Bishop-Phelps-Bolloba's theorem on bounded closed convex sets

This paper deals with the \emph{Bishop-Phelps-Bollob\'as property} (\emph{BPBp} for short) on bounded closed convex subsets of a Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove that the \emph{BPBp} holds for bounded linear functionals on arbitrary bounded closed convex subsets of a real Banach space. We show that for all finite dimensional Banach spaces $X$ and $Y$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed convex subset $D$ of $X$, and also that for a Banach space $Y$ with property $(\beta)$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of an arbitrary Banach space $X$. For a bounded closed absorbing convex subset $D$ of $X$ with positive modulus convexity we get that the pair $(X,Y)$ has the \emph{BPBp} on $D$ for every Banach space $Y$. We further obtain that for an Asplund space $X$ and for a locally compact Hausdorff $L$, the pair $(X, C_0(L))$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of $X$. Finally we study the stability of the \emph{BPBp} on a bounded closed convex set for the $\ell_1$-sum or $\ell_{\infty}$-sum of a family of Banach spaces

First detection of 22 GHz H2O masers in TX Camelopardalis

Simultaneous time monitoring observations of H$_{2}$O $6_{16}-5_{23}$, SiO $J$ = 1--0, 2--1, 3--2, and $^{29}$SiO $v$ = 0, $J$ = 1--0 lines were carried out in the direction of the Mira variable star TX Cam with the Korean VLBI Network single dish radio telescopes. For the first time, the H$_{2}$O maser emission from TX Cam was detected near the stellar velocity at five epochs from April 10, 2013 ($\phi$ = 3.13) to June 4, 2014 ($\phi$ = 3.89) including minimum optical phases. The intensities of H$_{2}$O masers are very weak compared to SiO masers. The variation of peak antenna temperature ratios among SiO $v$ = 1, $J$ = 1--0, $J$ = 2--1, and $J$ = 3--2 masers is investigated according to their phases. The shift of peak velocities of H$_{2}$O and SiO masers with respect to the stellar velocity is also investigated according to observed optical phases. The H$_{2}$O maser emission occurs around the stellar velocity during our monitoring interval. On the other hand, the peak velocities of SiO masers show a spread compared to the stellar velocity. The peak velocities of SiO $J$ = 2--1, and $J$ = 3--2 masers show a smaller spread with respect to the stellar velocity than those of SiO $J$ = 1--0 masers. These simultaneous observations of multi-frequencies will provide a good constraint for maser pumping models and a good probe for investigating the stellar atmosphere and envelope according to their different excitation conditions.Comment: 10 page

Does Managerial Risk-Taking Incentive for R&D Investments Translate to Future Earnings?

The convex pay-off structure of executive stock options (ESO) incentivizes CEOs to increase their firm stock-return volatility, thereby increasing their wealth in option portfolio. In this paper, I address two research questions. I first test if this managerial incentive induces executives to take on more risky projects in R&D that increases stock- return volatility, hence, boosting their personal wealth. I derive vega to measure managerial incentive, and vega is a dollar change in ESO for a 0.01 change in stock- return volatility. I find that there is a positive and statistically significant relationship between vega and R&D investment, which suggests that managers whose wealth is closely tied to stock options are more incentivized to invest in risky R&D projects to increase their wealth and stock-return volatility. This result is statistically significant and robust after adjusting for inflation and controlling for firm and industry-fixed effects. With this finding, I proceed to test if managerial risk-taking incentive for R&D investments translate to future earnings. Lev and Sougiannis (1996) establish that future earnings is a function of both tangible and intangible assets, and R&D increases with firm’s subsequent earnings. Since R&D spending changes with managerial incentive, I test if the interactive variable of vega and R&D has a positive effect on firm’s future earnings. I find that managerial incentive for undertaking R&D investments has a positive and statistically significant association with future earnings under industry-fixed effects specifications. When controlling for firm-fixed effects, the result yielded similar results to that of industry-fixed effects, but with less statistical significance. Lastly, for robustness check, I run the regression with a balanced panel data of tenured-CEOs, who stay with the firm for five years. I find that the result is positive and statistically significant for industry-fixed effects. However, for firm-fixed effects, I only find statistical significance at year t+k (k=3). This suggests that the realization of R&D investment to future earnings is not prevalent throughout all years when R&D decisions are made by incentivized, long-standing CEOs