The main purpose of this paper is to better understand groups that do not have the unique product property. In particular, the goal is to better understand Promislow's example, G, of such a group. In doing so, we will develop methods for generating examples of other sets that do not have the unique product property. With these methods we can show that there exists other distinct 14 element, square, non-unique product sets in G that are not inversions or translations. Also, this paper answers the question as to whether every non-unique product set can have only 14 elements in the negative by producing a 17 element square n.u.p. set. The secondary purpose of this paper is to demonstrate that in the group ring K[G], there are no units of support size 3. / Master of Science

近年，網路商店如雨後春筍般興起，業者想在網路零售市場佔有一席之地並非易事，此種情況持續惡化是由於業者採用低價競爭策略所致，也使得網路商店之間的差異化程度消失殆盡。「體驗經濟」概念，根據顧客的慾望來營造體驗情境，提供業者一個可作為差異化基礎的思考方向。網路提供了多元的方式營造獨特的購物情境，當消費者沉浸於選購產品的樂趣中且內心需求被充分填滿時，將可提升消費者實際購買產品的可能性。 　　由於網際網路和電腦的普及，女性在資訊科技的使用上和以往相較之下已不致於造成太大困難，調查資料亦顯示女性網路購物群族在近幾年有漸增趨勢；除此，家庭中大部分品項的購物決策落在女性手中。基於上述原因，網路商店若想擴大收益，應重視女性市場的發展潛力。本研究關切的課題為網路商店提供何種體驗才能有效地留住女性顧客。 　　本研究以Schmitt之策略體驗模組作為體驗行銷架構，以產品特性為干擾變數，探討體驗行銷模組和顧客保留強度之間的關係。本研究採用網路問卷調查法蒐集樣本資料，並利用階層多元迴歸分析法來驗證整體架構。研究結果顯示，感官體驗、思考體驗、行動體驗和關聯體驗對顧客保留強度具有正向影響，行動體驗之影響程度較微弱，而情感體驗對顧客保留的效果未被確立。在產品特性對體驗行銷模組和顧客保留強度之間關係的干擾效果部分，風險變數的干擾效果未被確立；努力變數對思考體驗和顧客保留之間的關係具有顯著的干擾效果，且是決定女性消費者是否在網路商店購買產品的最關鍵因素。網路商店業者若想成功留住女性顧客，須營造具有啟發性與充滿新資訊的體驗情境，使女性消費者願意付出更多的努力沉浸於該情境中，進而在心境上自然而然地轉移至購物的決定。 / E-stores are springing up quickly for the past decade, making it increasingly difficult for retailers to survive in the Internet retailing market. The situation is worsened by low-price competitive strategy. To online shoppers, the differences among e-stores are shrinking. Facing this difficulty of differentiating themselves, the concept of Experiential Economy seems to come to the rescue for online retailers, because it suggests creating differentiation through offering experiences according to customer desire. Internet is especially promising in the construction of unique shopping environment without incurring high cost. By satisfying the psychological needs of customers, retailers can expect to differentiate themselves and close more deals. 　　Nowadays the use of Internet is equally popular between males and females. Survey data also showed that female online shoppers have increased in recent years. In addition, studies showed household purchasing decisions are largely undertaken by females. To strengthen their market advantage, retailers should pay more attention to female shoppers. Thus the purpose of this study is to examine which types of online experiences help to retain female customers more effectively. 　　The experiential marketing construct of this study is based on Schmitt’s strategic experiential modules (SEMs). This study empirically examines the effects among the experiential marketing modules, product properties, and customer retention intensity. The results show that SENSE, THINK, ACT and SOCIAL modules have positive effects on customer retention. The effect of the ACT module is confirmed, although much weaker, while the effect of the FEEL module is not confirmed. As for the moderating effects of product properties between the experiential marketing modules and customer retention, the result does not confirm the moderating effect of the risk factor of product properties; however, the effort factor in the product properties has significant moderate effect between the THINK module and customer retention. It is very interesting to discover female customers’ experiential preference that is described in the THINK module, because intuitively male customers, rather than female customers, are perceived to exhibit such preference. To retain female customers, online retailers need to construct an experiential condition which is rich in new information and is appealing to consumers’ creative thinking.

This dissertation reviews the theory of fast matrix multiplication from a multilinear-algebraic point of view, as well as recent fast matrix multiplication algorithms based on discrete Fourier transforms over nite groups. To this end, the algebraic approach is described in terms of group algebras over groups satisfying the triple product Property, and the construction of such groups via uniquely solvable puzzles. The higher order singular value decomposition is an important decomposition of tensors that retains some of the properties of the singular value decomposition of matrices. However, we have proven a novel negative result which demonstrates that the higher order singular value decomposition yields a matrix multiplication algorithm that is no better than the standard algorithm. / Mathematical Sciences / M. Sc. (Applied Mathematics)

This dissertation reviews the theory of fast matrix multiplication from a multilinear-algebraic point of view, as well as recent fast matrix multiplication algorithms based on discrete Fourier transforms over nite groups. To this end, the algebraic approach is described in terms of group algebras over groups satisfying the triple product Property, and the construction of such groups via uniquely solvable puzzles. The higher order singular value decomposition is an important decomposition of tensors that retains some of the properties of the singular value decomposition of matrices. However, we have proven a novel negative result which demonstrates that the higher order singular value decomposition yields a matrix multiplication algorithm that is no better than the standard algorithm. / Mathematical Sciences / M. Sc. (Applied Mathematics)