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Department of Creative Design EngineeringToday, the online market is showing an increasing growth. One of the characteristics of the online market is that it is so dependent on the visual aspect that, the appearance is more influential to the consumer. Another is that the same products are being sold across countries. Considering customers are not identical in terms of user characteristics, it may not be ideal to sell a product in one form. Therefore, the study attempted to find out how the form is differently perceived according to user characteristics such as culture, age, and gender. In order to identify the cultural characteristic in form preference, three countries, the United States, South Korea, and Germany were selected, that represents North America, Asia, and Europe respectively and have distinctive characteristics according to, the Hofstede cultural dimension. An online survey was also conducted with 177 online shoppers whose 27 and 53 years old: 50 Americans(25 males and 25 females), 77 South Koreans (29 males and 48 females), and German( 25 males and 25 females). Three types of form were defined according to the relations between function and use context: stereotypical form, appearance metaphorical form, and context-driven metaphorical form. Among, 20 consumer products having the three types of form and at the same time being sold in the online market, five product types (pencil sharpener, ladle, luggage tag, chopstick rest, and knife sharpener) were finally chosen by using four designer???s intercoder reliability as stimuli for the survey. The products were further classified into two categories regarding culture: the culturally dependent product and culturally independent product. A pair comparison method was adopted in which the 15 product images were pairwise compared to find out which form is preferred and in which way it is perceived in terms of user experience. The overall finding indicates that context-driven metaphorical form was most preferred regardless of cultural background. The reason behind was that context-driven metaphorical form is perceived as aesthetically pleasing. However, perceived experiences varied between countries. Germany preferred more in functional form, South Korean was more in form delivering more personal value, and Americans preferred form related more to functional and personal value. However, Stereotypical product as a most functional product has no objection from three countries. Even with this result, the functional experience did not lead to the purchasing product in online shopping. Also, the overall preferred product seems to have aesthetic and value experience almost identical. Demographic variables such as age and gender have no influence in form preference. From the findings are considered in design-driven marketing for a particular cultural group, it would help more competitive in the online market.ope

Arithmetic of the moduli of hyperelliptic curves and principally polarized Abelian surfaces over global fields

We use geometric methods to establish an upper bound for counting stable hyperelliptic curves with a marked Weierstrass section ordered by height of discriminant at most $\mathcal{B}$ over $\mathbb{P}^{1}_{\mathbb{F}_q}$ with characteristic $p > 2g+1$; the acquired estimate is of order $\mathcal{O}_q\left( \mathcal{B}^{\frac{2g+3}{4g+2}} \right)$. We sharpen the estimate for each genus $g \ge 2$; specifically when $g=2$, this renders an estimate on the number of principally polarized Abelian surfaces over $\mathbb{F}_q(t)$. Through the global fields analogy, we formulate analogous new heuristics for counting stable hyperelliptic curves with a marked rational Weierstrass point or principally polarized Abelian surfaces over $\mathbb{Q}$. In Appendix, we determine the sharp estimate for counting elliptic curves with prescribed level structures or multiple marked points over $\mathbb{P}^{1}_{\mathbb{F}_q}$.Comment: 35 pages. The paper has been substantially reorganized throughout with a significantly improved Introduction. The Appendix (reinforced by Changho Han) has been integrated from arXiv:2002.06527. Comments welcome

Height moduli on cyclotomic stacks and counting elliptic curves over function fields

For proper stacks, unlike schemes, there is a distinction between rational and integral points; we show that this distinction exactly accounts for the main term and lower order terms appearing in counts of elliptic curves over function fields. More generally, using the theory of twisted stable maps and the stacky height functions recently introduced by Ellenberg, Zureick-Brown, and the third author, we construct finite type moduli spaces which parametrize rational points of fixed height on a large class of stacks, so-called cyclotomic stacks. As a by product, we obtain the Northcott property as well as a generalization of Tate's algorithm for cyclotomic stacks, and propose an answer to a question of Venkatesh.Comment: 56 pages, comments welcomed

Arithmetic of the moduli of fibered algebraic surfaces with heuristics for counting curves over global fields

University of Minnesota Ph.D. dissertation. May 2018. Major: Mathematics. Advisor: Craig Westerland. 1 computer file (PDF);vi, 61 pages.The classical theory of algebraic surfaces is essential in both geometry and number theory. The study of fibrations lies at the heart of the Enriques-Kodaira classification of compact complex surfaces as well as the Mumford-Bombieri classification of algebraic surfaces in positive characteristic. In my work, I consider the moduli of fibered algebraic surfaces through the moduli of fibrations and produce its arithmetic invariants of motivic nature with the aspiration of finding relevant applications to number theory under the global fields analogy