The property that a graph has an embedding in the projective plane is closed under taking minors. Thus by the well known Graph Minor theorem of Robertson and Seymour, there exists a finite list of minor-minimal graphs, call it L, such that a given graph G is projective planar if and only if G does not contain any graph isomorphic to a member of L as a minor. Glover, Huneke and Wang found 35 graphs in L, and Archdeacon proved that those are all the members of L, but Archdeacon's proof never appeared in any refereed journal. In this thesis we develop a modern approach and technique for finding the list L, independent of previous work. Our approach is based on conditioning on the connectivity of a member of L. Assume G is a member of L. If G is not 3-connected then the structure of G is well understood. In the case that G is 3-connected, the problem breaks down into two main cases, either G has an internal separation of order three or G is internally 4-connected. In this thesis we find the set of all 3-connected minor minimal non-projective planar graphs with an internal 3-separation. For proving our main result, we use a technique which can be considered as a variation and generalization of the method that Robertson, Seymour and Thomas used for non-planar extension of planar graphs. Using this technique, besides our main result, we also classify the set of minor minimal obstructions for a-, ac-, abc-planarity for rooted graphs. (A rooted graph (G,a,b,c) is a-planar if there exists a split of the vertex a to a' and a' in G such that the new graph G' obtained by the split has an embedding in a disk such that the vertices a', b, a', c are on the boundary of the disk in the order listed. We define b- and c-planarity analogously. We say that the rooted graph (G,a,b,c) is ab-planar if it is a-planar or b-planar, and we define abc-planarity analogously.)

We study projective completions of affine algebraic varieties (defined over an algebraically closed field K) which are given by filtrations, or equivalently, integer valued `degree like functions' on their rings of regular functions. For a polynomial map P := (P_1, ..., P_n): X -> K^n of affine varieties with generically finite fibers, we prove that there are completions of the source such that the intersection of completions of the hypersurfaces {P_j = a_j} for generic (a_1, ..., a_n) in K^n coincides with the respective fiber (in short, the completions `do not add points at infinity' for P). Moreover, we show that there are `finite type' completions with the latter property, i.e. determined by the maximum of a finite number of `semidegrees', by which we mean degree like functions that send products into sums. We characterize the latter type completions as the ones for which ideal I of the `hypersurface at infinity' is radical. Moreover, we establish a one-to-one correspondence between the collection of minimal associated primes of I and the unique minimal collection of semidegrees needed to define the corresponding degree like function. We also prove an `affine Bezout type' theorem for polynomial maps P with finite fibers that admit semidegrees corresponding to completions that do not add points at infinity for P. For a wide class of semidegrees of a `constructive nature' our Bezout-type bound is explicit and sharp.

We study projective completions of affine algebraic varieties (defined over an algebraically closed field K) which are given by filtrations, or equivalently, integer valued `degree like functions' on their rings of regular functions. For a polynomial map P := (P_1, ..., P_n): X -> K^n of affine varieties with generically finite fibers, we prove that there are completions of the source such that the intersection of completions of the hypersurfaces {P_j = a_j} for generic (a_1, ..., a_n) in K^n coincides with the respective fiber (in short, the completions `do not add points at infinity' for P). Moreover, we show that there are `finite type' completions with the latter property, i.e. determined by the maximum of a finite number of `semidegrees', by which we mean degree like functions that send products into sums. We characterize the latter type completions as the ones for which ideal I of the `hypersurface at infinity' is radical. Moreover, we establish a one-to-one correspondence between the collection of minimal associated primes of I and the unique minimal collection of semidegrees needed to define the corresponding degree like function. We also prove an `affine Bezout type' theorem for polynomial maps P with finite fibers that admit semidegrees corresponding to completions that do not add points at infinity for P. For a wide class of semidegrees of a `constructive nature' our Bezout-type bound is explicit and sharp.

En donnant accès à la théorie de la géométrie projective sous l'angle des médias interactifs, le projet Perspective théâtrale sur la géométrie projective permet une expérience unique d'apprentissage et de communication en ligne. De la formulation des objectifs à la maquette, il a fallu s'approprier les contenus, les catégoriser, les diviser, les relier, les structurer. Ce mémoire fait état de la démarche de structuration des ressources médiatisées d'un cours de géométrie projective et d'une pièce de théâtre sur la vie du mathématicien créateur de cette théorie, puis de la diffusion de ces contenus sur la Toile, par baladodiffusion ou en mode présentiel, en ayant recours au Web collaboratif et sémantique. Ces nouveaux contextes d'échange permettent de passer outre les contraintes de distance, de temps et de disponibilités des personnes intéressées, tout en transmettant des informations à jour sur un sujet et en faisant participer activement les utilisateurs à façonner et partager leur expérience d'apprentissage. L'information sémantique attachée à chacune des unités médiatiques permet une appropriation des contenus sous de multiples facettes: linéairement, constructivement, artistiquement. Une ontologie ajoute une enveloppe conjonctive aux contenus, donnant une structure de navigation cohérente. Cette ontologie permet à la fois de gérer les différentes ressources multimédias du projet, de construire le portail les diffusant et d'offrir aux usagers des interfaces interactives pour les manipuler. Des créateurs aux usagers, tous manipulent et profitent de la structure de l'ontologie et des ressources qui la composent. Brain Cuts, un éditeur de courts métrages, est un exemple d'outil permettant aux usagers d'agréger eux-mêmes les ressources multimédias du cours. Les nouveaux outils qu'apporte l'avènement du Web sémantique aideront peut-être à construire un écosystème de connaissances (Knowledge Ecosystem) sur la Toile. Ce projet sert de plateforme expérimentale à ces nouveaux moyens interactifs en éducation. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Médias interactifs, Toile, Web, Web sémantique, Ontologie, Téléapprentissage, Théâtre, Mathématiques, Géométrie projective, Gestion des connaissances.

Halogen lamps are mostly applied as a light source to the traditional lamp for medical treatment due to its proper color temperature, but it has its disadvantages such as ultraviolet rays and infrared rays which will be harmful to the patients and faculties in the hospitals under long-term exposure. Consequently, using light emitting diode(LED) as a new light source instead of the traditional halogen lamp will be the trend of the future. The purpose of this study is to design a projective LED dental lamp that can achieve the goals of 200mm¡Ñ100mm for light shape and 11000lux illuminance energy by using the optics simulation software, LightTools. Firstly, a single LED lamp module with a high focusing hollow tubular light guide structure was designed and developed comparing with the solid light guide structure used in many commercial projective dental lamp, the hollow tubular light guide structure can decrease illuminance energy lose due to the absorption by tube material. Because the required objective light shape could not be achieved by using the designed light guide structure only, so a lens component was adopted and designed in order to shrink the output light shape to the required size. Finally, through the specific arrangement of position and angle of each LED lamp module, a projective LED dental lamp with 9 LEDs lamp modules which conform with the required illuminance energy was proposed.

This thesis aimed to examine the process of projective identification in the couple relationship by focusing on two areas of investigation: Firstly, how projective identification operates &ldquo / within&rdquo / an individual regarding the associations among early parenting experiences, personality and couple relationship / secondly how projective identification operates between two partners in the couple relationship regarding partners&rsquo / similarities and complementarities have been focused. Initially, several multiple regressions were run to examine the relationships among the parenting, personality and couple relationship. Afterwards, several intra-class partial pairwise correlatons were conducted to reveal similarities and complementarities of the partners regarding their early maladaptive parenting experiences, personality constructs and couple relationship variables. Paulson Daily Living Inventory, Separation-Individuation Inventory and Splitting Scale were translated into Turkish and psychometric studies were conducted. For the main study, 356 participants (178 male and 178 female), who are cohabiting partners to each other, were achieved through snowball sampling method. Early maladaptive parenting experiences of the participants were examined by Young Parenting Inventory. Personality constructs contained &ldquo / separation individuation process&rdquo / and &ldquo / splitting defense&rdquo / as the theoretical correlates of projective identification, and &ldquo / early maladaptive schemas&rdquo / of the individuals. Couple relationship variables were &ldquo / relationship satisfaction&rdquo / , &ldquo / emotional dependency&rdquo / and &ldquo / jealousy&rdquo / . Findings of the study revealed that projective identification has bidirectional relatedness with the personality and couple relationship of the individual. Multiple regression analyses showed theoretically consistent associations among an individual&rsquo / s parenting experiences, personality and couple relationship. Intra-class partial pairwise correlations showed similarities and complementarities between two partners. Findings were discussed in the light of relevant literature.

Master thesis, Master's degree program Marketing, Economic School Linnaeus University, Växjö Sweden, Spring semester 2015. Author: Andersson Anthon, Guntell Robin Tutor: Soniya Billore Examiner: Anders Pehrsson Title: Advancing the COO Construct From an Affective Dimension: The Application of Projective Technique Purpose: The purpose in this article is to break from traditional research and its accompanying cognitive research methods in order to advance the COO field from a more accurate perspective that also involves an affective dimension as well. Design/methodology/approach: Drawing from prior research in the COO field, the methodology accounted for assumptions that were tested in collage technique and ad copy technique. Findings: The results shows that some people only seems to be susceptible to COO influence when communicating emotional CSAs nonverbally, whilst some people only reveal rational CSAs when being cognitively asked about COO influence in a directed manner. As a result, the present findings might suggest that prior research in the academic field might suffer from bias. Practical implications: In the light of COO, managers should bear in mind that some people cannot be targeted with solely rely on a cognitive marketing communication strategy. More specifically, the ad copy technique provides guidelines for appropriate design of advertisements when one consider to serving the brand’s origin as salient cue in consumers’ minds. Originality/value: Advancing the COO construct with using collage technique, this study is to the best our knowledge the second to account for an affective dimension as well.

Η διπλωματική εργασία κινείται γύρω από το θεώρημα Quillen-Suslin (1976): “Κάθε πεπερασμένα γενόμενο προβολικό module επί του δακτυλίου των πολυωνύμων k[x_1,…,x_m ] (όπου k σώμα) είναι ελεύθερο”. Το πρόβλημα ξεκίνησε το 1955, όταν ο J. P. Serre, σε υποσημείωση της ένδοξης εργασίας του “Faisceaux Algebriques Coherents” (σελίδα 243), σημειώνει: “ On ignore s’il existe des A-modules projectifs de type fini qui ne soient pas libres” (A=k[x_1,…x_m ], k σώμα).* Το πρόβλημα λύθηκε από τους Quillen και Suslin (ανεξάρτητα) είκοσι χρόνια μετά. Για την απόδειξη του θεωρήματος είναι απαραίτητο το αποτέλεσμα που οφείλεται στον ίδιο τον Serre (1958): “ Κάθε πεπερασμένα γενόμενο προβολικό k[x_1,…,x_m ]-module P είναι σταθερά ελεύθερο” (δηλαδή το P δέχεται πεπερασμένα γενόμενο ελεύθερο συμπλήρωμα F, ώστε το P⊕F να είναι ελεύθερο). Στo Κεφάλαιο 2 αυτής της εργασίας, θα παρουσιάσουμε την απόδειξη του ανωτέρω θεωρήματος του Serre και τελικά, στο Κεφάλαιο 3, θα σκιαγραφήσουμε την απόδειξη του θεωρήματος Quillen-Suslin, με τη μέθοδο του Suslin. *Αγνοούμε αν υπάρχουν πεπερασμένα γενόμενα προβολικά A-modules που δεν είναι ελεύθερα. / This work is about the Quillen-Suslin Theorem (1976): “If k is a field , then every finitely generated projective k[x_1,…,x_m ]-module is free”. This problem started in 1955, when J.P. Serre, in his glorious paper “FaisceauxAlgebriquesCoherents” (page 243), noted: “On ignore s’ilexiste des A-modules projectifs de type fini qui ne soient pas libres ” (A=k[x_1,…x_m ],k is field).* This problem was solved from Quillen and Suslin (independently) twenty years after. For the proof of this theorem is necessary the result, due to Serre (1958): “Every finitely generated projective k[x_1,…,x_m ]-module P is stably free ” (ie. P admits a finitely generated free complement F, so that P⊕F is free). In Chapter 2 of this work, we will represent the proof of the above Serre’s Theorem and, finally, in Chapter 3, we will sketch the proof of Quillen-Suslin's Theorem, with Suslin’s method. *We ignore, if exist finitely generated projective A-modules, that they are not free.

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ABSTRACT The discriminative ability and interrater reliability of one quantitative method of scoring Kinetic Family Drawings, (KFDJs), was explored, focusing on a little researched population - that of sexually abused versus non-referred Zulu speaking females between 7 and 11 years of age. An additional 20 indicators, suggested by various research to be frequent in the human figure drawings of (Western) sexually abused children, were also evaluated. The KFD's of 28 subjects were obtained. The 14 experimental group subjects were drawn from an organisation which deals extensively with the child survivors and perpetrators of sexual abuse. The 14 control group subjects were drawn from alocal primary school and had no known history of sexual abuse. Results were interpreted empirically. Results suggested that although the scoring system may be reliable, it is sensitive to the training, theoretical stance, etc. of the user. It was also suggested that the indicators used were not, as used by the scorers, able to distinguish between the KFDJs of the control and experimental groups. The relevance of certain of the indicators to South African populations was questioned since they were not scored at all by the scorers. In view of the researcher's perception of shortcomings with this approach, she attempted to describe more fully that which was depicted in the KFD's collected. Finally, several comments on the utility of viewing drawings from social constructivist, deconstructionist and social constructionist understandings as a complement to qualitative and quantitative approaches to the KFD were made. Suggestions as to how the KFD could be fruitfully used were proffered. It was contended that the KFD technique is not suitable for the use of lower level health care workers, that KFD's may have value in therapeutic settings, and that quantitative methods are simply one set of meanings which could be used to (partly) understand KFD's - attending to the child's context and the meanings he/she attributes to the various aspects of the KFD was contended to be important. / Thesis (M.Ed.) - University of Natal, Pietermaritzburg, 1999.