On Area-preserving and Length-preserving Nonlocal Flow of Convex Closed Plane Curves

For any $\alpha>0,$ we study $k^{\alpha}$-type length-preserving and area-preserving nonlocal flow of convex closed plane curves and show that these two types of flow evolve such curves into round circles in $C^{\infty}$-norm.$\$Other relevant $k^{\alpha}$-type nonlocal flow is also discussed when $\alpha\geq1.\$Comment: Published in 'Calculus of Variations and Partial Differential Equations

Improving Accuracy of Virtual Machine Power Model by Relative-PMC Based Heuristic Scheduling

Conventional utilization-based power model is effective for measuring the power consumption of physical machines. However, in virtualized environments its accuracy cannot be guaranteed because of the recursive resource accessing among multiple virtual machines. In this paper, we present a novel virtual machine scheduling algorithm, which uses Performance-Monitor-Counter as heuristic information to compensate the recursive power consumption. Theoretical analysis indicates that the error of virtual machine power model can be quantitative bounded when using the proposed scheduling algorithm. Extensive experiments based on standard benchmarks show that the error of virtual machine power measurements can be significantly reduced comparing with the classic credit-based scheduling algorithm

Low-mass Active Galactic Nuclei on the Fundamental Plane of Black Hole Activity

It is widely known that in active galactic nuclei (AGNs) and black hole X-ray binaries (BHXBs), there is a tight correlation among their radio luminosity ($L_R$), X-ray luminosity ($L_X$) and BH mass (\mbh), the so-called `fundamental plane' (FP) of BH activity. Yet the supporting data are very limited in the \mbh regime between stellar mass (i.e., BHXBs) and 10$^{6.5}$\,\msun\ (namely, the lower bound of supermassive BHs in common AGNs). In this work, we developed a new method to measure the 1.4 GHz flux directly from the images of the VLA FIRST survey, and apply it to the type-1 low-mass AGNs in the \cite{2012ApJ...755..167D} sample. As a result, we obtained 19 new low-mass AGNs for FP research with both \mbh\ estimates (\mbh \approx 10^{5.5-6.5}\,\msun), reliable X-ray measurements, and (candidate) radio detections, tripling the number of such candidate sources in the literature.Most (if not all) of the low-mass AGNs follow the standard radio/X-ray correlation and the universal FP relation fitted with the combined dataset of BHXBs and supermassive AGNs by \citet{2009ApJ...706..404G}; the consistency in the radio/X-ray correlation slope among those accretion systems supports the picture that the accretion and ejection (jet) processes are quite similar in all accretion systems of different \mbh. In view of the FP relation, we speculate that the radio loudness $\mathcal{R}$ (i.e., the luminosity ratio of the jet to the accretion disk) of AGNs depends not only on Eddington ratio, but probably also on \mbh.Comment: ApJ accepte