Cheung Wing-chuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 80-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction to CR manifolds --- p.6 / Chapter 1.1 --- Non-equivalence of real analytic hypersurfaces in C2 --- p.6 / Chapter 1.2 --- CR manifold and Levi form --- p.9 / Chapter 1.3 --- The real hyperquadrics --- p.16 / Chapter 2 --- Normal Forms --- p.22 / Chapter 2.1 --- Formal theory of normal forms --- p.22 / Chapter 2.2 --- Geometric theory of normal forms --- p.33 / Chapter 3 --- Connections and Curvatures --- p.45 / Chapter 3.1 --- Solution of the equivalence problem --- p.45 / Chapter 3.2 --- Geometric interpretation of the solution --- p.59 / Chapter 4 --- Chains --- p.65 / Chapter 4.1 --- Identification of the two definitions of chains --- p.65 / Chapter 4.2 --- Chain-preserving maps --- p.73 / Chapter 4.3 --- Some pathological behaviour of chains --- p.76 / Bibliography --- p.80

The development of technology has made the world a smaller place where communicating instantaneously irrespective of the geographical location is a way of life. Electronic Forms (E-FORMS) are an easy way to communicate efficiently with students. At present, universities are still using old systems for communication where efforts to improve the system is a lethargic process. As most of these universities are still using student forms manually, the introduction of E-FORMS will speed up the whole process and positively impact in communicating efficiency. In addition, the inconvenience of making numerous visits to the university is sometimes seen as a hassle but due to lack of Information Technology (IT) development in universities, this is the usual pattern still seen at most universities. In this study, the use of E-FORMS at universities is proposed to help students and university staff to communicate effectively and efficiently. As it is still a fairly new concept, the study proposes the many features involved in E-FORMS communication. The Researcher has chosen California State University San Bernardino (CSUSB) to do this study. This study consists of the detailed design of the proposed E-FORMS Application System at CSUSB. The design provides a more efficient and supportive system that is easy to use while maintaining student privacy and flexibility. The solution is designed taking into consideration the use of PeopleSoft Enterprise. This proposed system upgrades the existing CSUSB form management system. It is a step forward to a more efficient and the operative system.

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.

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.

No description available.

Thesis--Bonn. Extra t.p. with thesis statement inserted. / Includes bibliographical references (p. 45).

Thesis (Ph. D.)--University of Chicago, 1921. / Published also without thesis note.

Thesis--M.A., University of Hong Kong. / Typescript.

No description available.

Let S2k(N) be the space of cusp forms of weight 2k and level N. Atkin-Lehner theory shows that S2k(N) can be decomposed into the oldspace and its orthogonal complement newspace. Again, from Atkin-Lehner theory, it follows that there exists a basis of newspace whose elements are simultaneous eigenforms of all the Hecke operators. Such eigenforms when normalized are called primitive forms. In 1932, Petersson introduced a harmonic weighted sum of the Fourier coefficients of an orthogonal basis B2k(N) for S2k(N), denoted by _2k;N . Petersson connected _2k;N to Kloosterman sums and Bessel functions, which is now known as the Petersson trace formula. The Petersson trace formula shows that _2k;N is independent of the choice of orthogonal basis. It is known that the oldspace decomposes into the images of newspaces of different levels under the scaling operator Bd where d is a proper divisor of N. It is of interest to derive a Petersson-type trace formula for primitive forms. In 2001, H. Iwaniec, W. Luo and P. Sarnak obtained an expression of Petersson-type trace formula for primitive forms in terms of _2k;N , when the level N is squarefree. Their method is to construct a special orthogonal basis for S2k(N). Using their approach, D. Rouymi has extended similar results to the case of prime power level in 2011. In this thesis, the case of arbitrary levels is investigated. Analogously, a special orthogonal basis is constructed and a Petersson-type trace formula for primitive forms in terms of _2k;N is found. The result established in this thesis recovers the results of H. Iwaniec, W. Luo and P. Sarnak, and D. Rouymi respectively for the cases of squarefree and prime power levels. / published_or_final_version / Mathematics / Master / Master of Philosophy