Les premiers travaux que je présente ici developpent des méthodes asymptotiques qui permettent d'étudier une “continuité du spectre” <br />pour l'opérateur de Laplace agissant sur les fonctions ou les formes différentielles d'une variété compacte:<br />– l'influence d'excision de petits voisinages tubulaires (avec diverses conditions au bord)<br />– l'influence d'ajout d'anses fines<br />Les résultats donnent aussi des asymptotiques des formes propres.<br />Il s'appliquent à l'étude du spectre continu sur des variétés périodiques.<br />Les travaux du second groupe concernent les opérateurs pseudo-différentiels et le calcul semi-classique :<br />– comparaison des spectres de Dirichlet et Neumann pour l'opérateur d'élasticité<br />– localisation semi-classique du spectre joint de plusieurs opérateurs pseudo-différentiels qui commutent.

Nous avons dans ce travail testé avec succès la méthode RBF sur le problème raide, le problème de la concentration d'un contaminant, le modèle Black-Scholes et le modèle du champ classique d'un méson. Notre contribution a été importante lors de la résolution de l'équation non linéaire de Klein-Gordon. La convergence et l'efficacité de la méthode a été montré grâce au RMSE entre la solution analytique et la solution numérique. L'introduction mise à part, cette thèse a été composé de quatre chapitres. Le premier exprime l'interpolant radial dans la base du sous-espace des interpolés. Le second estime l'erreur d'interpolation dans des cas particuliers de la fonction radiale de base et fournit les meilleures constantes dans les majorations de l'erreur. Le troisième consacré au problème de la quasi-interpolation a aussi permis d'établir l'existence et l'unicité de la solution du champ classique d'un méson grâce à la théorie des semi-groupes et au théorème du point fixe de Banach. Le quatrième a été consacré aux applications numériques. Une simulation numérique a été faite pour le problème de la concentration d'un contaminant. Nous avons terminé par une conclusion et perspectives en désignant les futurs lignes de recherche sur le sujet.

Cette thèse est un travail conjointement sur l'espace de modules $\mathscr<br />M$ des connexions plates du fibré principal $S\times G$ d'une sphère de<br />Riemann $S$ (ayant $n\geq 3$ bords), où $G=\GL{N,\C}$ et sur l'algèbre de<br />lacets $\tilde\g=\gl{N,\C}(\!(\l^\mi)\!)$. <br /><br />Dans un premier temps, nous étudions une hiérarchie de bidérivations<br />quadratiques sur $\tilde\g$. En particulier, grâce au processus de fusion<br />introduit par Alekseev, Kosmann-Schwarzbach et Meinrenken en 2002, nous<br />extrayons parmi elles une structure $\PB^Q_1$ de quasi-Poisson sur<br />$\tilde\g$. Celle-ci se restreint au sous-espace<br />$\tilde\g_n=\set{\sum_{k=0}^nx^{[k]}\l^k}$.<br /><br />Nous montrons ensuite un résultat de réduction dans un contexte de<br />bidérivation de quasi-Poisson. Il permet d'équipper le quotient $\mathscr<br />A/G:=\set{\Id\l^n+\l Y(\l)+\Id|Y\in\tilde\g_{n-2}}/G$ d'une structure de<br />Poisson induite par $\PB^Q_1$.<br /><br />En s'appuyant sur le système intégrable de Beauville sur<br />$\tilde\g_{n-2}/G$, nous montrons que la famille de fonctions $({\text{tr}}<br />X^k(a))_{k\in\N,a\in\C}$ constitue un système intégrable sur $\mathscr<br />A/G$. Les fonctions que nous considérons sur l'espace de modules $\mathscr<br />M$ sont les tiré-en-arrière $(\mathscr<br />T^*{\text{tr}X^k(a)})_{k\in\N,a\in\C}$, où $\mathscr T:G^n\to\tilde\g_n$<br />est un morphisme de quasi-Poisson et un difféomorphisme local. Nous<br />utilisons ces propriétés de $\mathscr T$ pour montrer que cette famille de<br />fonctions constitue un système intégrable sur $\mathscr M$.

Thesis (MA)--University of Montana, 2009. / Contents viewed on November 30, 2009. Title from author supplied metadata. Includes bibliographical references.

Thesis (Ed. D.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains viii, 57 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 48-54).

This single case study explored the relationship between non-academic interventions that supported student psychosocial factors and remedial math success. The theoretical framework proposed that remedial math success was linked to psychosocial factors as described by Bandura’s social cognitive theory rather than merely cognitive factors possessed by the student. The literature review revealed that remedial math success in community colleges was chronically problematic, that psychosocial factors were fundamental to human development and learning and well supported by neuroscience, and that above average academic success has long been positively correlated with programs of non-academic interventions. According to the findings of this study, non-academic interventions such as case management, cohorts, accelerated remedial math coursework, childcare, and emergency financial assistance, provided psychosocial support essential to learning and development, which in turn resulted in extraordinary success in remedial math completion. The conclusion drawn from the findings is that effective psychosocial support is essential to achieving exceptional remedial math success rates. / text

Motivée par des applications en géophysique et ingénierie sismique, cette thèse cherche à contribuer à l'étude de phénomènes de propagation d'ondes en milieux élastiques non bornés. Nous développons des techniques mathématiques et numériques pour résoudre des problèmes de diffraction en régime harmonique, dans des domaines infinis extérieurs et demi-infinis localement perturbés. En plus, nous introduisons une nouvelle condition aux limites du type impédance en élasticité, laquelle généralise la condition de frontière libre utilisée d'habitude pour décrire la surface de la terre en problèmes géophysiques. Les ondes de surface qui apparaissent avec cette condition aux limites sont étudiées. Nous montrons l'existence de l'onde de Rayleigh et comment elle dépend de l'impédance. En plus, nous prouvons qu'il apparaît une onde de surface additionnelle dans un cas particulière. Pour traiter numériquement les domaines non bornés, nous considérons des approches basées sur des conditions aux limites exactes et des méthodes d'équations intégrales de frontière. Les premières s'appliquent à des domaines extérieurs, pendant que les deuxièmes s'emploient pour les deux types de domaine. Un accent particulier est mis sur les équations intégrales et les méthodes d'éléments de frontière pour résoudre des problèmes de diffraction dans des demi-plans localement perturbés. Nous calculons de manière efficace et précise la fonction de Green d'un demi-plan élastique avec des conditions aux limites d'impédance, à l'aide d'une méthode de calcul qui combine de façon appropriée des techniques analytiques et numériques. Nous proposons aussi une méthode d'équations intégrales de frontière basée sur la fonction de Green calculée. Finalement, les procédures numériques sont validées en utilisant des problèmes benchmark appropriés.

For any graph parameter, the removal of a vertex from a graph can increase the parameter, decrease the parameter, or leave the parameter unchanged. This dissertation focuses on the case where the removal of a vertex decreases the parameter for the cases of independent domination and total domination. A graph is said to be independent domination vertex-critical, or i-critical, if the removal of any vertex decreases the independent domination number. Likewise, a graph is said to be total domination vertex-critical if the removal of any vertex decreases the total domination number. Following these notions, a graph is independent domination bicritical, or i-bicritical, if the removal of any two vertices decreases the independent domination number, and a graph is total domination bicritical if the removal of any two vertices decreases the total domination number. Additionally, a graph is called strong independent domination bicritical, or strong i-bicritical, if the removal of any two independent vertices decreases the independent domination number by two. Construction results for i-critical graphs, i-bicritical graphs, strong i-bicritical graphs, total domination critical graphs, and total domination bicritical graphs are studied. Many known constructions are extended to provide necessary and sufficient conditions to build critical and bicritical graphs. New constructions are also presented, with a concentration on i-critical graphs. One particular construction shows that for any graph G, there exists an i-critical, i-bicritical, and strong i-bicritical graph H such that G is an induced subgraph of H. Structural properties of i-critical graphs, i-bicritical graphs, total domination critical graphs, and total domination bicritical graphs are investigated, particularly for the connectedness and edge-connectedness of critical and bicritical graphs. The coalescence construction, which has appeared in earlier literature, constructs a graph with a cut-vertex and this construction is studied in great detail for i-critical graphs, i-bicritical graphs, total domination critical graphs, and total domination bicritical graphs. It is also shown that strong i-bicritical graphs are 2-connected and thus the coalescence construction is not useful in this case. Domination vertex-critical graphs (graphs where the removal of any vertex decreases the domination number) have been studied in the literature. A well-known result gives an upper bound on the diameter of such graphs. Here similar techniques are used to provide upper bounds on the diameter for i-critical graphs, strong i-bicritical graphs, and total domination critical graphs. The upper bound for the diameter of i-critical graphs trivially gives an upper bound for the diameter of i-bicritical graphs. For a graph G, the gamma-graph of G is the graph where the vertex set is the collection of minimum dominating sets of G. Adjacency between two minimum dominating sets in the gamma-graph occurs if from one minimum dominating set a vertex can be removed and replaced with a vertex to arrive at the other minimum dominating set. One can think of adjacency between minimum dominating sets in the gamma-graph as a swap of two vertices between minimum dominating sets. In the single vertex replacement adjacency model these two vertices can be any vertices in the minimum dominating sets, and in the slide adjacency model these two vertices must be adjacent in G. (Hence the gamma-graph obtained from the slide adjacency model is a subgraph of the gamma-graph obtained in the single vertex replacement adjacency model.) Results for both adjacency models are presented concerning the maximum degree, the diameter, and the order of the gamma-graph when G is a tree. / Graduate / 0405 / michaedwards@gmail.com

Graphics calculators have become an integral part of many introductory college mathematics courses. There has been little research to show the effects of introducing technology, along with an emphasis on the interrelationships of the numeric, symbolic, graphical, and verbal forms of functions, for courses that are traditionally considered pre-college mathematics. The major purpose of this study was to determine if changes in mathematics anxiety and attitudes occurred in Intermediate Algebra classes and to determine whether these changes were dependent on age, gender of student, and experience of instructor. The relationship between beginning levels of math anxiety and successful completion of the class were also examined.All sections of Intermediate Algebra taught at Grand Valley State University during the Winter semester of 1995 participated in the study. The first week of class, 479 students completed the initial survey. The final week of class, 264 of those students completed the survey again. In addition to gender and age of student, the survey instrumentcontained questions from seven of the Fennema-Sherman Mathematics Attitudes Scales. Each scale contained 12 questions, answered on a five point Likert type scale. High scores on the questionnaire indicated a positive attitude. Students in four sections were asked open ended questions every other week. At the end of the semester, instructors were given a questionnaire to determine their perceptions of how student's attitudes and anxieties changed.MANOVA for repeated measures using SPSS was used to perform the analyses with respect to age, gender, and teacher experience, over time. Faculty responses indicated they thought attitudes and levels of math anxiety improved over the semester. Although most groups did show some improvement, no significant change occurred. The only statistically significant differences detected were in math anxiety by gender and a combination of math anxiety and attitude by age. Females had higher levels of math anxiety (N = 166, initial M = 29.96, final M = 30.80) than males (N =.98, initial M = 33.87, final M = 34.79)and while older students appeared more math anxious, they also reflected a more positive attitude about mathematics. / Department of Educational Leadership

Math skills are critical for future success in school (Eccles, 1997), as school-entry math knowledge is the strongest predictor of later academic achievement (Claessens, Duncan, & Engel, 2009). Researchers have found that teachers of young children spend less time teaching mathematics than other subject areas (Phillips & Meloy, 2012), and there is a lack of formal early mathematics instruction for young children’s understanding of early numeracy (Chard et al., 2008). However, preschoolers are developmentally ready for mathematics and are more able to learn math concepts than previously believed (Balfanz, Ginsburg, & Greenes, 2003). While there is a recent increase of literature on math with young children, there is a scarcity of research related to young children with disabilities in the field of mathematics, particularly utilizing evidence based interventions. The current study investigates one intervention integrating mathematics within children’s literature for preschoolers with disabilities. This study was a quasi-experimental group design, with one treatment group and one comparison group (N = 50 participants). Targeted early numeracy skills included: (1) one-to-one correspondence, (2) quantity comparison, and (3) numeral identification. The 20-minute intervention was conducted three days per week for six weeks; the comparison group received a typical small group storybook reading of the same literature book with no elaborations. The Test of Early Mathematics Ability, Third Edition (TEMA-3; Ginsburg & Baroody, 2003) was used as a pre and post standardized assessment, and analyzed using one-way ANCOVAs controlling for pretest scores. The Preschool Numeracy Indicators (PNI; Floyd, Hojnoski, & Key, 2006) was used as a weekly curriculum based measurement and analyzed by one-way ANCOVAS and by individual and group means for descriptive data. After the intervention, the children in the treatment group scored significantly higher in the areas of total math ability, quantity comparison, and one-to-one counting fluency than the comparison group. Implications include possibilities for further integrating mathematics within literature for preschoolers with disabilities, the benefits of intentional storybook selection for this type of intervention, and the recognition of the importance of introducing mathematical topics to preschoolers with disabilities in order of developmental cognitive readiness.