most cases, an insignificant effect on the row unit's cleaning performance.

Strip-tillage implements remove the residue from previous crops and form a seedbed ready for planting. An experiment was conducted to evaluate 5 row-cleaning devices. The proportion of residue removed by the implement was used as the performance indicator. Each of the 5 devices was evaluated at 2 speeds and orientations on the implement. The devices were tested in two blocks (fields) of corn residue (one high residue and one medium residue), and one field of wheat residue. An analysis was conducted, using a mixed-effects model, to compare the performance of the cleaners operating in the different conditions. All cleaners performed well, with no statistical difference in mean performance. All row cleaners performed more consistently in wheat residue, compared with performance in corn residue. Numerically, the consistency of the different cleaners was different, with one configuration performing less consistently than the other four. Edge-effects of the outside row unit of the implement had, in most cases, an insignificant effect on the row unit's cleaning performance.

No description available.

A novel approach for the design and synthesis of membrane separation systems has been developed. The theory is shown to be applicable to both batch and continuous membrane operations, and has been formulated in such a way that it is valid for any type of membrane. In this thesis, however, only vapour permeation and pervaporation membranes are incorporated for illustration purposes. The method, which employs a graphical technique, allows one to calculate and visualise the change in composition of the retentate. An integral part of the approach was the derivation of the Membrane Residue Curve Map (M-RCM), and the related differential material balance which describes it. By definition, this plot shows the change, in time, of the retentate composition in a batch still. However, it has been shown that the M-RCM is applicable to conventional continuously-operated membrane units, as well as infinite reflux membrane columns. Finite reflux columns and cascades have been examined by using column sections (CS): any column, or arrangement, no matter how complex, can be broken down into smaller units, namely CS. The development of the Difference Point Equation (DPE) for non-constant flow allowed one to generate, and interpret, profiles for individual CS’s, which can ultimately be connected to form a membrane column arrangement. The profiles, which are more complex than those obtained in the M-RCM, exhibit a unique behavior. Since there is varying flow, the reflux is continually changing, orientating the profile so as to seek a stable node that is “mobile”. Thus, the movement of CS profile is dictated by the location and direction of the pinch point locus. Finally, having membrane permeators examined in an analogous manner to other separation methods, allows for easy synthesis and design of combinations of different processes. Hybrid distillation-membrane systems are analyzed by incorporating CS’s and the appropriate DPE’s which describe each. Investigating the arrangement as a thermally-coupled column introduces a novel way of synthesizing hybrids. Regions of feasibility, which are dictated by the relevant pinch point loci of each separation method, are ultimately sought.

Field and greenhouse bioassay experiments were conducted to evaluate the effects of mesotrione soil residues on injury and yield of soybean, green bean, pea, cucumber, sugar beet and lettuce. There was a significant difference of mesotrione carryover between studies which can be explained by differences in soil pH and moisture. The conventional and the simulated field residue carryover studies successfully measured mesotrione persistence and rotational crop sensitivity. The simulated residue carryover study provided a more rigorous test of rotational crop sensitivity to mesotrione residues than the conventional residue carryover study, especially at higher doses for the more sensitive crops. The greenhouse bioassay was a simple and sensitive tool in detecting small amounts of herbicides present in the soil. Dose-response curves developed for sugar beet and green bean indicate similarities between results from the greenhouse and from the field mesotrione residue carryover study. Under similar environmental and soil conditions to those observed in these studies and using similar dose applications, sugar beet, green bean and cucumber injury and yield reductions are likely when these crops are grown in soils containing mesotrione residues.

Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.

Thesis (M. Ag. Sci) -- University of Adelaide, Dept. of Agriculture, 1967. / Includes bibliography.

Submitted by Diogo Barreiros (diogo.barreiros@ufba.br) on 2017-02-06T16:59:36Z No. of bitstreams: 1 dissertacao_mestrado_jose-grimaldo.pdf: 19406681 bytes, checksum: d108855fa0fb0d44ee5d1cb59579a04c (MD5) / Approved for entry into archive by Vanessa Reis (vanessa.jamile@ufba.br) on 2017-02-07T11:51:58Z (GMT) No. of bitstreams: 1 dissertacao_mestrado_jose-grimaldo.pdf: 19406681 bytes, checksum: d108855fa0fb0d44ee5d1cb59579a04c (MD5) / Made available in DSpace on 2017-02-07T11:51:58Z (GMT). No. of bitstreams: 1 dissertacao_mestrado_jose-grimaldo.pdf: 19406681 bytes, checksum: d108855fa0fb0d44ee5d1cb59579a04c (MD5) / Accuracy in image object detection has been usually achieved at the expense of much computational load. Therefore a trade-o between detection performance and fast execution commonly represents the ultimate goal of an object detector in real life applications. Most images are composed of non-trivial amounts of background information, such as sky, ground and water. In this sense, using an object detector against a recurring background pattern can require a signi cant amount of the total processing time. To alleviate this problem, search space reduction methods can help focusing the detection procedure on more distinctive image regions. / Among the several approaches for search space reduction, we explored saliency information to organize regions based on their probability of containing objects. Saliency detectors are capable of pinpointing regions which generate stronger visual stimuli based solely on information extracted from the image. The fact that saliency methods do not require prior training is an important benefit, which allows application of these techniques in a broad range of machine vision domains. We propose a novel method toward the goal of faster object detectors. The proposed method was grounded on a multi-scale spectral residue (MSR) analysis using saliency detection. For better search space reduction, our method enables fine control of search scale, more robustness to variations on saliency intensity along an object length and also a direct way to control the balance between search space reduction and false negatives caused by region selection. Compared to a regular sliding window search over the images, in our experiments, MSR was able to reduce by 75% (in average) the number of windows to be evaluated by an object detector while improving or at least maintaining detector ROC performance. The proposed method was thoroughly evaluated over a subset of LabelMe dataset (person images), improving detection performance in most cases. This evaluation was done comparing object detection performance against different object detectors, with and without MSR. Additionally, we also provide evaluation of how different object classes interact with MSR, which was done using Pascal VOC 2007 dataset. Finally, tests made showed that window selection performance of MSR has a good scalability with regard to image size. From the obtained data, our conclusion is that MSR can provide substantial benefits to existing sliding window detectors