Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.

Mutually unbiased bases is an important topic in the recent quantum system researches. Although there is much work in this area, many problems related to mutually unbiased bases are still open. For example, constructing a complete set of mutually unbiased bases in the Hilbert spaces with composite dimensions has not been achieved yet. This thesis defines a weaker concept than mutually unbiased bases in the Hilbert spaces with composite dimensions. We call this concept, weak mutually unbiased bases. There is a duality between such bases and the geometry of the phase space Zd × Zd, where d is the phase space dimension. To show this duality we study the properties of lines through the origin in Zd × Zd, then we explain the correspondence between the properties of these lines and the properties of the weak mutually unbiased bases. We give an explicit construction of a complete set of weak mutually unbiased bases in the Hilbert space Hd, where d is odd and d = p1p2; p1, p2 are prime numbers. We apply the concept of weak mutually unbiased bases in the context of quantum tomography and quantum cryptography. / Egyptian government.

No description available.

Switched reluctance machines (SRMs) are well known for their simple and robust structure, facilitating their increasing application in many sectors, for example vacuum cleaners, where domestic machines operate at high-speed, 50,000 RPM being typical. Conventional SRMs (CSRMs) use a decoupled concentrated phase winding so that torque is predominantly only generated due to the self-inductance, which limits utilization of the machine electrical circuits. In this thesis, the toroidal winding SRM (TSRM) is introduced, which operates based on the variation of mutual inductance between different phases. The toroidal winding introduces additional winding space, and the winding is practically easy to implement, both features that lead to a relatively higher copper filling factor. The toroidal winding also benefits the machine thermal performance, as the winding is directly exposed on the machine periphery and thus accessible to cooling. All these make TSRMs interesting and meaningful for further study. Following a comprehensive comparison of CSRM and TSRM characteristics, a general torque equation is presented that is applicable to both CSRM and TSRM. Two 12-switch converters are proposed to drive three-phase TSRMs. Moreover, sinusoidal current excitation with a commercial three-phase half-bridge converter has been suggested as an alternative converter solution for TSRMs. Accordingly, a three-phase six-stator-pole, four-rotor-pole CSRM is designed and optimized with a speed of up to 50,000 rpm in this thesis. A TSRM is resized to achieve the same envelope dimension as a benchmark CSRM. Thus, a comparative study between high-speed CSRM and TSRMs has been carried out. They have both been prototyped and tested. The findings suggest that the TSRM is superior, considering machine mass and wire temperature management. The TSRM has a better torque output at lower speeds because copper losses are dominant. However, the CSRM has more advantages at higher speeds due to lower iron losses and lower DC voltage requirements. / Thesis / Doctor of Philosophy (PhD)

Thesis (PdD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: A Latin square of order n is an n×n array containing an arrangement of n distinct symbols with the property that every row and every column of the array contains each symbol exactly once. It is well known that Latin squares may be used for the purpose of constructing designs which require a balanced arrangement of a set of elements subject to a number of strict constraints. An important application of Latin squares arises in the scheduling of various types of balanced sports tournaments, the simplest example of which is a so-called round-robin tournament — a tournament in which each team opposes each other team exactly once. Among the various applications of Latin squares to sports tournament scheduling, the problem of scheduling special types of mixed doubles tennis and table tennis tournaments using special sets of three mutually orthogonal Latin squares is of particular interest in this dissertation. A so-called mixed doubles table tennis (MDTT) tournament comprises two teams, both consisting of men and women, competing in a mixed doubles round-robin fashion, and it is known that any set of three mutually orthogonal Latin squares may be used to obtain a schedule for such a tournament. A more interesting sports tournament design, however, and one that has been sought by sports clubs in at least two reported cases, is known as a spouse-avoiding mixed doubles round-robin (SAMDRR) tournament, and it is known that such a tournament may be scheduled using a self-orthogonal Latin square with a symmetric orthogonal mate (SOLSSOM). These applications have given rise to a number of important unsolved problems in the theory of Latin squares, the most celebrated of which is the question of whether or not a set of three mutually orthogonal Latin squares of order 10 exists. Another open question is whether or not SOLSSOMs of orders 10 and 14 exist. A further problem in the theory of Latin squares that has received considerable attention in the literature is the problem of counting the number of (essentially) different ways in which a set of elements may be arranged to form a Latin square, i.e. the problem of enumerating Latin squares and equivalence classes of Latin squares of a given order. This problem quickly becomes extremely difficult as the order of the Latin square grows, and considerable computational power is often required for this purpose. In the literature on Latin squares only a small number of equivalence classes of self-orthogonal Latin squares (SOLS) have been enumerated, namely the number of distinct SOLS, the number of idempotent SOLS and the number of isomorphism classes generated by idempotent SOLS of orders 4 n 9. Furthermore, only a small number of equivalence classes of ordered sets of k mutually orthogonal Latin squares (k-MOLS) of order n have been enumerated in the literature, namely main classes of 2-MOLS of order n for 3 n 8 and isotopy classes of 8-MOLS of order 9. No enumeration work on SOLSSOMs appears in the literature. In this dissertation a methodology is presented for enumerating equivalence classes of Latin squares using a recursive, backtracking tree-search approach which attempts to eliminate redundancy in the search by only considering structures which have the potential to be completed to well-defined class representatives. This approach ensures that the enumeration algorithm only generates one Latin square from each of the classes to be enumerated, thus also generating a repository of class representatives of these classes. These class representatives may be used in conjunction with various well-known enumeration results from the theory of groups and group actions in order to determine the number of Latin squares in each class as well as the numbers of various kinds of subclasses of each class. This methodology is applied in order to enumerate various equivalence classes of SOLS and SOLSSOMs of orders up to and including order 10 and various equivalence classes of k-MOLS of orders up to and including order 8. The known numbers of distinct SOLS, idempotent SOLS and isomorphism classes generated by idempotent SOLS are verified for orders 4 n 9, and in addition the number of isomorphism classes, transpose-isomorphism classes and RC-paratopism classes of SOLS of these orders are enumerated. The search is further extended to determine the numbers of these classes for SOLS of order 10 via a large parallelisation of the backtracking treesearch algorithm on a number of processors. The RC-paratopism class representatives of SOLS thus generated are then utilised for the purpose of enumerating SOLSSOMs, while existing repositories of symmetric Latin squares are also used for this purpose as a means of validating the enumeration results. In this way distinct SOLSSOMs, standard SOLSSOMs, transposeisomorphism classes of SOLSSOMs and RC-paratopism classes of SOLSSOMs are enumerated, and a repository of RC-paratopism class representatives of SOLSSOMs is also produced. The known number of main classes of 2-MOLS of orders 3 n 8 are verified in this dissertation, and in addition the number of main classes of k-MOLS of orders 3 n 8 are also determined for 3 k n−1. Other equivalence classes of k-MOLS of order n that are enumerated include distinct k-MOLS and reduced k-MOLS of orders 3 n 8 for 2 k n − 1. Finally, a filtering method is employed to verify whether any SOLS of order 10 satisfies two basic necessary conditions for admitting a common orthogonal mate with its transpose, and it is found via a computer search that only four of the 121 642 class representatives of RC-paratopism classes of SOLS satisfy these conditions. It is further verified that none of these four SOLS admits a common orthogonal mate with its transpose. By this method the spectrum of resolved orders in terms of the existence of SOLSSOMs is improved in that the non-existence of such designs of order 10 is established, thereby resolving a longstanding open existence question in the theory of Latin squares. Furthermore, this result establishes a new necessary condition for the existence of a set of three mutually orthogonal Latin squares of order 10, namely that such a set cannot contain a SOLS and its transpose / AFRIKAANSE OPSOMMING: ’n Latynse vierkant van orde n is ’n n × n skikking van n simbole met die eienskap dat elke ry en elke kolom van die skikking elke element presies een keer bevat. Dit is welbekend dat Latynse vierkante gebruik kan word in die konstruksie van ontwerpe wat vra na ’n gebalanseerde rangskikking van ’n versameling elemente onderhewig aan ’n aantal streng beperkings. ’n Belangrike toepassing van Latynse vierkante kom in die skedulering van verskeie spesiale tipes gebalanseerde sporttoernooie voor, waarvan die eenvoudigste voorbeeld ’n sogenaamde rondomtalietoernooi is — ’n toernooi waarin elke span elke ander span presies een keer teenstaan. Onder die verskeie toepassings van Latynse vierkante in sporttoernooi-skedulering, is die probleem van die skedulering van spesiale tipes gemengde dubbels tennis- en tafeltennistoernooie deur gebruikmaking van spesiale versamelings van drie paarsgewys-ortogonale Latynse vierkante in hierdie proefskrif van besondere belang. In sogenaamde gemengde dubbels tafeltennis (GDTT) toernooi ding twee spanne, elk bestaande uit mans en vrouens, op ’n gemengde-dubbels rondomtalie wyse mee, en dit is bekend dat enige versameling van drie paarsgewys-ortogonale Latynse vierkante gebruik kan word om ’n skedule vir s´o ’n toernooi op te stel. ’n Meer interessante sporttoernooi-ontwerp, en een wat al vantevore in minstens twee gerapporteerde gevalle deur sportklubs benodig is, is egter ’n gade-vermydende gemengde-dubbels rondomtalie (GVGDR) toernooi, en dit is bekend dat s´o ’n toernooi geskeduleer kan word deur gebruik te maak van ’n self-ortogonale Latynse vierkant met ’n simmetriese ortogonale maat (SOLVSOM). Hierdie toepassings het tot ’n aantal belangrike onopgeloste probleme in die teorie van Latynse vierkante gelei, waarvan die mees beroemde die vraag na die bestaan van ’n versameling van drie paarsgewys ortogonale Latynse vierkante van orde 10 is. Nog ’n onopgeloste probleem is die vraag na die bestaan van SOLVSOMs van ordes 10 en 14. ’n Verdere probleem in die teorie van Latynse vierkante wat aansienlik aandag in die literatuur geniet, is die bepaling van die getal (essensieel) verskillende maniere waarop ’n versameling elemente in ’n Latynse vierkant gerangskik kan word, m.a.w. die probleem van die enumerasie van Latynse vierkante en ekwivalensieklasse van Latynse vierkante van ’n gegewe orde. Hierdie probleem raak vinnig baie moeilik soos die orde van die Latynse vierkant groei, en aansienlike berekeningskrag word dikwels hiervoor benodig. Sover is slegs ’n klein aantal ekwivalensieklasse van self-ortogonale Latynse vierkante (SOLVe) in die literatuur getel, naamlik die getal verskillende SOLVe, die getal idempotente SOLVe en die getal isomorfismeklasse voortgebring deur idempotente SOLVe van ordes 4 n 9. Verder is slegs ’n klein aantal ekwivalensieklasse van geordende versamelings van k onderling ortogonale Latynse vierkante (k-OOLVs) in die literatuur getel, naamlik die getal hoofklasse voortgebring deur 2-OOLVs van orde n vir 3 n 8 en die getal isotoopklasse voortgebring deur 8-OOLVs van orde 9. Daar is geen enumerasieresultate oor SOLVSOMs in die literatuur beskikbaar nie. In hierdie proefskrif word ’n metodologie vir die enumerasie van ekwivalensieklasse van Latynse vierkante met behulp van ’n soekboomalgoritme met terugkering voorgestel. Hierdie algoritme poog om oorbodigheid in die soektog te minimeer deur net strukture te oorweeg wat die potensiaal het om tot goed-gedefinieerde klasleiers opgebou te word. Hierdie eienskap verseker dat die algoritme slegs een Latynse vierkant binne elk van die klasse wat getel word, genereer, en dus word ’n databasis van verteenwoordigers van hierdie klasse sodoende opgebou. Hierdie klasverteenwoordigers kan tesame met verskeie welbekende groepteoretiese telresultate gebruik word om die getal Latynse vierkante in elke klas te bepaal, asook die getal verskeie deelklasse van verskillende tipes binne elke klas. Die bogenoemde metodologie word toegepas om verskeie SOLV- en SOLVSOM-klasse van ordes kleiner of gelyk aan 10 te tel, asook om k-OOLV-klasse van ordes kleiner of gelyk aan 8 te tel. Die getal verskillende SOLVe, idempotente SOLVe en isomorfismeklasse voortgebring deur SOLVe word vir ordes 4 n 9 geverifieer, en daarbenewens word die getal isomorfismeklasse, transponent-isomorfismeklasse en RC-paratoopklasse voortgebring deur SOLVe van hierdie ordes ook bepaal. Die soektog word deur middel van ’n groot parallelisering van die soekboomalgoritme op ’n aantal rekenaars ook uitgebrei na die tel van hierdie klasse voortgebring deur SOLVe van orde 10. Die verteenwoordigers van RC-paratoopklasse voortgebring deur SOLVe wat deur middel van hierdie algoritme gegenereer word, word dan gebruik om SOLVSOMs te tel, terwyl bestaande databasisse van simmetriese Latynse vierkante as validasie van die resultate ook vir hierdie doel ingespan word. Op hierdie manier word die getal verskillende SOLVSOMs, standaardvorm SOLVSOMs, transponent-isomorfismeklasse voortgebring deur SOLVSOMs asook RC-paratoopklasse voortgebring deur SOLVSOMs bepaal, en word ’n databasis van verteenwoordigers van RC-paratoopklasse voortgebring deur SOLVSOMs ook opgebou. Die bekende getal hoofklasse voortgebring deur 2-OOLVs van ordes 3 n 8 word in hierdie proefskrif geverifieer, en so ook word die getal hoofklasse voortgebring deur k- OOLVs van ordes 3 n 8 bepaal, waar 3 k n−1. Ander ekwivalensieklasse voortgebring deur k-OOLVs van orde n wat ook getel word, sluit in verskillende k-OOLVs en gereduseerde k-OOLVs van ordes 3 n 8, waar 2 k n − 1. Laastens word daar van ’n filtreer-metode gebruik gemaak om te bepaal of enige SOLV van orde 10 twee basiese nodige voorwaardes om ’n ortogonale maat met sy transponent te deel kan bevredig, en daar word gevind dat slegs vier van die 121 642 klasverteenwoordigers van RC-paratoopklasse voortgebring deur SOLVe van orde 10 aan hierdie voorwaardes voldoen. Dit word verder vasgestel dat geeneen van hierdie vier SOLVe ortogonale maats in gemeen met hul transponente het nie. Die spektrum van afgehandelde ordes in terme van die bestaan van SOLVSOMs word dus vergroot deur aan te toon dat geen sulke ontwerpe van orde 10 bestaan nie, en sodoende word ’n jarelange oop bestaansvraag in die teorie van Latynse vierkante beantwoord. Verder bevestig hierdie metode ’n nuwe noodsaaklike bestaansvoorwaarde vir ’n versameling van drie paarsgewys-ortogonale Latynse vierkante van orde 10, naamlik dat s´o ’n versameling nie ’n SOLV en sy transponent kan bevat nie. / Harry Crossley Foundation / National Research Foundation

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

The purpose of this study was to determine if sensitivity training encouraged significantly more members to form mutually therapeutic relationships than did traditional group counseling, and to determine, if the members who formed the largest numbers of mutually therapeutic relationships increased both in self-awareness and self-actualization significantly more through sensitivity training than through the traditional form of group counseling. This study concluded from its findings that the sensitivity group members' relationships were more transitory or short-lived that were the relationships formed by the members of the traditional group. The formation of mutually therapeutic relationships, built on empathy, congruence, and positive regard, appeared to increase self-awareness, and a traditional form of group counseling may be better at achieving this than a sensitivity-training group. The sensitivity-training group appeared to deal best with material in the present, or "here-and-now," while the traditional group was more effective in dealing with intrinsic material outside the group and in the past.

正交主效應計畫(Orthogonal main-effect plans)因可無相關地估計主效應，故常被應用於一般工業上作為篩選因子之用。然而，實驗通常費時耗財。因此，如何設計一個較經濟且有效的計劃是很重要的。回顧過去相關的研究，Jacroux (1992)提供了最小正交主效應計劃的充份條件及正交主效應計畫之最少實驗次數表(Jacroux 1992)，張純明(1998)針對此表提出修正與補充。在此，我們再次的補足此表。 正交主效應計畫中，如有重複實驗點，則純誤差可被估計，且據此檢定模型之適合度。Jacroux (1993)及張純明(1998)皆曾提出具最多部份重複之正交主效應計畫(Partially replicated orthogonal main-effect plans)。在此，我們討論所有三因子部份重複正交主效應計畫中，可能重複之最大次數，且具體提出建構此最大部份重複之最小正交主效應計畫之方法。 / Orthogonal main-effect plans (OMEP's), being able to estimate the main effects without correlation, are often employed in industrial situations for screening purpose. But experiments are expensive and time consuming. When an economical and efficient design is desired, a minimal orthogonal main-effect plans is a good choice. Jacroux (1992) derived a sufficient condition for OEMP's to have minimal number of runs and provided a table of minimal OMEP run numbers. Chang (1998) corrected and supplemented the table. In this paper, we try to improve the table to its perfection. A minimal OMEP with replicated runs is appreciated even more since then the pure error can be estimated and the goodness-of-fit of the model can be tested. Jacroux (1993) and Chang (1998) gave some partially replicated orthogonal main-effect plans (PROMEP's) with maximal number of replicated points. Here, we discuss minimal PROMEP's with 3 factors in detail. Methods of constructing minimal PROMEP's with replicated runs are provided, and the number of replicated runs are maximal for most cases.

<p>There is a growing interplay of competing realities facing the international community in the general areas of innovation, technological advancement and overall economic development. The highly industrialised wealthy nations, largely located on the Northern hemisphere are on the one hand undoubtedly at the forefront in global research, technology and infrastructure development. The developing and least developed countries on the other hand are mostly situated on the Southern hemisphere. They are not as wealthy or technologically advanced as their&nbsp / Northern counterparts, but are naturally endowed with unique variations of plant, animal and micro-organism species occurring in natural ecosystems, as well as the traditional knowledge on&nbsp / how to use these unique species. This knowledge has been adjudged to be responsible for the sustainable maintenance of the earth&rsquo / s biodiversity. Increasing exploitation of biodiversity,&nbsp / spurred on by the competing realities identified above, has left the earth in a present state of alarm with respect to the uncontrolled loss of biodiversity. The traditional knowledge of local&nbsp / peoples has significantly offered leads to research institutes from the North in developing major advancements in drugs, cosmetics and agriculture. Little or no compensation has however been seen to go back to the indigenous&nbsp / communities and countries that provide resources, and indicate various possibilities through their traditional knowledge to the use of such resources. Efforts by some biodiversity rich countries to&nbsp / ddress this trend through legislation developed in accordance with the principles of the Convention on Biological Diversity have been frustrated due to the inability to enforce their domestic laws outside their borders. Theft of genetic resources and its associated traditional knowledge&nbsp / from such countries has therefore remained a major challenge. Against this backdrop, and on the&nbsp / insistence of biodiversity-rich developing countries, an international regime on access and benefit sharing was negotiated and its final text adopted in 2010. This international regime is as&nbsp / contained in the Nagoya Protocol. This research sets out to examine whether the Nagoya Protocol offers a final solution to the protection of traditional knowledge associated with biodiversity in&nbsp / biodiverse countries. It further examines the importance of domestic legislation in achieving the objectives of the Protocol. The research has been tailored to African biodiverse countries, and&nbsp / seeks these answers within the context of Africa.<br /> &nbsp / </p>

<p>There is a growing interplay of competing realities facing the international community in the general areas of innovation, technological advancement and overall economic development. The highly industrialised wealthy nations, largely located on the Northern hemisphere are on the one hand undoubtedly at the forefront in global research, technology and infrastructure development. The developing and least developed countries on the other hand are mostly situated on the Southern hemisphere. They are not as wealthy or technologically advanced as their&nbsp / Northern counterparts, but are naturally endowed with unique variations of plant, animal and micro-organism species occurring in natural ecosystems, as well as the traditional knowledge on&nbsp / how to use these unique species. This knowledge has been adjudged to be responsible for the sustainable maintenance of the earth&rsquo / s biodiversity. Increasing exploitation of biodiversity,&nbsp / spurred on by the competing realities identified above, has left the earth in a present state of alarm with respect to the uncontrolled loss of biodiversity. The traditional knowledge of local&nbsp / peoples has significantly offered leads to research institutes from the North in developing major advancements in drugs, cosmetics and agriculture. Little or no compensation has however been seen to go back to the indigenous&nbsp / communities and countries that provide resources, and indicate various possibilities through their traditional knowledge to the use of such resources. Efforts by some biodiversity rich countries to&nbsp / ddress this trend through legislation developed in accordance with the principles of the Convention on Biological Diversity have been frustrated due to the inability to enforce their domestic laws outside their borders. Theft of genetic resources and its associated traditional knowledge&nbsp / from such countries has therefore remained a major challenge. Against this backdrop, and on the&nbsp / insistence of biodiversity-rich developing countries, an international regime on access and benefit sharing was negotiated and its final text adopted in 2010. This international regime is as&nbsp / contained in the Nagoya Protocol. This research sets out to examine whether the Nagoya Protocol offers a final solution to the protection of traditional knowledge associated with biodiversity in&nbsp / biodiverse countries. It further examines the importance of domestic legislation in achieving the objectives of the Protocol. The research has been tailored to African biodiverse countries, and&nbsp / seeks these answers within the context of Africa.<br /> &nbsp / </p>