Sharp results for spherical metric on flat tori with conical angle 6π\pi at two symmetric points

A conjecture about the existence or nonexistence of solutions to the curvature equation (1.1) defined on a rectangle torus $E_{\tau},$ $\tau\in i\mathbb{R}_{>0}$ with four conical singularties at its symmetric points is proposed in [3]. See Conjecture 1. For the purposes to understand this problem, in this paper, we study the following equation: \Delta u+e^{u}=8\pi(\delta_{0}+\delta_{\frac{\omega_{k}}{2}})\text{in}E_{\tau}\,\tau\in\mathbb{H}\, \label{a} where $\frac{\omega_{k}}{2}$ is one of the half periods of $E_{\tau}$, i.e., the case $(m_{0},m_{1},$ $m_{2},m_{3})$ $=(1,1,0,0)$, $(1,0,1,0)$, $(1,0,0,1)$ for $k=1,2,3,$ respectively. Among others, we prove that the existence of \textit{non-even family of solutions} (see the definition in Section 1 ) is related to the existence of solutions for the equation with single conical singularity: $$\Delta u+e^{u}=8\pi\delta_{0}\text{ in }E_{\tau}\text{, }\tau\in \mathbb{H}\text{.}$$ Consequently, equation (0.1) does not have any non-even family of solutions for all $k=1,2,3$. As an application, we completely understand the solution structure of the equation (0.1) for rectangle torus and give a confirmative answer for this conjecture in this three cases. See Theorem 1.3

The effects of social responsibility on company value: a real options perspective of Taiwan companies

Corporate social responsibility (CSR) is a subject that has garnered considerable attention in recent years. This study conducts the empirical study by using a real options perspective to examine whether a company’s CSR commitment tends to increase its market value. According to Taiwan’s CommonWealth Magazine, this study distinguishes CSR and non-CSR companies. The paper estimates and compares the real options values of CSR and non-CSR companies and shows that high percentage of the company value is attributed to real options. This study finds that a company’s commitment to fulfilling its social responsibility increases its real options value and that the higher the number of CSR Awards won by a company, the higher its real options value. Compared with 10 years ago, investors now pay more attention to companies’ CSR performance. In addition, the higher a company’s size, systematic risk, fixed asset ratio, debt ratio, or skewness in stock returns, the higher a real options value is likely to be

Acculturation of International Student In Hawaiʻi: Case Of The East-West Center

M.A.M.A. Thesis. University of Hawaiʻi at Mānoa 201

Application of Spatial Bayesian Hierarchical Models to fMRI Data

Bayesian modelling has attracted great interest in cognitive science and offered a flexible and interpretable way to study cognitive processes using functional magnetic resonance imaging data. In this chapter, a spatial Bayesian hierarchical model is applied to an event-related fMRI study of cognitive control using the Simon test. We consider a sparse spatial generalized linear mixed-effects model to capture the spatial dependence among activated voxels and temporal parameters and to benefit computationally by reducing dimensionality. We demonstrate that the proposed model has the capability of identification of the brain areas related to cognitive tasks. Moreover, the reduction in the false positive rate is observed in the simulation study, and the relevant brain regions involved in processing cognitive control are clearly detected in a real-life fMRI example