Extensions of a result of Elekes and R\'onyai

Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing many points of a cartesian product. In 2000, Elekes and R\'onyai proved that if the graph of a polynomial contains $cn^2$ points of an $n\times n\times n$ cartesian product in $\mathbb{R}^3$, then the polynomial has the form $f(x,y)=g(k(x)+l(y))$ or $f(x,y)=g(k(x)l(y))$. They used this to prove a conjecture of Purdy which states that given two lines in $\mathbb{R}^2$ and $n$ points on each line, if the number of distinct distances between pairs of points, one on each line, is at most $cn$, then the lines are parallel or orthogonal. We extend the Elekes-R\'onyai Theorem to a less symmetric cartesian product. We also extend the Elekes-R\'onyai Theorem to one dimension higher on an $n\times n\times n\times n$ cartesian product and an asymmetric cartesian product. We give a proof of a variation of Purdy's conjecture with fewer points on one of the lines. We finish with a lower bound for our main result in one dimension higher with asymmetric cartesian product, showing that it is near-optimal.Comment: 23 page

Firm Productivity and the Foreign-Market Entry Decision

We use Japanese firm-level data to examine how a firm?s productivity affects its choice of foreign-market entry strategy. We study a sequence of decisions, starting with the choice between exporting and foreign direct investment (FDI). In the case of FDI, the firm faces two options: greenfield investment or merger and acquisition (M&A). If it selects greenfield investment, it has two ownership choices: whole ownership or a joint venture. Controlling for industry- and country-specific characteristics, we find that the more productive a firm is, the more likely it is to choose FDI rather than exporting, greenfield investment rather than M&A, and whole ownership rather than a joint venture. We also find that the assumed sequence of decisions fits the data better than alternative specifications. --Foreign direct investment,merger and acquisition,joint venture,greenfield investment,firm heterogeneity,productivity

Effect of Surface Preparation Methods on Mechanical Properties of 3D Structures Fabricated by Stereolithography and 3D Printing for Electroless Ni Plating

Stereolithography (SL) and 3D Printing (3DP) are useful technologies for three-dimensional prototyping applications, providing highly accurate and detailed part geometries with high quality surface finishes. It is desired to improve the materials performance of the existing photocurable SL and 3DP resins for rapid tooling and other functional applications by applying a nickel (Ni) coating. In this work, surface preparation methods for electroless plating of commercial photopolymer resins such as NanoFormTM15120 (NanoForm) and Objet FullCure®840 (Veroblue) were explored in order to enhance the structural integrity of RP components. This study examined different surface preparation methods (chemical etching) and their effect on the surface morphology and mechanical strength of the polymers. It was observed that surface preparation of the resins significantly affected the mechanical properties and Ni plating of the substrate polymers. This is a critical step, since the Ni film takes on the surface structure of the substrate.Mechanical Engineerin

Asset Ownership and Foreign-Market Entry

This paper examines the link between a firm?s owership of productive assets and its choice of foreign-market entry strategy. We find that, controlling for industry- and country-specific characteristics, the most productive firms (i.e., those owning the most assets) will enter through greenfield investment, less productive ones will choose M&A, and the least productive ones will export. In addition, the most productive firms are shown to prefer whole ownership to a joint venture. These predictions are confirmed in an econometric analysis of Japanese firm-level data. --Foreign direct investment,merger and acquisition,joint venture,greenfield investment,firm heterogeneity,productivity

Whole versus Shared Ownership of Foreign Affiliates

This paper studies why multinational firms often share ownership of a foreign affiliate with a local partner even in the absence of government restrictions on ownership. We show that shared ownership may arise, if (i) the partner owns assets that are potentially important for the investment project, and (ii) the value of these assets is private information. In this context shared ownership acts as a screening device. Our model predicts that the multinational?s ownership share is increasing in its productivity, with the most productive multinationals choosing not to rely on a foreign partner at all. This prediction is shown to be consistent with data on the ownership choices of Japanese multinationals. --Foreign direct investment,ownership,joint venture,productivity

The Choice of Market Entry Mode: Greenfield Investment, M&A and Joint Venture

Multinationals may enter a host market by different modes of foreign direct investment (FDI). This paper examines the choice of FDI mode, and shows that the profitability of greenfield investment influences this choice not only directly, but also indirectly since it determines the outside option of potential acquisition targets and joint venture partners. In particular, even if greenfield investment is a viable option, the multinational may prefer a joint venture to M&A, and M&A to greenfield investment, provided that M&A and joint venture both involve sufficiently low fixed costs. The reason is that the profitability of greenfield investment both reduces the acquisition price in the case of M&A, and gives local firms an incentive to agree to a joint venture. --Foreign direct investment,multinational firms,merger and acquisition,joint venture,greenfield investment

Asset Ownership and Foreign-Market Entry

This paper examines the link between a firm’s ownership of productive assets and its choice of foreign-market entry strategy. We find that, controlling for industry- and country-specific characteristics, the most productive firms (i.e., those owning the most assets) will enter through greenfield investment, less productive ones will choose M&A, and the least productive ones will export. In addition, the most productive firms are shown to prefer whole ownership to a joint venture. These predictions are confirmed in an econometric analysis of Japanese firm-level data.foreign direct investment, merger and acquisition, joint venture, greenfield investment, firm heterogeneity, productivity