Thesis (Ph. D.)--University of California, San Diego, 2000. / Vita. Includes bibliographical references (leaves 236-253).

Στην παρούσα εργασία θα μελετήσουμε κάποιες συνθήκες υπό τις οποίες συγκεκριμένες κλάσεις πολλαπλοτήτων σημαιών (flag manifolds) δέχονται ομογενείς ισογεωδαισιακές καμπύλες. Μια λεία πολλαπλότητα M διάστασης n είναι ένας Hausdorff και 2ος αριθμήσιμος τοπολογικός χώρος, τοπικά ομοιομορφικός με έναν Ευκλείδειο χώρο διάστασης n, εφοδιασμένος με μια διαφορική δομή. Ένα παράδειγμα πολλαπλότητας διάστασης 2 είναι μια επιφάνεια του χώρου. Ο εφοδιασμός μιας λείας πολλαπλότητας M με μια μετρική g στον εφαπτόμενο χώρο κάθε σημείου της επιτρέπει την εισαγωγή γεωμετρικών ιδιοτήτων στην M (μήκη καμπυλών, καμπυλότητα κλπ.). Μια σημαντική κλάση καμπυλών σε μια πολλαπλότητα M είναι οι γεωδαισιακές καμπύλες που έχουν την ιδιότητα να ελαχιστοποιούν την απόσταση μεταξύ δύο αρκετά κοντινών σημείων της M. Επιπλέον, δεδομένου ενός σημείου p μιας πολλαπλότητας M και εφαπτόμενου διανύσματος v στο p, υπάρχει μοναδική γεωδαισιακή καμπύλη διερχόμενη από το p με κατεύθυνση το v. Μια ομάδα Lie G είναι μια λεία πολλαπλότητα με δομή ομάδας τέτοια ώστε οι πράξεις του πολλαπλασιασμού και αντιστροφής να είναι διαφορίσιμες. Μια τέτοια ομάδα είναι και η μοναδιαία σφαίρα. Βασικό χαρακτηριστικό των ομάδων Lie είναι ότι η γεωμετρία τους παραμένει αναλλοίωτη σε όλα τα σημεία τους. Συνεπώς, η μελέτη της γεωμετρίας μιας ομάδας Lie G ανάγεται στη μελέτη της γεωμετρίας σε μια περιοχή του ουδετέρου στοιχείου της e και συγκεκριμένα, στη μελέτη της άλγεβρας Lie της G, δηλαδή τον εφαπτόμενο διανυσματικό χώρο της G στο e. Οι πολλαπλότητες που γενικεύουν αυτή την ιδιότητα ονομάζονται ομογενείς χώροι. Ένας ομογενής χώρος είναι μια λεία πολλαπλότητα M στην οποία δρα με συγκεκριμένο τρόπο μια ομάδα Lie G. Η G ορίζει μια γεωμετρία στην M που είναι αναλλοίωτη σε κάθε σημείο της M. Αυτό επιτυγχάνεται με τον ορισμό των G-αναλλοίωτων μετρικών στον ομογενή χώρο M. Στην περίπτωση που η G είναι συμπαγής και ημιαπλή ο ομογενής χώρος ονομάζεται πολλαπλότητα σημαιών. Αποδεικνύεται ότι κάθε ομογενής χώρος M δέχεται ομογενείς γεωδαισιακές καμπύλες, δηλαδή γεωδαισιακές που αποτελούν τροχιές, μέσω της δράσης της G στη M, μιας κατηγορίας υποομάδων της G που ονομάζονται μονοπαραμετρικές υποομάδες. Στην παρούσα εργασία θα μελετήσουμε την ύπαρξη ισογεωδαισιακών καμπυλών σε πολλαπλότητες σημαιών, δηλαδή καμπυλών που είναι ομογενείς γεωδαισιακές ανεξάρτητα της G-αναλλοίωτης μετρικής που θα ορίσουμε στην πολλαπλότητα. / In this thesis we study homogeneous geodesics on certain classes of flag manifolds.

In an era that national flags are dying off (Sletmo 2001) there is no dispute about the success of Greek flagged shipping. How can a small nation like Greece retain the highest percentage of all national fleets? Literature identifies that this success is due to several reasons. However, what are the elements that contribute to the success of Greek-flagged shipping? This study establishes that ‘the success of Greek ocean-going flagged shipping is a blend of a tendency for governments to experiment with various policies intended to promote national competitiveness, individual entrepreneurship, the cluster as well as culture, knowledge and skill’. Litrature from different disciplines and sources are summarised, compared, contrasted, and synthesised in order to develop a coherent outcome and gain a new perspective in the respective field. Since “policy is like beauty in the eye of the beholder…” (Roe 2007c) a multilevel, holistic, exploratory, inductive, deductive, abductive, and overall pragmatic methodological approach is considered, as the only viable option for complex research questions related to maritime policy. A three-method approach is applied with every method contributing to each other: the Timeline A to Ω and Literature Analysis, Delphi Method, and the Application of Porter’s diamond on national competitiveness. The belief that traditional flags are dying off, implies that they are not dead yet. The Greek Registry, and every ship registry is a system of people, organisations , and processes and it is that system that contributes to the success of the flag. Contrary to the belief of some players, government policy affects the size and the quality of the national flag ocean-going fleet undertaking various polices intented to promote national competitiveness. This study contributes to academic knowledge as well as to the Greek and any other registry’s competitiveness, as well as to the govenemental decision making and development of maritime policies. Recommendations are made for the Greek flag and the maritime policy, as well as for the application of the GREKON MODEL to the real maritime world and academia.

abstract: The uncrossing partially ordered set $P_n$ is defined on the set of matchings on $2n$ points on a circle represented with wires. The order relation is $\tau'\leq \tau$ in $P_n$ if and only if $\tau'$ is obtained by resolving a crossing of $\tau$. %This partial order has been studied by Alman-Lian-Tran, Huang-Wen-Xie, Kenyon, and Lam. %The posets $P_n$ emerged from studies of circular planar electrical networks. Circular planar electrical networks are finite weighted undirected graphs embedded into a disk, with boundary vertices and interior vertices. By Curtis-Ingerman-Morrow and de Verdi\`ere-Gitler-Vertigan, the electrical networks can be encoded with response matrices. By Lam the space of response matrices for electrical networks has a cell structure, and this cell structure can be described by the uncrossing partial orders. %Lam proves that the posets can be identified with dual Bruhat order on affine permutations of type $(n,2n)$. Using this identification, Lam proves the poset $\hat{P}_n$, the uncrossing poset $P_n$ with a unique minimum element $\hat{0}$ adjoined, is Eulerian. This thesis consists of two sets of results: (1) flag enumeration in intervals in the uncrossing poset $P_n$ and (2) cyclic sieving phenomenon on the set $P_n$. I identify elements in $P_n$ with affine permutations of type $(0,2n)$. %This identification enables us to explicitly describe the elements in $P_n$ with the elements in $\mathcal{MP}_n$. Using this identification, I adapt a technique in Reading for finding recursions for the cd-indices of intervals in Bruhat order of Coxeter groups to the uncrossing poset $P_n$. As a result, I produce recursions for the cd-indices of intervals in the uncrossing poset $P_n$. I also obtain a recursion for the ab-indices of intervals in the poset $\hat{P}_n$, the poset $P_n$ with a unique minimum $\hat0$ adjoined. %We define an induced subposet $\mathcal{MP}_n$ of the affine permutations under Bruhat order. Reiner-Stanton-White defined the cyclic sieving phenomenon (CSP) associated to a finite cyclic group action on a finite set and a polynomial. Sagan observed the CSP on the set of non-crossing matchings with the $q$-Catalan polynomial. Bowling-Liang presented similar results on the set of $k$-crossing matchings for $1\leq k \leq 3$. In this dissertation, I focus on the set of all matchings on $[2n]:=\{1,2,\dots,2n\}$. I find the number of matchings fixed by $\frac{2\pi}{d}$ rotations for $d|2n$. I then find the polynomial $X_n(q)$ such that the set of matchings together with $X_n(q)$ and the cyclic group of order $2n$ exhibits the CSP. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2018

Made available in DSpace on 2014-06-11T19:30:22Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-03-29Bitstream added on 2014-06-13T19:19:05Z : No. of bitstreams: 1 seyssel_r_me_ia.pdf: 2214244 bytes, checksum: 4b95670ca493223d961fde5ba5e501dc (MD5) / Este trabalho tem por meta verificar problemas objetivos e subjetivos na concepção e definição da bandeira nacional brasileira e como isto pode afetar ou não, intelectual e culturalmente, os brasileiros. Afora as dificuldades de sua reprodução/manufatura correta, dada sua forma com minúcias - por exemplo: a colocação e tamanho das estrelas, a inclinação exata da faixa branca central e a correta tonalidade do azul -, nossa bandeira certamente apresenta falhas tanto de design e aspectos simbólicos quanto de comunicação e psico-sóciocultural. Esta dissertação pretende determinar o porquê desses problemas, de onde surgiram, como possivelmente afetam as pessoas em geral e oferece uma das possíveis soluções, neste caso uma que pode ser considerada a mais simples. Desta forma, modificando somente um dos elementos básicos do design, a bandeira brasileira ganharia um grande e verdadeiro significado, aproximando-se da sinonímia brasil e da cor brasil e do que a nacionalidade brasil pode significar. / The aim of this work is to verify the objective and subjective problems related to the conception and definition of the Brazilian National flag, and how this may affect or not, intellectual and cultural roots of the Brazilian people. Regardless the difficulties in its correct reproducing/manufacturing, for having stamped some details - for instance: the size and the position of the stars, the exact inclination of the central white stripe, the correct blue tone -, surely our flag shows failures both in design and in symbolic, communication and psycho-sociocultural aspects. This dissertation intends to point out the reasons for the referred problems, where they come from, in what way they may influence people in general and offers one suggestion that could correspond to the one of the possible solutions, in this case the one which could be considered the simplest one. Thus, by modifying only one of the basic elements of the design, the Brazilians flag would get a greater and real meaning, getting closer to what the word 'brazil', the colour 'brazil' and the Brazilian nationality can mean.

La Corse figure parmi les zones les plus criminogènes d'Europe alors que ceux qui y vivent, et les touristes qui la visitent, en parlent volontiers comme d'un paradis terrestre. Cette thèse tente d'interroger ce paradoxe en faisant appel aux concepts de la psychanalyse pour ouvrir de nouvelles pistes permettant d'éclairer autrement le phénomène de la violence insulaire dans un débat déjà largement ouvert par les spécialistes des sciences humaines et bien sûr les journalistes. En prenant appui sur la théorie du signifiant élaborée par Jacques Lacan nous analyserons le drapeau, cet emblème qui identifie une communauté à l'international et auxquels les membres de cette communauté s'identifient généralement. Deux versions historiques seront étudiées : celui à tête de Maure et celui à l'effigie de L'Immaculée Conception de la Vierge Marie qui lui succède pendant la révolution pour l'indépendance, en 1735. Cette confrontation permet de soutenir que, si la Corse ne parvient pas à passer de la horde à l'État, c'est en partie en lien avec les signifiants proposés aux insulaires par son héraldique lesquels ne favorisent pas la compréhension des lois exogamiques et donc les passages que constituent les complexes d'OEdipe et de castration. La définition du terrorisme comme « guerre psychologique » justifie le recours à la psychanalyse pour en détecter les ressorts à travers une thématique qu'elle connaît bien : la notion de limite et de franchissement des limites à l'oeuvre dans toutes les formes de terrorisme. / Corsica is one of the most crimogenic areas in Europe, even though the residents and visiting tourists refer to it as an earthly paradise. This dissertation attempts to examine this paradox by calling on concepts of psychoanalysis in order to explore new avenues that may be able to provide insight and otherwise shed light on the phenomenon of insular violence in a debate that is already largely open and discussed by social science specialists and, of course, journalists. Based on the theory of the Signifier, developed by Jacques Lacan, we will analyse the flag, the symbol which identifies a community to the rest of the world and to which members of this community generally identify themselves. Two historical versions will be studied: that of the Saracen's head and the effigy of the lmmaculate Conception of the Blessed Virgin, which succeeded it during the revolution for independence in 1735. Such a confrontation enables the supposition that if Corsica is unable to pass from mob rule to State rule, this is partly in connection with the signifiers suggested to the islanders by their genealogy which does not encourage the understanding of exogamous laws and thus the routes leading to Oedipus and castration complexes. The definition of terrorism as "psychological war" justifies the use of psychoanalysis to discover its origins by means of a thematic which it is very familiar with: the notion of limits and transgressing limits.

Nesta tese estudamos dois problemas em digrafos: um problema de empacotamento e um problema de contagem. Estudamos o problema de empacotamento máximo de arborescências no digrafo aleatório D(n,p), onde cada possvel arco é inserido aleatoriamente ao acaso com probabilidade p = p(n). Denote por (D(n,p)) o maior inteiro possvel 0 tal que, para todo 0 l , temos ^(l-1)_i=0 (l-i)|{v in d^in(v) = i}| Provamos que a quantidade máxima de arborescências em D(n,p) é (D(n,p)) assintoticamente quase certamente. Nós também mostramos estimativas justas para (D(n, p)) para todo p [0, 1]. As principais ferramentas que utilizamos são relacionadas a propriedades de expansão do D(n, p), o comportamento do grau de entrada do digrafo aleatório e um resultado clássico de Frank que serve como ligação entre subpartições em digrafos e a quantidade de arborescências. Para o problema de contagem, estudamos a densidade de subtorneios fortemente conexos com 5 vértices em torneios grandes. Determinamos a densidade assintótica máxima para 5 torneios bem como as famlias assintóticas extremais de cada torneios. Como subproduto deste trabalho caracterizamos torneios que são blow-ups recursivos de um circuito orientado com 3 vértices como torneios que probem torneios especficos de tamanho 5. Como principal ferramenta para esse problema utilizados a teoria de álgebra de flags e configurações combinatórias obtidas através do método semidefinido. / In this thesis we study two problems dealing with digraphs: a packing problem and a counting problem. We study the problem of packing the maximum number of arborescences in the random digraph D(n,p), where each possible arc is included uniformly at random with probability p = p(n). Let (D(n,p)) denote the largest integer 0 such that, for all 0 l , we have ^(l-1)_i=0 (l-i)|{v in d^in(v) = i}|. We show that the maximum number of arc-disjoint arborescences in D(n, p) is (D(n, p)) asymptotically almost surely. We also give tight estimates for (D(n, p)) for every p [0, 1]. The main tools that we used were expansion properties of random digraphs, the behavior of in-degree of random digraphs and a classic result by Frank relating subpartitions and number of arborescences. For the counting problem, we study the density of fixed strongly connected subtournaments on 5 vertices in large tournaments. We determine the maximum density asymptotically for five tournaments as well as unique extremal sequences for each tournament. As a byproduct of this study we also characterize tournaments that are recursive blow-ups of a 3-cycle as tournaments that avoid three specific tournaments of size 5. We use the theory of flag algebras as a main tool for this problem and combinatorial settings obtained from semidefinite method.

This thesis is divided into two parts, each part exploring a different topic within the general area of nonlinear algebra. In the first part, we study several applications of tensors. First, we study tensor networks, and more specifically: uniform matrix product states. We use methods from nonlinear algebra and algebraic geometry to answer questions about topology, defining equations, and identifiability of uniform matrix product states. By an interplay of theorems from algebra, geometry, and quantum physics we answer several questions and conjectures posed by Critch, Morton and Hackbusch. In addition, we prove a tensor version of the so-called quantum Wielandt inequality, solving an open problem regarding the higher-dimensional version of matrix product states. Second, we present new contributions to the study of fast matrix multiplication. Motivated by the symmetric version of matrix multiplication we study the plethysm S^k(sl_n) of the adjoint representation sl_n of the Lie group SL_n . Moreover, we discuss two algebraic approaches for constructing new tensors which could potentially be used to prove new upper bounds on the complexity of matrix multiplication. One approach is based on the highest weight vectors of the aforementioned plethysm. The other approach uses smoothable finite-dimensional algebras. Finally, we study the Hessian discriminant of a cubic surface, a recently introduced invariant defined in terms of the Waring rank. We express the Hessian discriminant in terms of fundamental invariants. This answers Question 15 of the 27 questions on the cubic surface posed by Bernd Sturmfels. In the second part of this thesis, we apply algebro-geometric methods to study matroids and flag matroids. We review a geometric interpretation of the Tutte polynomial in terms of the equivariant K-theory of the Grassmannian. By generalizing Grassmannians to partial flag varieties, we obtain a new invariant of flag matroids: the flag-geometric Tutte polynomial. We study this invariant in detail, and prove several interesting combinatorial properties.

Renewable energy sources are vital to reduce dependence on fossil fuels that are harmful for the environment and release greenhouse gases causing global warming. Wind energy is a natural source of energy that is abundant in the environment. While wind turbines are most popular, convenient, and used to harvest energy at large scales, there have been recent studies focusing on harvesting energy from the wind for microdevices. Such micro wind energy harvesters can decrease dependence on batteries. In this study, a novel, framed flag micro wind harvester was designed and tested, and its behavior at three different wind speeds was experimentally examined in a wind tunnel. The main purpose of this study is to determine the geometric and wind speed conditions under which regular flapping occurs in the flag material. A high-speed camera was used to visualize the motion of the harvester at different wind speeds and at various parametric ratios of the flag material length to the frame length. The movies taken by the camera are analyzed using Image J software to find the flapping frequency, flapping angle, and the amplitude. Nondimensional parameters such as the Re number and St number also are calculated. This study finds that parametric ratios of 1.1 and 1.2 with the medium wind speed condition of 5 m/s are optimal flapping conditions. These optimal conditions would conveniently allow the use of piezoelectric material as the flag material in order to harvest energy. Further, an advantage of this novel design over previous designs is that the wind harvester naturally aligns with the wind direction and is thus omnidirectional.

Introduction: Identifying patients at risk for chronic musculoskeletal pain can inform evaluation and treatment decisions. The ability of physical therapists to assess patients’ risk for chronic pain without use of validated tools has been questioned. The Ӧrebro Musculoskeletal Pain Questionnaire (OMPQ) is used to determine risk for chronic pain. Methods: The aim of this pragmatic study was to prospectively quantify the agreement between physical therapists’ assessment of patients’ risk for chronic symptoms compared to the OMPQ. Patients were asked to complete the OMPQ during the initial visit. Physical therapists, blinded to OMPQ risk classification, carried out their usual patient assessment procedures. The physical therapists rated patients as either high or low risk for chronic pain based on their clinical assessment. Agreement between therapist and OMPQ was determined using Cohen’s Kappa (κ) and screening accuracy compared clinician risk to the OMPQ risk classification (reference standard) by way of contingency table analysis. Results: Ninety-six (96) patients’ risk classifications and 15 corresponding physical therapists’ risk estimates were available for analysis. The OMPQ identified a 47% prevalence for high risk of chronic pain. Agreement (κ and 95% confidence interval) between physical therapist rating and OMPQ was slight, κ = 0.272 (0.033–0.421), p = .026. Therapists’ sensitivity and specificity (95% CI) for determining risk classifications were 60.0% (44.3–74.3) and 62.8% (48.1–75.6), respectively. The positive and negative likelihood ratios (95% CI) were 1.61 (1.05–2.47) and 0.64 (0.42–0.97). Discussion: The use of validated self-report questionnaires are recommended to supplement clinician prognosis for patients at risk of chronic musculoskeletal pain.