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When defining a structure to fulfill a set of axioms that are similar to those prescribed by Euclid, one must select a set of points and then define what is meant by a line and what is meant by a circle. When properly defined these labels will have properties which are similar to their counterparts in the (complex) plane, the lines and circles which Euclid undoubtedly had in mind. In this manner, the geometer may employ his intuition from the complex plane to prove theorems about other systems. Most "finite geometries" have clearly defined notions of points and lines but fail to define circles. The two notable exceptions are the circles in a finite affine plane and the circles in a Mobius plane. Using the geometry of Euclid as motivation, we strive to develop structures with both lines and circles. The only successful example other than the complex plane is the affine plane over a finite field, where all of Euclid's geometry holds except for any assertions involving order or continuity. To complement the prolific work concerning finite geometries and their lines, we provide a general definition of a circle, or more correctly, of a collection of circles and present some preliminary results concerning the construction of such structures. Our definition includes the circles of an affine plane over a finite field and the circles in a Mobius plane as special cases. We develop a necessary and sufficient condition for circularity, present computational techniques for determining circularity and give varying constructions. We devote a chapter to the use of circular designs in coding theory. It is proven that these structures are not useful in the theory of error-correcting codes, since more efficient codes are known, for example the Reed-Muller codes. However, the theory developed in the earlier chapters does have applications to Cryptology. We present five encryption methods utilizing circular structures.

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It was not until the 20th century that combinatorial design theory was studied as a formal subject. This field has many applications, for example in statistical experimental design, coding theory, authentication codes, and cryptography. Major approaches to the problem of discovering new t-designs rely on (i) the construction of large sets of t designs, (ii) using prescribed automorphism groups, (iii) recursive construction methods. In 2017 and 2018, Tran Van Trung introduced new recursive techniques to construct t – (v, k, λ) designs. These methods are of purely combinatorial nature and require using "ingredient" t-designs or resolutions whose parameters satisfy a system of non-linear equations. Even after restricting the range of parameters in this new method, the task is computationally intractable. In this work, we enhance Tran Van Trung's "Basic Construction" by a robust and efficient hybrid computational apparatus which enables us to construct hundreds of thousands of new t – (v, k, Λ) designs from previously known ingredient designs. Towards the end of the dissertation we also create a new family of 2-resolutions, which will be infinite if there are infinitely many Sophie Germain primes. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

RESUME L’évolution des stratégies de croissance des jeunes entreprises La recherche sur la croissance des jeunes entreprises s’est fortement développée au cours des trente dernières années. La situation est particulièrement marquée en Europe où le nombre de jeunes entreprises en forte croissance est réduit alors qu’il est admis que ce type d’entreprises contribue à la création d’un nombre important d’emplois. La communauté scientifique reconnaît que la recherche actuellement disponible manque d’intégration, d’ancrage théorique et d’approches longitudinales. De ce fait, elle n’est pas en mesure d’expliquer comment et pourquoi les jeunes entreprises adoptent différentes stratégies de croissance et suivent des trajectoires hétérogènes. L’objectif de cette thèse est de produire un cadre analytique, aussi intégré et dynamique que possible, permettant de mieux comprendre le pourquoi et le comment de la croissance des jeunes entreprises. Pour faire face à ce défi, elle s’inscrit dans la foulée des travaux séminaux de Gartner et Marchesnay respectivement sur le cadre d’analyse de la création d’entreprise et le système de gestion des petites et moyennes entreprises. Elle adopte le paradigme épistémologique du réalisme critique et recourt essentiellement à la méthode des cas. L’approche générale se veut donc longitudinale, qualitative et exploratoire. La recherche est développée en trois temps qui correspondent à autant de chapitres présentés sous forme d’articles scientifiques. Le chapitre 1 remonte aux sources de sept grandes approches de recherche qui ont été adoptées pour expliquer la croissance des jeunes entreprises. Il montre que, prise isolément, aucune d’entre elles ne peut expliquer la croissance mais il souligne également à quel point elles se répondent et se complètent. Le chapitre 2 propose une modélisation systémique qui capitalise sur l’approche configurationnelle telle que développée par Miller et Mintzberg et celle par les processus telle que développée par Van de Ven. Ces deux approches permettent en effet d’intégrer de nombreux acquis des recherches existantes. La modélisation développée suggère que les jeunes entreprises adoptent des configurations associées à différentes stratégies qui mettent en cohérence les éléments caractéristiques de la démarche entrepreneuriale (c’est-à-dire l’entrepreneur, les activités, les ressources, la structure organisationnelle et l’environnement) alors que ceux-ci évoluent sous l’influence de multiples processus. Le chapitre 3, rédigé en anglais, s’intéresse plus particulièrement au cas des jeunes entreprises de services informatiques. Il approfondit la modélisation proposée au chapitre 2 dans un contexte où les entreprises sont, entre autres, confrontées au choix de se développer en tant que sociétés de services et/ou ont l’opportunité de se redéployer vers le développement de logiciels. Sur le plan méthodologique, l’approche choisie consiste à développer une typologie de configurations stratégiques déduite des littératures académique et pratique puis à comparer les idéaux-types qui la compose aux configurations réellement adoptées par des entreprises. La modélisation et la typologie sont testées et conceptuellement confirmées par plusieurs études de cas d’entreprises belges. L’ensemble confirme bien que le développement des jeunes entreprises passe bien par l’adoption de configurations successives, associables à différentes stratégies de croissance, sans que celles-ci et leurs séquences soient prédéterminées du fait de l’influence concomitante de plusieurs processus. Bien qu’essentiellement conceptuelle, la thèse confirme le bien-fondé de l’adoption conjointe des approches par les configurations et par les processus pour la compréhension du phénomène complexe qu’est la croissance. Elle ouvre également une porte à de futurs travaux de validation quantitative. Au niveau de la pratique, elle permet d’envisager le développement d’outils d’aide à la décision pour les entrepreneurs afin de les sensibiliser aux conditions et implications de différentes stratégies de croissance. ABSTRACT The evolution of the growth strategies of young firms Research on the growth of young firms has developed significantly over the last thirty years. The situation is particularly noteworthy in Europe, where there is only a limited number of young firms experiencing strong growth, even though it is widely recognised that this type of firm contributes to the creation of a substantial amount of jobs. The scientific community recognises that the currently available research is lacking in terms of integration, theoretical anchoring and longitudinal approaches. Consequently, it is not able to explain how and why young firms adopt different growth strategies and follow heterogeneous trajectories. The aim of this thesis is to create an analytical framework, which is as integrated and dynamic as possible, so as to make it possible to understand the why and the wherefore behind the growth of young firms. In order to respond to this challenge, the thesis follows in the footsteps of the seminal works of Gartner and Marchesnay respectively, on the conceptual framework for describing new venture creation and the management system of small and medium enterprises. It adopts the epistemological paradigm of ‘critical realism’ and makes use, essentially, of the case study method. The general approach is therefore intended to be longitudinal, qualitative and exploratory. The research is developed in three stages, which correspond to the same number of chapters set out in the form of scientific papers. Chapter 1 goes back to the sources of the seven major research approaches that have been adopted in order to explain the growth of young firms. It demonstrates that, when considered in isolation, none of them can fully explain the growth of young firms, but it also highlights the extent to which they respond to, and complete, one another. Chapter 2 proposes a systemic model that capitalises on the configurational approach as developed by Miller and Mintzberg, as well as the process approach as developed by Van de Ven. Indeed, these two approaches make it possible to integrate a large number of elements that have already been established through existing research. The model suggests that young firms adopt configurations associated with different strategies that tie the key elements of the entrepreneurial phenomenon (namely the entrepreneur, the activities, the resources, the organisational structure and the environment), while these elements change under the influence of numerous processes. The third chapter, which has been written in English, places particular focus on young IT services firms. It takes a more in-depth look at the model proposed in chapter 2 in a context in which firms are, amongst other things, faced with the choice of developing as service firms and/or have the opportunity to turn their efforts and attention towards software development. From a methodological point of view, the chosen approach consists in the development of a typology of strategic configurations deduced from academic and practical literature and then to compare the ideal types with the configurations that have been actually adopted by the firms. The model and typology are tested and conceptually confirmed by several case studies of Belgian companies. The overall findings serve to confirm the fact that the development of young firms is achieved through the adoption of successive configurations that are associated with different growth strategies, without these and their sequences being predetermined because of the influence of multiple simultaneous processes. Although it is essentially conceptual in nature, the thesis confirms the relevance of the joint adoption of the configurational- and process-approaches in order to understand the complexity of the growth phenomenon. It also opens up the door to quantitative validation research work. In terms of its practical application, the thesis enables us to start the development of a toolbox that may help entrepreneurs in the decision-making process so as to raise their awareness regarding the conditions and implications of different growth strategies.

Thesis (Ph. D.)--University of Rhode Island, 2004. / Typescript. Includes bibliographical references (leaves 66-68).

Th. 3e cycle--Inform.--Lille 1, 1978. N°: 735.

Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Traditional radio astronomy imaging techniques assume that the interferometric array is coplanar, with a small field of view, and that the two-dimensional Fourier relationship between brightness and visibility remains valid, allowing the Fast Fourier Transform to be used. In practice, to acquire more accurate data, the non-coplanar baseline effects need to be incorporated, as small height variations in the array plane introduces the w spatial frequency component. This component adds an additional phase shift to the incoming signals. There are two approaches to account for the non-coplanar baseline effects: either the full three-dimensional brightness and visibility model can be used to reconstruct an image, or the non-coplanar effects can be removed, reducing the three dimensional relationship to that of the two-dimensional one. This thesis describes and implements the w-projection and w-stacking algorithms. The aim of these algorithms is to account for the phase error introduced by non-coplanar synthesis arrays configurations, making the recovered visibilities more true to the actual brightness distribution model. This is done by reducing the 3D visibilities to a 2D visibility model. The algorithms also have the added benefit of wide-field imaging, although w-stacking supports a wider field of view at the cost of more FFT bin support. For w-projection, the w-term is accounted for in the visibility domain by convolving it out of the problem with a convolution kernel, allowing the use of the two-dimensional Fast Fourier Transform. Similarly, the w-Stacking algorithm applies a phase correction in the image domain to image layers to produce an intensity model that accounts for the non-coplanar baseline effects. This project considers the KAT7 array for simulation and analysis of the limitations and advantages of both the algorithms. Additionally, a variant of the Högbom CLEAN algorithm was used which employs contour trimming for extended source emission flagging. The CLEAN algorithm is an iterative two-dimensional deconvolution method that can further improve image fidelity by removing the effects of the point spread function which can obscure source data. / AFRIKAANSE OPSOMMING: Tradisionele beeldvormingstegnieke in radio-astronomie aanvaar dat die interferometriese skikking samevlakkig is. Dit beteken dat die twee-dimensionele Fourier verhouding tussen helderheid en sigbaarheid geldig bly en dat die Vinnige Fourier Transform aangewend kan word. Klein hoogtevariasies in die skikkingsvlak bring die w-ruimtelike frekwensiekomponent mee, wat ’n faseverskuiwing in die inkomende seine tot gevolg het. Dus, in praktyk, moet die bydrae van die nie-samevlakkige basislyneffekte in ag geneem word om sodoende die akkuraatheid van die data te verhoog. Twee benaderings kan gevolg word om die nie-samevlakkige basislyneffekte in ag te neem: Metodes wat die volle drie dimensionele helderheid en sigbaarheidsmodel gebruik kan toegepas word om ’n beeld te herbou, andersins kan die nie-samevlakkige effekte verwyder word om sodoende die drie-dimensionele verhouding te verminder tot ’n twee-dimensionele verhouding. Hierdie tesis beskryf en implementeer die ‘w-projeksie’ en ‘w-stapel’ algoritmes. Die doel van hierdie algoritmes is om die fasefout wat deur nie-samevlakkige sinteseskikkingskonfigurasies veroorsaak word, reg te stel. Hierdie regstelling maak die herwinde sigbaarheid van die beeld meer getrou aan die werklike helderheidsverspreidingsmodel. ’n Bykomende voordeel van die algoritmes is beeldvorming van wye-veld ruimtewaarnemings. In ‘w-projection’ word die w-term in die sigbaarheidsdomein in ag geneem deur die ruimtelike frekwensiekomponent met behulp van ’n konvolusiekern vanuit die probleem te verwyder. Die twee-dimensionele Vinnige Fourier Transform kan gevolglik toegepas word. Soortgelyk hieraan, wend die ‘w-Stacking’ algoritme ’n fasekorreksie aan tot ’n reeks beeldlae, om sodoende ’n beeld te verkry wat die nie-samevlakkige basislyneffekte in ag neem. Die KAT7 teleskoop is gebruik in die simulasie en analiese van die tekortkominge en voordele van beide algoritmes. ’n Hibriede weergawe van die Högbom CLEAN algoritme is bykomend oorweeg. Hierdie algoritme is ’n iteratiewe twee-dimensionele dekonvolusiemetode wat die betroubaarheid van beelde verbeter deur die verskansingseffek van puntverspreidingsfunksies te verwyder. Verder gebruik die Högbom CLEAN algoritme kontoersnoeiing om uitgebreide bron-emisies te identifiseer.

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