This thesis consists of seven chapters. Chapter 1 is an introduction to the infinite products. Here we provide a proof for representing sine function as an infinite product. This chapter also describes the notation used throughout the thesis as well as the method used to prove the identities. Each of the other chapters may be read independently, however some chapters assume familiarity with the Jacobi triple product identity. Chapter 2 is about the Jacobi triple product identity as well as several implications of this identity. In Chapter 3 the quintuple product identity and some of its special cases are derived. Even though there are many known proofs of this identity since 1916 when it was first discovered, the proof presented in this chapter is new. Some beautiful formulas in number theory are derived at the end of this chapter. The simplest two dimensional example of the Macdonald identity, A2, is investigated in full detail in Chapter 4. Ian Macdonald first outlined the proof for this identity in 1972 but omitted many of the details hence making his work hard to follow. In Chapters 5 and 6 we somewhat deviate from the method which uses the two specializations to evaluate the constant term and prove Winquist's identity and Macdonald's identity for G2. Some of the work involved in proving G2 identity is new. Finally in Chapter 7 we discuss the work presented with some concluding remarks as well as underlining the possibilities for the future research. Throughout the thesis we point to the relevant papers in this area which might provide different strategies for proving above identities.

Firms invested numerous resources in enhancing brand equity. The overall efforts in enhancing design, researching, manufacturing, marketing mix, quality, customer satisfaction, etc are all necessary conditions needed for a firm to enhance its brand equity. Among them, enhancing product identity is one of the ways available. Firms have been developing corporate identity systems (CIS) for years, yet beyond distinctive shop signs, trademarks and layouts, they could spend efforts on products. Firms could develop products with high identity, and use them on enhancing their own brand popularity. If combined with other advantages possessed by a firm, the brand equity must thus be further enhanced. This is the key issue when Taiwan¡¦s industries are trying to transform into OBM. This thesis served ³¯°ê²»¡¦s (1995) six dimensions on product styles as the basis, and tried to verify the hypothesis that Apple¡¦s series products possess high identity. This research also examined the relation between customer satisfaction and product identity. In addition, this study added the marketing mix, user and using conditions as variables in order to understand the comments of Apple¡¦s users (consumers) on Apple¡¦s series products. This study also conducted questionnaire surveys with aforementioned dimensions, participated in Apple users¡¦ gatherings and interviewed employees in Apple¡¦s channels in Tainan and Kaohsiung. The outcomes indicate that high identity is found on the exterior of Apple¡¦s products, and high satisfactions are found regardless of user and using condition. On marketing mix, however, results are indicating that the satisfactions of Apple¡¦s marketing mix are generally low, yet high scores are still documented on dimensions of Apple¡¦s brand equity. This research discovered that product identity dimension and marketing mix dimension bear positive relations with brand equity, and the customer satisfaction was performed as a mediating factor. Insignificant loadings are found on the user and using condition factors.

This study mainly investigates the roles of product design and advertising in conferring identity related meanings upon products and associating them with certain consumer identities. For this purpose, firstly, the concept of identity and increasing centrality of objects in its construction and expression are explored. Secondly, the nature and dynamics of the relationship between people and objects are discussed with a specific emphasis on the identity related aspects of this relationship. Then, a more detailed discussion is held on the roles played by product design and advertising in the process of identity construction through designed products. Finally, a case study on a selected product group is presented in order to illustrate the theoretical discussions in previous chapters.

The basic notion of this study is related with visual attributes of products which reflect the identity of the company as well as form and design consistency which is a factor forming corporate identity. The sub-notions of the topic are elaborated in the literature review. The efforts which aimed at finding out the distinguishing characteristics of products focused on certain sample products. Digital camera is selected for the field study. The objective of the study is to put evidence that firms can be distinguished from each other with the help of visual attributes of their products and to determine which factors are effective throughout this process.