We introduce a notion of non-local perimeter which is defined through an arbitrary positive Borel measure on Rᵈ which integrates the function 1 ∧ |x|. Such definition of non-local perimeter encompasses a wide range of perimeters which have been already studied in the literature, including fractional perimeters and anisotropic fractional perimeters. The main part of the article is devoted to the study of the asymptotic behaviour of non-local perimeters. As direct applications we recover well-known convergence results for fractional perimeters and anisotropic fractional perimeters.

This study investigates the concessioning of the commuter rail subsystem, which was discussed in the White Paper on National Transport Policy. The theoretical divide between private and public sector enterprise is investigated in terms of a principal-agent approach. The hypothesis underlying the fundamental shift of services traditionally provided by government enterprise to the private sector is X-efficiency gains under a concession regime. There are, however, potential challenges under a concession regime that must be anticipated. Challenges are identified in terms of an incomplete contract approach with its underpinning source manifested in a bounded rationality concept. The study investigates how rail concessionaires are regulated under a concession regime from an economics perspective and various price mechanisms are explored. The study provides strategies to deal with challenges under a rail concession regime with a view to minimising conflicts that will arise between the parties involved in a concession agreement. / Transport, Logistics & Tourism / M.Comm.(Transport Economics)

Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved. If A(f2) is the Banach algebra of functions holomorphic in the bounded domain Q in Cn and continuous on the boundary and if p is a point in Q, then the following problem is known as Gleason’s Problem for A(Q) : Is the maximal ideal in A(Q) consisting of functions vanishing at p generated by (Zl ~Pl) , ■■■ , (Zn - Pn) ? A sufficient condition for solving Gleason’s Problem for A(Q) for all points in Q is given. In particular, this condition is fulfilled by a convex domain Q with Lipi+£-boundary (0 &lt; e &lt; 1) and thus generalizes a theorem of S.L.Leibenzon. One of the ideas in the methods of proof is integration along specific polygonal lines. If Gleason’s Problem can be solved in a point it can be solved also in a neighbourhood of the point. It is shown, that the coefficients in this case depends holomorphically on the points. Defining a projection from the spectrum of a uniform algebra of holomorphic functions to Cn, one defines the fiber in the spectrum over a point as the elements in the spectrum that projects on that point. Defining a kind of maximum modulus property for domains in Cn, some problems concerning the fibers and the number of elements in the fibers in certain algebras of bounded holomorphic functions are solved. It is, for example, shown that the set of points, over which the fibers contain more than one element is closed. A consequence is also that a starshaped domain with the maximum modulus property has schlicht /y°°-envelope of holomorphy. These kind of problems are also connected with Gleason’s problem. A survey paper on general properties of algebras of bounded holomorphic functions of several variables is included. The paper, in particular, treats aspects connecting iy°°-envelopes of holomorphy and some areas in the theory of uniform algebras. / <p>Diss. (sammanfattning) Umeå : Umeå universitet, 1994, härtill 6 uppsatser</p> / digitalisering@umu

To improve quality of software systems, change-based fault prediction and scope-bounded checking have been used to predict or detect faults during software development. In fault prediction, changes to program source code, such as added lines or deleted lines, are used to predict potential faults. In fault detection, scope-bounded checking of programs is an effective technique for finding subtle faults. The central idea is to check all program executions up to a given bound. The technique takes two basic forms: scope-bounded static checking, where all bounded executions of a program are transformed into a formula that represents the violation of a correctness property and any solution to the formula represents a counterexample; or scope-bounded testing where a program is tested against all (small) inputs up to a given bound on the input size. Although the accuracies of change-based fault prediction and scope-bounded checking have been evaluated with experiments, both of them have effectiveness and efficiency limitations. Previous change-based fault predictions only consider the code modified by a change while ignoring the code impacted by a change. Scope-bounded testing only concerns the correctness specifications, and the internal structure of a program is ignored. Although scope-bounded static checking considers the internal structure of programs, formulae translated from structurally complex programs might choke the backend analyzer and fail to give a result within a reasonable time. To improve effectiveness and efficiency of these approaches, we introduce local semantic analysis into change-based fault prediction and scope-bounded checking. We use data-flow analysis to disclose internal dependencies within a program. Based on these dependencies, we identify code segments impacted by a change and apply fault prediction metrics on impacted code. Empirical studies with real data showed that semantic analysis is effective and efficient in predicting faults in large-size changes or short-interval changes. While generating inputs for scope-bounded testing, we use control-flow to guide test generation so that code coverage can be achieved with minimal tests. To increase the scalability of scope-bounded checking, we split a bounded program into smaller sub-programs according to data-flow and control-flow analysis. Thus the problem of scope-bounded checking for the given program reduces to several sub-problems, where each sub-problem requires the constraint solver to check a less complex formula, thereby likely reducing the solver’s overall workload. Experimental results show that our approach provides significant speed-ups over the traditional approach. / text

在這篇論文裡，我們將要討論一類古典的問題，這類問題已經經由許多方法解決，例如：遞迴關係式、差分方程式、尤拉公式等等。接著我們歸納低維度的特性，並藉由定義出一組方程式-標準n維空間分割系統-來推廣這些特性到一般的$n$維度空間中。然後我們利用演算法來提供一個更直接的組合論證法。最後，我們會把問題再細分成有界區域與無界區域的個數。 / In this article, we will discuss a class of classical questions had been solved by Recurrence Relation, Difference Equation, and Euler's Formula, etc.. And then, we construct a system of equations -Standard Partition System of n-Dimensional Space- to generalize the properties of maximizing the number of regions made up by k partitioner in an n-dimensional space and look into the construction of each dimension. Also, we provide a more directly Combinatorial Argument by Algorithm for this kind of question. At last, we focus on the number of bounded regions and unbounded regions in sense of maximizing the number of regions.

在這篇論文中，我們探討了最近在有界雙容忍序中的一些成果。同時， 我們提供一些標準的簡短證明，包含有界雙容忍序的等價種類， 單位有界雙容忍序與適當有界雙容忍序的關係。 我們的目標是希望能在有界雙容忍序的現今地位上，去提供新的洞悉，並給未來學習者一個方向。 / In the paper、we study recent work on some classes of bounded bitolerance orders. Also, we provide the short proofs of some of classical results on bounded bitolerance orders, including the equivalent classes of bounded bitolerance orders、the relation of unit and proper bitolerance orders. Our goal is to provide the fresh insights into the current status of research in the area while suggesting directions for the future.

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Dans les régions rurales, la gestion de l'eau induit des changements techniques et des transformations des pratiques agricoles auxquels font face les agriculteurs. Leurs comportements mitigés comprennent à la fois un désir d'innovation et un attachement au terroir à travers des usages, des pratiques et des représentations. Cet attachement identitaire a été souvent considéré comme obstacle à l'introduction de nouvelles techniques et non comme opportunité à saisir. Le présent travail, fondé sur le cas de Diar Hojjej (zone côtière du Cap Bon, Tunisie), se propose, en tenant compte de l'identité du territoire, de comprendre dans quelle mesure l’entrepreneuriat rural peut constituer un moteur pour porter une zone à contrainte environnementale forte – l’eau d’irrigation- vers un développement agricole durable. L'identité du territoire serait-elle uniquement un frein à l'entreprenariat rural? Et quel serait le modèle d'entreprenariat le plus pertinent? [etc.] / In rural areas, water management induces changes in technologies and in agricultural practices that face farmers. Farmers’ behaviors include both a desire for innovation and a land attachment through local customs, practices and representations. This identity attachment has often been regarded as an obstacle to the introduction of new techniques rather than an opportunity to be seized. This work, based on the case of Diar Hojjej (a coastal area of Cap Bon, Tunisia) aims to understand how rural entrepreneurship can be an engine to convey a strong environmental constraint area (water irrigation) to sustainable agricultural development, while taking into account the territory’s identity. The territory’s identity would it only be an obstacle to rural entrepreneurship? And what would be the most relevant model of entrepreneurship? [etc.]

Cette thèse a pour objet l'évaluation du risque de crédit par une approche comportementale dans un contexte d'information asymétrique et de rationalité limitée. Nous cherchons à travers cette analyse, à concilier les « experts métiers » et les statisticiens, en intégrant le comportement humain dans la conception des outils quantitatifs d'évaluation du risque de crédit, en vue d'optimisation de la gestion de ce risque.L'évaluation du risque de crédit est basée sur des modèles et techniques statistiques de plus en plus avancées. Nous citons à titre d'exemple les modèles du Crédit Metrics et JP Morgan, le modèle KMV et le modèle Crédit Portfolio de Mekinsey ou encore les modèles de scoring introduits pour évaluer la qualité du risque des emprunteurs. Plusieurs travaux soulignent l'intérêt de ces modèles quantitatifs. En effet, Scot FRAME et al, ont montré que le recours aux modèles de scoring contribue effectivement à réduire le coût d'information dans les grandes banques américaines. Les résultats de ces modèles dépendent de la réalisation des facteurs de risque spécifiques à chaque emprunteur et de facteurs de risque systémique. Cependant, la crise financière actuelle a mis en lumière la défaillance de ces modèles, aussi bien les modèles théoriques de notation que les modèles opérationnels utilisés par les praticiens, dans l'évaluation du risque de crédit. Toutes ces constructions n'ont pas su intégrer parfaitement l'ensemble de l'information et traiter la complexité d'interactions entre les variables déterminant le risque car elles sont basées sur des techniques purement statistiques qui ne savent représenter que des relations linéaires entre le risque de défaut et les variables qui en sont à l'origine sans prendre en compte le comportement du gestionnaire du risque crédit, dans l'optimisation de sa gestion. Etant données les limites de l'approche quantitative, nous avons convergé vers une approche comportementale qui concilie les techniques statistiques et le comportement humain basée sur la prise en compte et la validation collective des règles de décision émergeant des discussions et confrontations. Cette approche comportementale qui prend en compte la rationalité des décideurs à travers un modèle expert nous permettra d'une part de construire un cadre d'analyse normatif permettant d'identifier et d'évaluer le risque de crédit et d'autre part intégrer ces règles dans les systèmes de décisions opérationnels.Notre recherche a un intérêt multiple. Elle apporte un éclairage théorique sur l'optimisation de la décision des banques, dans un contexte d'incertitude, à travers un modèle portant à la fois sur le caractère quantitatif des modèles d'évaluation du risque de crédit et le comportement humain. L'évaluation du risque de crédit à travers notre approche permettra également de déterminer le montant de capital économique nécessaire à la couverture du risque de crédit. Ainsi, elle permettra aux banques de mettre en place une allocation optimale des fonds propres et une tarification adéquate des crédits basée sur une évaluation précise du risque de crédit. Ce qui porte un grand intérêt aux banques et aux clients aussi. / This thesis focuses on the assessment of credit risk with a behavioral approach in a context of asymmetric information and bounded rationality. We seek through this analysis, to reconcile the "business experts" and statisticians, incorporating human behavior into the design of tools for quantitative assessment of credit risk in order to optimize the management of this risk.The assessment of credit risk is based on models and statistical techniques more advanced. We cite as examples of models JP Morgan Credit Metrics, model and KMV's Portfolio Credit Model Mekinsey or scoring models introduced to assess the quality of the risk of borrowers. Several studies underline the importance of these quantitative models. Indeed, Scot FRAME and AL showed that the use of scoring models is effective in reducing the cost of information in large U.S. banks. The results of these models depend on the realization of the risk factors specific to each borrower and systemic risk factors. However, the current financial crisis has highlighted the failure of these models, both theoretical models that rating business models used by practitioners in assessing credit risk. All these constructions have not been able to integrate fully all the information and treat the complexity of interactions between variables determining the risk because they are based on purely statisti cal techniques who can represent the linear relationships between risk default and the variables that are at the origin without taking into account the behavior of credit risk manager, in optimizing its management.Given the limitations of the quantitative approach, we have converged on a behavioural approach that combines statistical techniques and human behaviour based on consideration and validation of collective decision rules emerging from the discussions and confrontations. This behavioural approach that takes into account the rationality of decision makers through an expert model we will firstly build a normative framework for analysis to identify and assess credit risk and also integrate these rules systems in operational decisions.Our research has a substantial multiple. It sheds light on the theoretical optimization of the decision of the banks in a context of uncertainty through a model bearing both on the quantitative assessment models of credit risk and human behavior. The assessment of credit risk through our approach will also determine the amount of capital necessary to cover credit risk. Thus, it will allow banks to establish an optimal allocation of capital and adequate pricing of loans based on an accurate assessment of credit risk. This brings great interest to banks and customers too.

The thesis concerns the mathematical study of the calculus of variations and its application to liquid crystals. In the first chapter we examine vectorial problems in the calculus of variations with an additional pointwise constraint so that any admissible function <strong>n</strong> ε W^1,1(ΩM), and M is a manifold of suitable regularity. We formulate necessary and sufficient conditions for any given state <strong>n</strong> to be a strong or weak local minimiser of I. This is achieved using a nearest point projection mapping in order to use the more classical results which apply in the absence of a constraint. In the subsequent chapters we study various static continuum theories of liquid crystals. More specifically we look to explain a particular cholesteric fingerprint pattern observed by HP Labs. We begin in Chapter 2 by focusing on a specific cholesteric liquid crystal problem using the theory originally derived by Oseen and Frank. We find the global minimisers for general elastic constants amongst admissible functions which only depend on a single variable. Using the one-constant approximation for the Oseen-Frank free energy, we then show that these states are global minimisers of the three-dimensional problem if the pitch of the cholesteric liquid crystal is sufficiently long. Chapter 3 concerns the application of the results from the first chapter to the situations investigated in the second. The local stability of the one-dimensional states are quantified, analytically and numerically, and in doing so we unearth potential shortcomings of the classical Oseen-Frank theory. In Chapter 4, we ascertain some equivalence results between the continuum theories of Oseen and Frank, Ericksen, and Landau and de Gennes. We do so by proving lifting results, building on the work of Ball and Zarnescu, which relate the regularity of line and vector fields. The results prove to be interesting as they show that for a director theory to respect the head to tail symmetry of the liquid crystal molecules, the appropriate function space for the director field is S BV² (Ω,S<sup>2,/sup>). We take this idea and in the final chapter we propose a mathematical model of liquid crystals based upon the Oseen-Frank free energy but using special functions of bounded variation. We establish the existence of a minimiser, forms of the Euler-Lagrange equation, and find solutions of the Euler-Lagrange equation in some simple cases. Finally we use our proposed model to re-examine the same problems from Chapter 2. By doing so we extend the analysis we were able to achieve using Sobolev spaces and predict the existence of multi-dimensional minimisers consistent with the known experimental properties of high-chirality cholesteric liquid crystals.