Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow

We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the $\varepsilon$-Ricci flow on a closed surface. These new Harnack inequalities extend the previous differential Harnack inequalities for linear heat equations with potentials under the Ricci flow.Comment: 17 pages. New explanations added; Final versio

Two-charged non-extremal rotating black holes in seven-dimensional gauged supergravity: The single-rotation case

We construct the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case with only one rotation parameter and two independent charges. Using the Boyer-Lindquist coordinates, the metric is expressed in a generalized form of the ansatz previously presented in [S.Q. Wu, Phys. Rev. D 83 (2011) 121502(R)], which may be helpful to find the most general non-extremal two-charged rotating black hole with three unequal rotation parameters. The conserved charges for thermodynamics are also computed.Comment: 13 pages, elsarticle.cls, revised version with two typos removed and three references adde

Expander Graph and Communication-Efficient Decentralized Optimization

In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy. We discover that the so-called expander graphs are near-optimal choices. We propose three approaches to construct expander graphs for different numbers of nodes and node degrees. Our numerical results show that the performance of decentralized optimization is significantly better on expander graphs than other regular graphs.Comment: 2016 IEEE Asilomar Conference on Signals, Systems, and Computer

Imitation, local interaction, and efficiency: reappraisal

We revisit the model of Alos-Ferrer and Weidenholzer (2006) but under the assumption that risk-dominant equilibria are Pareto efficient. It is found that risk-dominant equilibria, non-risk-dominant equilibria, and some non-monomorphic states can emerge in the long run when players interact with their immediate neighbors only.Coordination game, imitation, local interaction

Interpolating between constrained Li-Yau and Chow-Hamilton Harnack inequalities for a nonlinear parabolic equation

We establish a one-parameter family of Harnack inequalities connecting the constrained trace Li-Yau differential Harnack inequality for a nonlinear parabolic equation to the constrained trace Chow-Hamilton Harnack inequality for this nonlinear equation with respect to evolving metrics related to Ricci flow on a 2-dimensional closed manifold. This result can be regarded as a nonlinear version of the previous work of Y. Zheng and the author (Arch. Math. 94 (2010), 591-600).Comment: 13 pages; references and explanations adde

The superposition of algebraic solitons for the modified Korteweg-de Vries equation

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Thermal Empirical Equations for Post-Flashover Compartment Fires

10th International Symposium on Fire Safety Science, College Park, MD, 19-24 June 2011Many useful correlation equations derived for estimating the heat release rate are believed to be adequate in fire engineering application. However, heat release rates in deriving those equations were mainly based on estimating mass loss rate of fuel. Flashover in a compartment fire had been studied experimentally on gasoline pool fires with results on heat release rate reported earlier. Transient heat release rates were measured by oxygen consumption calorimetry. The gas temperature curves at different locations in the room were measured instantaneously. Correlation equations on heat release rates with gas temperature reported in the literature will be reviewed and justified with the experimental results. It was observed that heat release rate estimated were lower than the experimental measurement.Department of Building Services EngineeringRefereed conference pape

The influences of various mixed dielectric fluids on the performance electrical discharge machining of AISI D2 hardened steel

This research mainly explores the influence of various mixed dielectric fluids on the performance of electrical discharge machining of AISI D2 hardened steels. In this investigation, four types of dielectric fluids such as pure kerosene, kerosene and chromium powder mixed, kerosene and Span-20 surfactant and the combination of kerosene with chromium powder and Span-20 surfactant were studied. The obtained results illustrated that the addition of chromium powder and Span-20 surfactant in the dielectric fluid obtained high material removal rate, low electrode wear rate and good surface finish. The presence of chromium powder will stabilize the gap distance between electrodes which promotes the occurrence of multiple discharges in one input pulse and particle agglomeration is reduced after Span-20 surfactant molecules cover the surface of debris and carbon dregs in kerosene solution. Combination of kerosene with chromium and Span-20 surfactant were found significant to improve the effects of carbon accumulation and drag discharge, and reduce unstable concentrated discharge

In vivo demonstration of enhancing gas-filled microbubble magnetic susceptibility with iron oxide nanoparticles

Short TE & Susceptibility MRI: No. 698Gas-filled microbubbles have been shown as an MR susceptibility contrast agent; however, microbubble susceptibility effect is relatively weak when compared with other contrast agents. Studies have indicated that, by embedding magnetic nanoparticles, the magnetic susceptibility of the shell can be increased, thus enhancing the microbubble susceptibility effect. In this study, we further demonstrated the synergistic effect of gas core with iron oxide nanoparticles in achieving the overall microbubble susceptibility effect and characterized in vivo enhancements of microbubble susceptibility effects by entrapping iron oxide nanoparticles at 7 T, leading to the practical use of microbubbles as an intravascular MRI contrast agent.postprin