Let <i>K</i> be a compact subset of complex <i>N</i>-dimensional space, where <i>N</i> ≥ 1. Let <i>H</i>(<i>K</i>) denote the functions analytic in a neighborhood of <i>K</i>. Let <i>R</i>(<i>K</i>) denote the closure of <i>H</i>(<i>K</i>) in <i>C</i>(<i>K</i>). We study the problem: What is <i>R</i>(<i>K</i>)? The study of <i>R</i>(<i>K</i>) is contained in the field of rational approximation. In a set of lecture notes, T. Gamelin [6] has shown a certain operator to be essential to the study of rational approximation. We study properties of this operator. Now let <i>K</i> be a compact subset of real <i>N</i>-dimensional space, where <i>N</i> ≥ 2. Let harm<i>K</i> denote those functions harmonic in a neighborhood of <i>K</i>. Let <i>h</i>(<i>K</i>) denote the closure of harm<i>K</i> in <i>C</i>(<i>K</i>). We also study the problem: What is <i>h</i>(<i>K</i>)? The study of <i>h</i>(<i>K</i>) is contained in the field of harmonic approximation. As well as obtaining harmonic analogues to our results in rational approximation, we also produce a harmonic analogue to the operator studied in Gamelin's notes. / Ph. D.

Innovative nano-scale devices have been developed to enhance future circuit design to overcome physical barriers hindering complementary metal-oxide semiconductor (CMOS) technology. Among the emerging nanodevices, resonant tunneling diodes (RTDs) have demonstrated promising electronic features due to their high speed switching capability and functional versatility. Great circuit functionality can be achieved through integrating heterostructure field-effect transistors (HFETs) in conjunction with RTDs to modulate effective negative differential resistance (NDR). However, RTDs are intrinsically suitable for implementing threshold logic rather than Boolean logic which has dominated CMOS technology in the past. To fully take advantage of such emerging nanotechnology, efficient design methodologies and design automation tools for threshold logic therefore become essential. In this thesis, we first propose novel programmable logic elements (PLEs) implemented in threshold gates (TGs) and multi-threshold threshold gates (MTTGs) by exploring RTD/ HFET monostable-bistable transition logic element (MOBILE) principles. Our three-input PLE can be configured through five control bits to realize all the three-variable logic functions, which is, to the best of our knowledge, the first single RTD-based structure that provides complete logic implementation. It is also a more efficient reconfigurable circuit element than a general look-up table which requires eight configuration bits for three-variable functions. We further extend the design concept to construct a more versatile four-input PLE. A comprehensive comparison of three- and four-input PLEs provides an insightful view of design tradeoffs between performance and area. We present the mathematical proof of PLE's logic completeness based on Shannon Expansion, as well as the HSPICE simulation results of the programmable and primitive RTD/HFET gates that we have designed. An efficient control bit generating algorithm is developed by using a special encoding scheme to implement any given logic function. In addition, we propose novel techniques of formulating a given threshold logic in conjunctive normal form (CNF) that facilitates efficient SAT-based equivalence checking for threshold logic networks. Three different strategies of CNF generation from threshold logic representations are implemented. Experimental results based on MCNC benchmarks are presented as a complete comparison. Our hybrid algorithm, which takes into account input symmetry as well as input weight order of threshold gates, can efficiently generate CNF formulas in terms of both SAT solving time and CNF generating time. / Master of Science

As the number of transistors per unit chip area increases, the power dissipation of the chip becomes a bottleneck. New nano-technology materials have been proposed as viable alternatives to CMOS to tackle area and power issues. The power consumption can be minimized by the use of reversible logic instead of conventional combinational circuits. Theoretically, reversible circuits do not consume any power (or consume minimal power) when performing computations. This is achieved by avoiding information loss across the circuit. However, use of reversible circuits to implement digital logic requires development of new Electronic Design Automation techniques. Several approaches have been proposed and each method has its own pros and cons. This often results in multiple designs for the same function. Consequently, this demands research in efficient equivalence checking techniques for reversible circuits. This thesis explores the optimization and equivalence checking of reversible circuits. Most of the existing synthesis techniques work in two steps — generate an original, often sub-optimal, implementation for the circuit followed optimization of this design. This work proposes the use of Binary Decision Diagrams for optimization of reversible circuits. The proposed technique identifies repeated gate (trivial) as well as non-contiguous redundancies in a reversible circuit. Construction of a BDD for a sub-circuit (obtained by sliding a window of fixed size over the circuit) identifies redundant gates based upon the redundant variables in the BDD. This method was unsuccessful in identifying any additional redundancies in benchmark circuits; however, hidden non-contiguous redundancies were consistently identified for a family of randomly generated reversible circuits. As of now, several research groups focus upon efficient synthesis of reversible circuits. However, little work has been done in identification of redundant gates in existing designs and the proposed peephole optimization method stands among the few known techniques. This method fails to identify redundancies in a few cases indicating the complexity of the problem and the need for further research in this area. Even for simple logical functions, multiple circuit representations exist which exhibit a large variation in the total number of gates and circuit structure. It may be advantageous to have multiple implementations to provide flexibility in choice of implementation process but it is necessary to validate the functional equivalence of each such design. Equivalence checking for reversible circuits has been researched to some extent and a few pre-processing techniques have been proposed prior to this work. One such technique involves the use of Reversible Miter circuits followed by SAT-solvers to ascertain equivalence. The second half of this work focuses upon the application of the proposed reduction technique to Reversible Miter circuits as a pre-processing step to improve the efficiency of the subsequent SAT-based equivalence checking. / Master of Science

The purpose of this essay is to analyze the translation of the specific technical language of railway transport from Swedish into German. The analysis is based on a self-conducted translation of selected passages of rules and regulations issued by the Swedish government agency Trafikverket (The Swedish Transport Administration). The following questions serve as a starting point: Which factors influence the final choice of a translation equivalent when several options are available? Which translation strategies can be used to close a lexical gap in the target language? And, furthermore, how can ”false friends” be identified so that terminological errors can be avoided in the target text? The essay is divided into two parts. The first part introduces major concepts such as equivalence, denotative equivalence and false friends. The second part consists of an analysis which discusses a selection of representative examples from the translation. The first part of the analysis focuses on cases where the target language provides several translation equivalents. By analyzing the semantics and comparing the related meanings of these equivalents, it was possible to pin down the most suitable term in the target language. In most cases the final term choice was confirmed by parallel texts. The second part discusses cases where the target language lacks an equivalent technical term. In most cases the lexical gaps could be closed by loaning the source-language term and adding a short explanation in the target text. The final section is devoted to false friends. By consulting parallel texts, several false friends in the target language were identified and also removed from an earlier version of the target text.

Reliant le moteur à turboréacteur à la voilure de l’avion, le mât-réacteur est une véritable « pièce maitresse » de l’avion. En effet, il transmet tous les efforts de l’avion au moteur. Il est soumis à des variations de températures allant de -40°C en croisière à290°C voir 400°C lors des phases de décollage. En plus, le mât-réacteur est à la merci de contraintes vibratoires très élevées qui,n’étant pas correctement maitrisées lors des analyses en tolérances aux dommages, peuvent conduire à la ruine de l’appareil. Entre290°C et 400°C, la martensite constitutive des composants en acier inoxydable martensitique durci par précipitation (15-5PH) du mât-réacteur, subit donc un vieillissement par transformation microstructurale. Ce vieillissement a un impact considérable sur les propriétés mécaniques, à savoir à une augmentation de la limite d’élasticité et de la contrainte à rupture aux dépens d’une réduction drastique de la ténacité et la ductilité. Afin de compléter la caractérisation des effets du vieillissement sur les propriétés mécaniques tout en considérant que ces structures sont dimensionnées suivant un principe de tolérance aux dommages, l’objectif de ce travail est d’étudier la résistance à la fissuration par fatigue de cet acier en fonction du vieillissement et de la température d’essai. La démarche adoptée repose sur une connaissance des comportements monotone et cyclique pour analyser les mécanismes en fissuration. Des essais de comportement cyclique ont ainsi été effectués à la température ambiante et à 300°C à différents niveaux de déformation imposés, sur l’acier 15-5PH dans son état de réception, puis pour des conditions vieillissement réalisées entre 300°C et 400°C et des temps d’exposition allant jusqu’à 10 000h. Les résultats obtenus mettent en évidence l’absence d’influence du vieillissement sur l’écrouissage cyclique de l’acier 15-5PH, aussi bien à température ambiant qu’à 300°C. Pour la plage de valeurs de ΔK balayée, le comportement en fissuration de l’acier 15-5PH sous amplitude de chargement constante n’est pas modifié par le vieillissement.Cependant, l’étendue du domaine stable de propagation est quant à elle réduite en fonction du degré de vieillissement à température ambiante. Cette réduction est due à la chute de ténacité du matériau avec le vieillissement. Les surfaces de rupture sont majoritairement transgranulaires pour toutes les conditions examinées. Toutefois, les régions proches de la rupture finale de certains états vieillis présentent des îlots de rupture statique à la température ambiante. Ces ilots sont inexistants à 300°C. Par ailleurs, sous l’effet de surcharges répétées, un effet retard sur la vitesse de fissuration a été mis en évidence. Ce retard est fonction à la fois du taux de surcharge, de la période de surcharge, du nombre de surcharge et du rapport de charge du chargement de base, mais est insensible au vieillissement. Par ailleurs, on dénote une fois de plus, une réduction de l’étendue du domaine de propagation stable à température ambiante. Des simulations de la propagation des fissures sous amplitude de chargement variable ont été effectuées à l’aide du modèle incrémental de prévisions de durées de vie en fissuration développé au LMT-Cachan. Les résultats issus de ce modèle ont ensuite fait l’objet d’une comparaison avec le modèle PREFFAS utilisé chez AIRBUS. Le modèle incrémental rend bien compte de certains effets de surcharges répétées. Il se révèle en outre moins conservatif que le modèle PREFFAS. Une méthodologie de prise en compte dans le modèle incrémental des effets de vieillissement fondée sur une équivalence temps/température de type Hollomon-Jaffe est enfin proposée. / Connecting the turbofan engine to the wing of the aircraft, the engine pylon is a true « masterpiece » of the aircraft. Indeed, it transmits all the aircraft engine efforts. It is subject to temperature variations from -40°C in cruise to 290°C-400°C during take off and landing. In addition, the engine pylon is a prey to very high vibratory stresses, which should be properly taken into account during damage tolerances analysis to avoid the loss of the aircraft. Between 290°C and 400°C, the martensite of components in precipitation-hardenable stainless steel (15-5 PH) of engine pylon undergoes microstructural transformation (« ageing »). This ageing has a significant impact on the mechanical properties, characterized by an increase in yield strength and tensile stress and drastic reduction in toughness and ductility. To complete the characterization of the effects of ageing on the mechanical properties while considering that these structures are designed according to a principle of damage tolerance, the aim of this work is to study the fatigue crack growth behavior (FCGB) of this material according to the ageing conditions and the test temperature. The approach is based on knowledge of monotonous and cyclic behavior to analyze the fatigue crack mechanisms. The cyclic behavior tests have been carried out at room temperature and 300°C at different strains imposed levels, on the 15-5PH steel in its as-received and then to the ageing conditions realized, between 300°C and 400°C and exposure times of up to 10 000h. The results highlight the lack of influence of ageing on the cyclic hardening of 15-5 PH steel, both at room temperature to 300°C. For the range of ΔK values tested, the FCGB of the 15-5PH steel under constant load amplitude is not affected by ageing. However, the extent of the stable propagation domain is itself reduced according to the degree of aging at room temperature. This reduction is due to the fall of fracture toughness due to ageing. The fracture surfaces are mainly transgranular for all conditions examined. However, the areas close to the final rupture ofsome ageing statements present islands indicative of a static failure mode at room temperature. These islands are absent to 300°C.Under the effect of repeated loads, a delayed effect on the crack velocity has been demonstrated. This delay is a function of the overload rate, overload period, the number of overloads and the baseline load ratio, but insensitive to ageing. Furthermore, are duction in the extent of the area stable propagation is also noticed at room temperature. Fatigue crack growth simulations undervariable amplitude loading were made through the incremental model for damage tolerance analysis developed by LMT-Cachan. The model results were then subject to a comparison with the PREFFAS model used at AIRBUS. The incremental model is well aware ofsome of the effects of repeated overloads. It also proves less conservative than the model PREFFAS. For taking account the effects of ageing in the incremental model, simply report the hardening observed on old material, the cyclic hardening parameters are notaffected. A methodology based on time/temperature equivalence provided by Hollomon-Jaffe - and taking into account the effects of ageing in the incremental model is finally proposed.

Let X be a Polish space and Q a measurable partition of X into Gδ equivalence classes. In 1978, S. M. Srivastava proved the existence of a Borel cross section for Q. He asked whether more can be concluded in case each equivalence class is uncountable. This question is answered here in the affirmative. The main result of the author is a proof that shows the existence of a Castaing Representation for Q.

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This paper contains an overview of some of the main 20th Century tendencies in translation theory. It focus especially on matters of equivalence, dynamic equivalence, formal equivalence, skopos, abusive fidelity and foreignizing translation or resistant translation and their implications for actual translations. This paper also includes translations prepared according to the principles of abusive fidelity, equivalence and dynamic equivalence, which are compared and commented.

Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2011. / Includes bibliography. / ENGLISH ABSTRACT: Latimer & MacDuffee showed in 1933 that there is a one-to-one correspondence between equivalence classes of matrices with a given minimum polynomial and equivalence classes of ideals of a certain ring. In the case where the matrices are taken over the integers, Behn and Van der Merwe developed an algorithm in 2002 to produce a representative in each equivalence class. We extend this algorithm to matrices taken over the ring Fq[T] of polynomials over a finite field and prove a modified version of the Latimer-MacDuffee theorem which holds for proper equivalence classes of matrices. / AFRIKAANSE OPSOMMING: Latimer & MacDuffee het in 1933 bewys dat daar 'n een-tot-een korrespondensie is tussen ekwivalensieklasse van matrikse met 'n gegewe minimumpolinoom en ekwivalensieklasse van ideale van 'n sekere ring. In die geval waar die matrikse heeltallige inskrywings het, het Behn en Van der Merwe in 2002 'n algoritme ontwikkel om verteenwoordigers in elke ekwivalensieklas voort te bring. Ons brei hierdie algoritme uit na die geval van matrikse met inskrywings in die ring Fq[T] van polinome oor 'n eindige liggaam en ons bewys 'n gewysigde weergawe van die Latimer-MacDuffee stelling wat geld vir klasse van streng ekwivalente matrikse.

This thesis aims to compare two Czech translations of John Steinbeck's novel Tortilla flat considering the theories of acknowledged translatologists (Levý, Knittlová, Krijtová). For Steinbeck's work differentiation of the language used in direct speech from the language used by the narrator by using colloquial and slang expressions is characteristic, so Steinbeck's translators were to cope with an uneasy task to find a functional equivalent of the different language layers in the target language. The thesis focuses among other on the means by which the differentiation was reached by two different translators considering the development of functional aspect in Czech translatology. A very significant element in Steinbeck's Tortilla Flat is the aim to outline the local atmosphere by using local names, facts and not translated Spanish expressions, which needs to be transferred to the target language considering the requirement both to preserve the local atmosphere in the translation and to create a translation, which is a valuable and understandable piece of literature in the target language.