Quantum Lefschetz Hyperplane Theorem

The mirror theorem is generalized to any smooth projective variety X. That is, a fundamental relation between the Gromov-Witten invariants of X and Gromov-Witten invariants of complete intersections Y in X is established

An Empirical Study: Evaluating the Impact of Economic, Human Resource, and Governance Factors to Foreign Direct Investment

The economic crisis in 2008 prompted the restructuring of the world economic and trade patterns. The global supply chain began to restructure, and international investment presented more diversified features. The COVID-19 Pandemic brings a new global economic crisis. which is likely to negatively impact many businesses that rely heavily on the Chinese market. Quarantine policies have forced people to stay at home, reducing public connectivity and leading to a slowdown in economic growth. The outbreak has also caused companies and factories to pause operations, affecting trade, travel, and consumption. International investors are increasingly concerned about economic uncertainties, which highlights the need to understand future trade potentials for foreign direct investment (FDI).This research aims to assess perceptions of the relative importance of economic, human resource and governance factors that increase attracting of FDI at the national level. I collect panel data with 4,761 observations cross 207 countries from 1996-2018, using FDI as dependent variable (DV) and three domain vectors of independent variables (IVs): Economic, human resource and governance. In this paper, using Pooled OLS and Fixed Effect (FE), leveraging the outcome of Hausman test to support the decision of choosing Fixed Effect as the appropriate model specification to my designed framework. The goal of this research is to explore the relationship among FDI, economic, human resource and governance factors. The result from the study demonstrates economic variables are the most crucial factor with positive impact on FDI. Next, export as one of the most influential variables cross all models, illustrates the importance of trade activities can promote foreign investment flow in global markets. Moreover, economic size is also another key factor that has a positive impact on FDI. There are a few data limitations which prevented the ability to expand observation period and sampling nations. First, I experience minor challenges for independent variables governance and RPC data collection which lead to choose this research to focus with data from 1996 to 2018 to avoid unbalanced panel data. Second, due to data availability I am unable to include other countries that may also have positive contribution to the study. One of the countries of interest I would like to include for future extension research is Taiwan, with its high involvement in export especially in high-technology and manufacturing sectors, adding Taiwan into the model may better support us to calibrate research validity for Asian region

Study of gossamer superconductivity and antiferromagnetism in the t-J-U model

The d-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean field theory for a two dimensional t-J model plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing the $U$ term is to partially impose the no double occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\delta$ and $U$ are studied. Using the standard value of $t/J=3.0$ and in the large $U$ limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\delta\sim0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\delta\sim0.15$. In the small $U$ limit, only the dSC order survives while the AF order disappears. As $U$ increased to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half filing, the system is in the dSC state for small $U$ and becomes an AF insulator for large $U$. Within the present mean field approach, We show that the ground state energy of the coexistent state is always lower than that of the pure dSC state.Comment: 7 pages, 8 figure