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The aim of our contribution is to clarify the relation between totally regular variables and Appell sequences of hypercomplex holomorphic polynomials (sometimes simply called monogenic power-like functions) in Hypercomplex Function Theory. After their introduction in 2006 by two of the authors of this note on the occasion of the 17th IKM, the latter have been subject of investigations by different authors with different methods and in various contexts. The former concept, introduced by R. Delanghe in 1970 and later also studied by K. Gürlebeck in 1982 for the case of quaternions, has some obvious relationship with the latter, since it describes a set of linear hypercomplex holomorphic functions all power of which are also hypercomplex holomorphic. Due to the non-commutative nature of the underlying Clifford algebra, being totally regular variables or Appell sequences are not trivial properties as it is for the integer powers of the complex variable z=x+ iy. Simple examples show also, that not every totally regular variable and its powers form an Appell sequence and vice versa. Under some very natural normalization condition the set of all para-vector valued totally regular variables which are also Appell sequences will completely be characterized. In some sense the result can also be considered as an answer to a remark of K. Habetha in chapter 16: Function theory in algebras of the collection Complex analysis. Methods, trends, and applications, Akademie-Verlag Berlin, (Eds. E. Lanckau and W. Tutschke) 225-237 (1983) on the use of exact copies of several complex variables for the power series representation of any hypercomplex holomorphic function.
There is a continuous exacerbation of environmental problems in big cities of today’s world, thereby, diminishing the quality of life in them. Of particular concern is the fact that today’s megacities are evolving in the developing world without corresponding growth in the economy, infrastructure and other human development indices. As urban population continues to grow in these cities of the Global South, governing institutions are usually unable to keep pace with their social responsibilities, thus, making the issue of urban governance very critical. This is because effective and efficient urban governance is highly essential for the creation, strengthening and sustenance of governing institutions.
Lagos, a mega-city of over 15.45 million people and the most populous metropolitan area on the African continent epitomizes the fundamental grave characteristics of the emerging megacities of the Global South, thereby, constituting an apt choice in understanding the emerging megacities of the next generation. Two out of every three Lagos residents live in slums and de-humanizing physical and social conditions. Many of them sleep, work, eat and cook under highway bridges, at the mercy of weather elements.
This research, therefore, evaluated urban governance through housing administration in Africa’s largest megacity. It examines the extent of housing problems in the city, the causal factors and the culpability of government agencies statutorily responsible for the provision, control and management of housing development in Lagos - the tenth largest city in the world. A representative geographic part of the city which manifests classic characteristics of slum life, listed by Mike Davis as the largest slum in Africa and the 6th largest in the world – Ajegunle - was adopted for case study. The research design combined rigorous literature search (desk research) with quantitative and, especially, qualitative approaches to data collection. The qualitative approach was more intensely adopted because government officials often respond to enquiries with ‘official answers and data’ which may not be reliable and the study had to rely on keen observation of physical traces, social interaction and personal investigation. The cross-sectional research method was adopted. Information was solicited from house-owners, building industry professionals, sociologists and officials of relevant government agencies, through research tools like questionnaires, interviews, focused group discussions and personal observations.
The analysis and discussion of these field data, in conjunction with the information from the desk research gave a better understanding of the status-quo, which informed the recommendations proposed in the dissertation for mitigating the problems. The research discovered that many of the statutory housing agencies have the capacity to effectively discharge their responsibilities. However, it was also shown that corruption and abdication of responsibilities by the staff of these agencies constitute primary causes of the chasm between the anticipated lofty outcome from the laudable building regulations/bye-laws and the appalling reality. It also discovered that lack of political will and apathy on the part of successive Governments of Lagos State to the improvement of housing conditions of the poor masses are major causes of the housing debacle in Lagos.
Several germane and realistic recommendations for redressing the situation were subsequently proffered. These include amongst others, the conduction of an accurate census for Lagos, in conjunction with credible international agencies, as a requisite basis for effective planning of any sort. The process of obtaining legal titles for land should also be made less cumbersome, while the housing administration process should be computerized; in order to reduce inter-personal contacts between applicants and government officials to the barest minimum, as a means of curbing the wide spread corruption in the system.
This paper is focused on the first numerical tests for coupling between analytical solution and finite element method on the example of one problem of fracture mechanics. The calculations were done according to ideas proposed in [1]. The analytical solutions are constructed by using an orthogonal basis of holomorphic and anti-holomorphic functions. For coupling with finite element method the special elements are constructed by using the trigonometric interpolation theorem.
THE INFLUENCE OF THE LOCAL CONCAVITY ON THE FUNCTIONING OF BEARING SHELL OF HIGH-RISE CONSTRUCTION
(2012)
Areas with various defects and damages, which reduce carrying capacity, were examined in a study of metal chimneys. In this work, the influence of the local dimples on the function of metal chimneys was considered. Modeling tasks were completed in the software packages LIRA and ANSYS. Parameters were identified, which characterize the local dimples, and a numerical study of the influence of local dimples on the stress-strain state of shells of metal chimneys was conducted. A distribution field of circular and meridional tension was analyzed in a researched area. Zones of influence of dimples on the bearing cover of metal chimneys were investigated. The bearing capacities of high-rise structures with various dimple geometries and various cover parameters were determined with respect to specified areas of the trunk. Dependent relationships are represented graphically for the decrease in bearing capacity of a cover with respect to dimples. Diameter and thickness of covers of metal chimneys were constructed according to the resulting data.
We briefly review and use the recent comprehensive research on the manifolds of square roots of −1 in real Clifford geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the complex imaginary unit j is replaced by a square root of −1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known and applied CFTs, which replaced the complex imaginary unit j only by blades (usually pseudoscalars) squaring to −1. A major advantage of real Clifford algebra CFTs is their completely real geometric interpretation. We study (left and right) linearity of the CFT for constant multivector coefficients in Cl(p,q), translation (x-shift) and modulation (w -shift) properties, and signal dilations. We show an inversion theorem. We establish the CFT of vector differentials, partial derivatives, vector derivatives and spatial moments of the signal. We also derive Plancherel and Parseval identities as well as a general convolution theorem.
Non-destructive techniques for damage detection became the focus of engineering interests in the last few years. However, applying these techniques to large complex structures like civil engineering buildings still has some limitations since these types of structures are
unique and the methodologies often need a large number of specimens for reliable results. For this reason, cost and time can greatly influence the final results.
Model Assisted Probability Of Detection (MAPOD) has taken its place among the ranks of damage identification techniques, especially with advances in computer capacity and modeling tools. Nevertheless, the essential condition for a successful MAPOD is having a reliable model in advance. This condition is opening the door for model assessment and model quality problems. In this work, an approach is proposed that uses Partial Models (PM) to compute the Probability Of damage Detection (POD). A simply supported beam, that can be structurally modified and
tested under laboratory conditions, is taken as an example. The study includes both experimental and numerical investigations, the application of vibration-based damage detection approaches and a comparison of the results obtained based on tests and simulations.
Eventually, a proposal for a methodology to assess the reliability and the robustness of the models is given.
Texts from the web can be reused individually or in large quantities. The former is called text reuse and the latter language reuse. We first present a comprehensive overview of the different ways in which text and language is reused today, and how exactly information retrieval technologies can be applied in this respect. The remainder of the thesis then deals with specific retrieval tasks. In general, our contributions consist of models and algorithms, their evaluation, and for that purpose, large-scale corpus construction.
The thesis divides into two parts. The first part introduces technologies for text reuse detection, and our contributions are as follows: (1) A unified view of projecting-based and embedding-based fingerprinting for near-duplicate detection and the first time evaluation of fingerprint algorithms on Wikipedia revision histories as a new, large-scale corpus of near-duplicates. (2) A new retrieval model for the quantification of cross-language text similarity, which gets by without parallel corpora. We have evaluated the model in comparison to other models on many different pairs of languages. (3) An evaluation framework for text reuse and particularly plagiarism detectors, which consists of tailored detection performance measures and a large-scale corpus of automatically generated and manually written plagiarism cases. The latter have been obtained via crowdsourcing. This framework has been successfully applied to evaluate many different state-of-the-art plagiarism detection approaches within three international evaluation competitions.
The second part introduces technologies that solve three retrieval tasks based on language reuse, and our contributions are as follows: (4) A new model for the comparison of textual and non-textual web items across media, which exploits web comments as a source of information about the topic of an item. In this connection, we identify web comments as a largely neglected information source and introduce the rationale of comment retrieval. (5) Two new algorithms for query segmentation, which exploit web n-grams and Wikipedia as a means of discerning the user intent of a keyword query. Moreover, we crowdsource a new corpus for the evaluation of query segmentation which surpasses existing corpora by two orders of magnitude. (6) A new writing assistance tool called Netspeak, which is a search engine for commonly used language. Netspeak indexes the web in the form of web n-grams as a source of writing examples and implements a wildcard query processor on top of it.
Safety operation of important civil structures such as bridges can be estimated by using fracture analysis. Since the analytical methods are not capable of solving many complicated engineering problems, numerical methods have been increasingly adopted. In this paper, a part of isotropic material which contains a crack is considered as a partial model and the proposed model quality is evaluated. EXtended IsoGeometric Analysis (XIGA) is a new developed numerical approach [1, 2] which benefits from advantages of its origins: eXtended Finite Element Method (XFEM) and IsoGeometric Analysis (IGA). It is capable of simulating crack propagation problems with no remeshing necessity and capturing singular field at the crack tip by using the crack tip enrichment functions. Also, exact representation of geometry is possible using only few elements. XIGA has also been successfully applied for fracture analysis of cracked orthotropic bodies [3] and for simulation of curved cracks [4]. XIGA applies NURBS functions for both geometry description and solution field approximation. The drawback of NURBS functions is that local refinement cannot be defined regarding that it is based on tensorproduct constructs unless multiple patches are used which has also some limitations. In this contribution, the XIGA is further developed to make the local refinement feasible by using Tspline basis functions. Adopting a recovery based error estimator in the proposed approach for evaluation of the model quality and performing the adaptive processes is in progress. Finally, some numerical examples with available analytical solutions are investigated by the developed scheme.
This paper presents a robust model updating strategy for system identification of wind turbines. To control the updating parameters and to avoid ill-conditioning, the global sensitivity analysis using the elementary effects method is conducted. The formulation of the objective function is based on M¨uller-Slany’s strategy for multi-criteria functions. As a simulationbased optimization, a simulation adapter is developed to interface the simulation software ANSYS and the locally developed optimization software MOPACK. Model updating is firstly tested on the beam model of the rotor blade. The defect between the numerical model and the reference has been markedly reduced by the process of model updating. The effect of model updating becomes more pronounced in the comparison of the measured and the numerical properties of the wind turbine model. The deviations of the frequencies of the updated model are rather small. The complete comparison including the free vibration modes by the modal assurance criteria shows the excellent coincidence of the modal parameters of the updated model with the ones from the measurements. By successful implementation of the model validation via model updating, the applicability and effectiveness of the solution concept has been demonstrated.