Generating functions express a sequence as coefficients arising from a power series in variables. They have many applications in combinatorics and probability. In this paper, we will investigate the important properties of four kinds of generating functions in one variables: ordinary generating unction, exponential generating function, probability generating function and moment generating function. Many examples with applications in combinatorics and probability, will be discussed. Finally, some well-known contest problems related to generating functions will be addressed.

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Depuis quelques années, Internet est devenu un média incontournable pour la diffusion de ressources multilingues. Cependant, les différences linguistiques constituent souvent un obstacle majeur aux échanges de documents scientifiques, culturels, pédagogiques et commerciaux. En plus de cette diversité linguistique, on constate le développement croissant de bases de données et de collections composées de différents types de documents textuels ou multimédias, ce qui complexifie également le processus de repérage documentaire. En général, on considère l’image comme « libre » au point de vue linguistique. Toutefois, l’indexation en vocabulaire contrôlé ou libre (non contrôlé) confère à l’image un statut linguistique au même titre que tout document textuel, ce qui peut avoir une incidence sur le repérage. Le but de notre recherche est de vérifier l’existence de différences entre les caractéristiques de deux approches d’indexation pour les images ordinaires représentant des objets de la vie quotidienne, en vocabulaire contrôlé et en vocabulaire libre, et entre les résultats obtenus au moment de leur repérage. Cette étude suppose que les deux approches d’indexation présentent des caractéristiques communes, mais également des différences pouvant influencer le repérage de l’image. Cette recherche permet de vérifier si l’une ou l’autre de ces approches d’indexation surclasse l’autre, en termes d’efficacité, d’efficience et de satisfaction du chercheur d’images, en contexte de repérage multilingue. Afin d’atteindre le but fixé par cette recherche, deux objectifs spécifiques sont définis : identifier les caractéristiques de chacune des deux approches d’indexation de l’image ordinaire représentant des objets de la vie quotidienne pouvant influencer le repérage, en contexte multilingue et exposer les différences sur le plan de l’efficacité, de l’efficience et de la satisfaction du chercheur d’images à repérer des images ordinaires représentant des objets de la vie quotidienne indexées à l’aide d’approches offrant des caractéristiques variées, en contexte multilingue. Trois modes de collecte des données sont employés : l’analyse des termes utilisés pour l’indexation des images, la simulation du repérage d’un ensemble d’images indexées selon chacune des formes d’indexation à l’étude réalisée auprès de soixante répondants, et le questionnaire administré aux participants pendant et après la simulation du repérage. Quatre mesures sont définies pour cette recherche : l’efficacité du repérage d’images, mesurée par le taux de succès du repérage calculé à l’aide du nombre d’images repérées; l’efficience temporelle, mesurée par le temps, en secondes, utilisé par image repérée; l’efficience humaine, mesurée par l’effort humain, en nombre de requêtes formulées par image repérée et la satisfaction du chercheur d’images, mesurée par son autoévaluation suite à chaque tâche de repérage effectuée. Cette recherche montre que sur le plan de l’indexation de l’image ordinaire représentant des objets de la vie quotidienne, les approches d’indexation étudiées diffèrent fondamentalement l’une de l’autre, sur le plan terminologique, perceptuel et structurel. En outre, l’analyse des caractéristiques des deux approches d’indexation révèle que si la langue d’indexation est modifiée, les caractéristiques varient peu au sein d’une même approche d’indexation. Finalement, cette recherche souligne que les deux approches d’indexation à l’étude offrent une performance de repérage des images ordinaires représentant des objets de la vie quotidienne différente sur le plan de l’efficacité, de l’efficience et de la satisfaction du chercheur d’images, selon l’approche et la langue utilisées pour l’indexation. / During the last few years, the Internet has become an indispensable medium for the dissemination of multilingual resources. However, language differences are often a major obstacle to the exchange of scientific, cultural, educational and commercial documents. Besides this linguistic diversity, many databases and collections now contain documents in various formats that can also adversely affect their retrieval process. In general, images are considered to be language-independent resources. Nevertheless, the image indexing process using either a controlled or uncontrolled vocabulary gives the image a linguistic status similar to any other textual document and thus leads to the same difficulties in their retrieval. The goal of our research is to first identify the differences between the indexing approaches using a controlled and an uncontrolled vocabulary for ordinary images of everyday-life objects and to then differentiate between the results obtained at the time of image retrieval. This study supposes that the two indexing approaches show not only common characteristics, but also differences that can influence image retrieval. Thus, this research makes it possible to indicate if one of these indexing approaches surpasses the other in terms of effectiveness, efficiency, and satisfaction of the image searcher in a multilingual retrieval context. For this study, two specific objectives are defined: to identify the characteristics of each approach used for ordinary image indexing of everyday-life objects that can effect image retrieval in a multilingual context; and to explore the differences between the two indexing approaches in terms of their effectiveness, their efficiency, and the satisfaction of the image searcher when trying to retrieve ordinary images of everyday-life objects indexed according to either approach in a multilingual retrieval context. Three methods of data collection are used: an analysis of the image indexing terms, a simulation of the retrieval of a set of images indexed according to each of the two indexing approaches conducted with sixty respondents, and a questionnaire submitted to the participants during and after the retrieval simulation. Four measures are defined in this research: the effectiveness of image retrieval measured by the success rate calculated in terms of the number of retrieved images; time efficiency measured by the average time, in seconds, used to retrieve an image; human efficiency measured in terms of the human effort represented per average number of queries necessary to retrieve an image; and the satisfaction of the image searcher measured by the self-evaluation of the participant of the retrieval process after each completed task. This research shows that in terms of ordinary image indexing representing everyday-life objects, the two approaches investigated are fundamentally distinct on the terminological, perceptual, and structural perspective. Additionally, the analysis of the characteristics of the two indexing approaches reveals that if the indexing language differs, the characteristics vary little within the same indexing approach. Finally, this research underlines that the two indexing approaches of ordinary images representing everyday-life objects have a retrieval performance that is different in terms of its effectiveness, efficiency, and satisfaction of the image searcher according to the approach and the language used for indexing.

A number of previous studies have examined lay counsellor training within a modernist paradigm. By contrast, this study collaboratively presents ways of training pastoral caregivers using a participatory approach to practical theology and pastoral care in the postmodern time in which we live. The research journey starts from the premise that postmodernity calls for the mediation of a new approach to practising theology, pastoral care and giving authority to ordinary members of the church through training in pastoral work. This work therefore describes Participatory Pastoral Care (PPC) training as a suggested way to train people of God to use participatory approaches. The research journey also explores how the PPC training constructions they participated in brought about transformations in the co-researchers' lives, relationships, caring practices and the societies in which they live. This practical theology research document introduces the participants as co-researchers and theologians. The recollections shared by the participants reveal a rich variety of stories as these participants reflect on their lives, caring practices and faith journeys. This research document is viewed through the lens of a postmodern epistemology that builds on social constructionist and poststructuralist perspectives. Thirty-three participants embarked on this feminist narrative participatory action research journey, not only to tell their stories, but also to negotiate and challenge ways of training pastoral caregivers within a participatory practical theological and pastoral approach. This research document informs the church, theological institutions and broader caregiver practices through narratives about what the participating members of various congregations find helpful in the co-construction of participatory pastoral training and what they do not find helpful. The methods used to gather the recollections of the participants were multiple reflexive conversations and the discussion of a semi-structured questionnaire. This research journey therefore offers a deeper understanding of the experience of being part of a postmodern construction of training for participatory pastoral caregivers that has the transformation of society as its theological aim. / Philosophy, Practical and Systematic Theology / D.Th. (Practical Theology - with specialisation in Pastoral Therapy)

In this thesis, I investigate dynamic and computational properties of prokaryotic signalling architectures commonly known as the Two Component Signalling networks and phosphorelays. The aim of this study is to understand the information processing capabilities of different prokaryotic signalling architectures by examining the dynamics they exhibit. I present original investigations into the dynamics of different phosphorelay architectures and identify network architectures that include a commonly found four step phosphorelay architecture with a capacity for tuning its steady state output to implement different signal-response behaviours viz. sigmoidal and hyperbolic response. Biologically, this tuning can be implemented through physiological processes like regulating total protein concentrations (e.g. via transcriptional regulation or feedback), altering reaction rate constants through binding of auxiliary proteins on relay components, or by regulating bi-functional activity in relays which are mediated by bifunctional histidine kinases. This study explores the importance of different biochemical arrangements of signalling networks and their corresponding response dynamics. Following investigations into the significance of various biochemical reactions and topological variants of a four step relay architecture, I explore the effects of having different types of proteins in signalling networks. I show how multi-domain proteins in a phosphorelay architecture with multiple phosphotransfer steps occurring on the same protein can exhibit multistability through a combination of double negative and positive feedback loops. I derive a minimal multistable (core) architecture and show how component sharing amongst networks containing this multistable core can implement computational logic (like AND, OR and ADDER functions) that allows cells to integrate multiple inputs and compute an appropriate response. I examine the genomic distribution of single and multi domain kinases and annotate their partner response regulator proteins across prokaryotic genomes to find the biological significance of dynamics that these networks embed and the processes they regulate in a cell. I extract data from a prokaryotic two component protein database and take a sequence based functional annotation approach to identify the process, function and localisation of different response regulators as signalling partners in these networks. In summary, work presented in this thesis explores the dynamic and computational properties of different prokaryotic signalling networks and uses them to draw an insight into the biological significance of multidomain sensor kinases in living cells. The thesis concludes with a discussion on how this understanding of the dynamic and computational properties of prokaryotic signalling networks can be used to design synthetic circuits involving different proteins comprising two component and phosphorelay architectures.

This diploma thesis deals with the ethical problems contemporary dying and relationships society to death. One is devoted to issue dysthanasia, that approached as manipulation with death. Work looks for sources of dysthanasia and one finds is in contemporary attitudes medicine and patients to deaths, dehumanization of medicine and diversion from traditions. That also looks for pathway to prevention of dysthanasia. One sees is in repeated humanization of medicine, in accept the concept futile treatment and the capabilities to distinguish ordinary and extraordinary means. This work offers the alternative of dysthanasia palliative care and seeks for a position of social worker in it.

Summaries in Afrikaans and English / Die wereldwye neiging in die onderwys wat bekend staan as lnsluiting is teweeggebring deur die reg van elke individu op onderrig, soos vasgele in die Universele Verklaring van Menseregte van 1948, tesame met die hernieude onderneming van die wereldgemeenskap' op die Wereldkonferensie oor Opvoeding vir Almal van 1990 om daardie reg, ten spyte van individuele • verskille, te verskans. Aile aanduidings is dat Suid-Afrika ook die beleid van lnsluiting sal aanvaar in die regering se pogings om die onderwys te hervorm. Hierdie beleid van lnsluiting hou groot implikasies in vir die onderwyser in, die gewone skole, aangesien hulle beida die voorwerp en die . agent is van sodanige hervorming. Daar word aanvaar dat die onderwyser se houding teenoor leerders in die algemeen 'n belangrike rol speel met betrekking tot die sukses van die onderrig- en leergebeure in die klaskamer. Hierdie houding word dikwels bepaal deur die · onderwyser se kennis van leerders in die klaskamer en sy vaardighede met betrekking tot hul onderrig. In die lig van die literatuurstudie, wat daarop dui dat onderwysers nie voldoende opleiding ontvang om aan die behoeftes van leerders met spesiale onderwysbehoeftes te voldoen nie, word in hierdie navorsing die houding van die onderwyser in die gewone skool teenoor die leerders met spesiale onderwysbehoeftes soos dit in die praktyk openbaar word bepaal. / The right of every individual to education, as enshrined in the 1948 Universal Declaration of Human Rights, and the renewing of the pledge made by the world community at the 1990 World Conference on Education for All to ensure that right, regardless of individual differences, gave rise to the worldwide trend in education known as Inclusion. All indications are that South Africa will also adopt the policy of Inclusion as part of the government's efforts to reform education. The policy of Inclusion has major implications for the teachers in the ordinary school, as they are both the subjects and the agents of reform. It is generally believed that teachers' attitudes towards learners plays a major role ·in the success of the teaching-learning events in the classroom. These attitudes are often influenced by .. the teachers' knowledge of the learners in their classrooms and their skill in teaching them. In view of literature that suggests that teachers are not adequately trained to meet the needs of learners, with special Educational needs, this study undertakes to investigate the attitude of teachers in the ordinary school towards learners with special educational needs, as it manifests in practice. / Educational Studies / M.Ed. (Ortopedagogiek)

The study was conducted across the four district municipalities in the Free State province of South Africa. The objective of the study was to determine socio-economic factors that affected livestock numbers among smallholder cattle and sheep farmers in the Free State province of South Africa. The research was qualitative and quantitative in nature. Proportionate random sampling method was used to collect data. The population comprised of smallholder cattle and sheep farmers that kept at least 30 livestock. Data between the 2008 and 2012 farming seasons were collected by administering well-structured questionnaires to 250 smallholder cattle and sheep farmers. Data collected were captured and analysed using the statistical package for social sciences (SPSS version 22 of 2013) to obtain frequency, cross-tabulation, descriptive statistics and ordinary least square (OLS) regression. Descriptive statistics results indicated that lack of camp systems, drought prevalence, increased feed costs, poor veterinary interventions, insufficient breeding stock, high cost of fuel and transportation, lack of equipment, diseases, stock theft and pilfering, and insufficient grazing land were the prevalent factors that affected cattle and sheep farming in the province.The OLS regression results indicated that the variables that significantly affected livestock numbers were district, household size, livestock numbers in 2008, planted pastures, grazing land condition, grazing land acquisition, service, advice / training, veterinary services, purchase of dosing products and sales per year. The results also indicated that the majority (96.8%) of the smallholder cattle and sheep farmers would like to increase their livestock numbers. It was therefore recommended that extension and veterinary services should be strengthened in the study area. In addition, it was recommended that smallholder livestock farmers should be encouraged to plant pastures to reduce pressure on the natural veld and make forage available throughout the year. Lastly, as a recommendation, government should provide subsidies with distribution policies that will ensure that all smallholder livestock farmers can benefit. / Agriculture and  Animal Health / M. Sc. (Agriculture)

In this work, our goal is to prove results on prolongation of solutions, uniform boundedness of solutions, uniform stability as well uniform asymptotic stability (in the classical sense of Lyapunov) for measure differential equations and for dynamic equations on time scales. In order to get our results, we employ the theory of generalized ODEs, since these equations encompass measure differential equations and dynamic equations on time scales. Therefore, to get our results, we start by proving the expected result for abstract generalized ODEs. Then, using the correspondence between the solutions of these equations and the solutions of measure differential equations (see [38]), we extend all the results to these the latter. After that, using the correspondence between the solutions of measure differential equations and the solutions of dynamic equations on time scales (see [21]), we extend all the results to these last equations. Finally, we investigate autonomous generalized ODEs and show that these equations do not enlarge the class of classical autonomous ODEs, even when we consider a more general class of functions as right-hand sides. All the new results presented in this work are contained in papers [16, 17, 18, 19]. / Neste trabalho, nosso objetivo e provar resultados sobre prolongamento de soluções, limitação uniforme de soluções, estabilidade uniforme e estabilidade uniforme assintótica (no sentido clássico de Lyapunov) para equações diferenciais em medida e para equações dinâmicas em escalas temporais. A fim de obter os nossos resultados, empregamos a teoria de EDOs generalizadas, uma vez que estas equações abrangem equações diferenciais em medida e equações dinâmicas em escalas temporais. Portanto, para obter nossos resultados, vamos começar por provar, os resultados que queremos para EDOs generalizadas abstratas. Em seguida, usando a correspondência entre as soluções de EDOs generalizadas e soluções de equações diferenciais em medida (ver [38]), estenderemos os resultados para estas ultimas equações. Depois disso, usando a correspondência entre as soluções de equações diferenciais em medida e as soluções de equações dinâmicas em escalas temporais (ver [21]), estenderemos todos os resultados para estas ultimas equações. Finalmente, investigamos EDOs generalizadas autônomas e mostramos que estas equações não aumentam a classe de EDOs autônomas clássicas, mesmo quando consideramos uma classe mais geral de funções nos lados direitos das equações. Os novos resultados encontrados estão contidos em [16, 17, 18, 19].

Dans ce travail de recherche, nous sommes intéresses par la modélisation de l'hématopoïèse. Les cellules souches hématopoïétiques (CSH) sont des cellules indifférenciées de la moelle osseuse, possédant la capacité de se renouveler et de se différencier (pour la production des globules rouges, globules blancs et les plaquettes). Le processus de l'hématopoïèse souvent révèle des irrégularités qui causent les maladies hématologiques. En modélisant la leucémie myéloide chronique (LMC), une maladie hématologique fréquente, nous représentons l'hématopoïèse des cellules normales et cancéreuses par un système d'équations différentielles ordinaires (EDO). L'homéostasie des cellules normales et différente de l'homéostasie des cellules cancéreuses, et dépend de quelques lignées des cellules normales et cancéreuses. Nous analysons la dynamique globale du modèle pour obtenir les conditions de régénération de l'hématopoïèse ou bien la persistance de la LMC. Nous démontrons aussi que la coexistence des cellules normales et cancéreuses ne peut avoir lieu pour longtemps. Imatinib est un traitement de base de la LMC, avec un dosage variant de 400 à 1000 mg par jour. Certains patients présentent des réponses différentes à la thérapie, pouvant être hématologique, cytogénétique et moléculaire. La thérapie échoue dans deux cas: le patient demande un temps plus long pour réagir, alors il s'agit d'une réponse suboptimale; ou bien le patient résiste après une bonne réponse initiale. Pour déterminer le dosage optimal, nécessaire à la réduction des cellules cancéreuses, nous représentons les effets de la thérapie par un problème de contrôle optimal. Notre but est de minimiser le cout du traitement et le nombre des cellules cancéreuses. La réponse suboptimale, la résistance et le rétablissement sont alors obtenus suivant l'influence de l'imatinib sur les taux de division et de mortalité des cellules cancéreuses. Nous étudions par ailleurs l'hématopoïèse selon un modèle structuré en age, décrivant l'évolution des CSH normales et cancéreuses. Nous démontrons que le taux de division des CSH cancéreuses joue un rôle important dans la détermination du contrôle optimal. En contrôlant la croissance des cellules normales et cancéreuses avec compétition inter spécifique, nous démontrons que le dosage optimal dépend de l'homéostasie des CSH cancéreuses. / Modelling hematopoiesis represents a feature of our research. Hematopoietic stem cells (HSC) are undifferentiated cells, located in bone marrow, with unique abilities of self-renewal and differentiation (production of white cells, red blood cells and platelets).The process of hematopoiesis often exhibits abnormalities causing hematological diseases. In modelling Chronic Myeloid Leukemia (CML), a frequent hematological disease, we represent hematopoiesis of normal and leukemic cells by means of ordinary differential equations (ODE). Homeostasis of normal and leukemic cells are supposed to be different and depend on some lines of normal and leukemic HSC. We analyze the global dynamics of the model to obtain the conditions for regeneration of hematopoiesis and persistence of CML. We prove as well that normal and leukemic cells can not coexist for a long time. Imatinib is the main treatment of CML, with posology varying from 400 to 1000 mg per day. Some affected individuals respond to therapy with various levels being hematologic, cytogenetic and molecular. Therapy fails in two cases: the patient takes a long time to react, then suboptimal response occurs; or the patient resists after an initial response. Determining the optimal dosage required to reduce leukemic cells is another challenge. We approach therapy effects as an optimal control problem to minimize the cost of treatment and the level of leukemic cells. Suboptimal response, resistance and recovery forms are obtained through the influence of imatinib onto the division and mortality rates of leukemic cells. Hematopoiesis can be investigated according to age of cells. An age-structured system, describing the evolution of normal and leukemic HSC shows that the division rate of leukemic HSC plays a crucial role when determining the optimal control. When controlling the growth of cells under interspecific competition within normal and leukemic HSC, we prove that optimal dosage is related to homeostasis of leukemic HSC.