The main goal of this Masters' thesis is to explore isomorphism types of quaternion algebras using the theory of quadratic forms, number theory and algebra. I would also present ways to characterize quaternion algebras, and talk about how quaternion algebras are important in Brauer groups by describing a theorem proved by Merkurjev in 1981.

We consider the convex parametric quadratic programming problem when the end of the parametric interval is caused by a multiplicity of possibilities ("ties"). In such cases, there is no clear way for the proper active set to be determined for the parametric analysis to continue. In this thesis, we show that the proper active set may be determined in general by solving a certain non-parametric quadratic programming problem. We simplify the parametric quadratic programming problem with a parameter both in the linear part of the objective function and in the right-hand side of the constraints to a quadratic programming without a parameter. We break the analysis into three parts. We first study the parametric quadratic programming problem with a parameter only in the linear part of the objective function, and then a parameter only in the right-hand side of the constraints. Each of these special cases is transformed into a quadratic programming problem having no parameters. A similar approach is then applied to the parametric quadratic programming problem having a parameter both in the linear part of the objective function and in the right-hand side of the constraints.

The main goal of this Masters' thesis is to explore isomorphism types of quaternion algebras using the theory of quadratic forms, number theory and algebra. I would also present ways to characterize quaternion algebras, and talk about how quaternion algebras are important in Brauer groups by describing a theorem proved by Merkurjev in 1981.

This report explores several geometric representations of quadratic equations and their solutions. Topics discussed include applications of geometry relating to solving quadratic equations using graphs and constructions as well as deriving compatible pairs of equations from Pythagorean triples. A brief discussion on the inclusion of advanced graphing methods and constructions into a secondary mathematics class is also included. / text

No description available.

Thesis (Ph. D.)--Carleton University, 1992. / Also available in electronic format on the Internet.

Thesis (Ph. D.)--University of Washington, 1986. / Vita. Bibliography: leaves [164]-168.

Τα βασικά ερωτήματα που καλύπτονται στη διπλωματική αυτή είναι κατά πόσο ένα δυναμικό σύστημα είναι γραμμικό ή μη γραμμικό, και για την περίπτωση της μη γραμμικότητας, να κατανοηθεί τι σημαίνει να απέχει πολύ ή λίγο από τη γραμμικότητα. Επιπλέον, στην περίπτωση που μπορούμε να γραμμικοποιήσουμε ένα μοντέλο, κατά πόσο αυτό είναι καλό ή κακό, προκειμένου να προχωρήσουμε στο σχεδιασμό ενός ελεγκτή για να πετύχουμε την επιθυμητή συμπεριφορά. Σχετικά με το σχεδιασμό του ελεγκτή, εξετάζονται διάφορα παραδείγματα μη γραμμικών συστημάτων με τον LQR και LQG και γίνονται συγκρίσεις όσον αφορά το αποτέλεσμα ελέγχου σε αυτές. / The subject of this thesis is nonlinear systems; Given a dynamic system we examine whether it is nonlinear or not, and in the case of non-linearity, how highly nonlinear the system is. It also checks the linearization of nonlinear systems and how close the linearized model is to the original, in order to proceed to the design of a control scheme based on the linear model. LQR and LQG control schemes were implemented and compared on the initial nonlinear model.

No description available.

For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields.