A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy...A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.展开更多
We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brick-wall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bek...We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brick-wall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bekenstein-Hawking＇s area-entropy formula. Then, by comparing with the original brick-wall method, we find that the result obtained by the thin film method is more reasonable avoiding some drawbacks, such as little mass approximation, neglecting logarithm term, and taking the term L^3 as a contribution of the vacuum surrounding the black hole, and the physical meaning of the entropy is more clearer.展开更多
The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predic...The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predict the droplet size distribution. This paper presents a new sub-model based on the deterministic aspects of liquid atomization process independent of the experimental data to provide the mean droplets diameter for using in the maximum entropy formulation(MEF). For this purpose, a theoretical model based on the approach of energy conservation law entitled energy-based model(EBM) is presented. Based on this approach, atomization occurs due to the kinetic energy loss. Prediction of the combined model(MEF/EBM) is in good agreement with the available experimental data. The energy-based model can be used as a fast and reliable enough model to obtain a good estimation of the mean droplets diameter of a spray and the combined model(MEF/EBM) can be used to well predict the droplet size distribution at the primary breakup.展开更多
With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann Robertson-Walker universe for the deformed Hofava-Lifshitz gravity. It is shown that, when the parameter ...With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann Robertson-Walker universe for the deformed Hofava-Lifshitz gravity. It is shown that, when the parameter of Hofava-Lifshitz gravity ω →∞, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Hofava-Lifshitz gravity.展开更多
Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorte...Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorted for this purpose. This article addresses solution of the Stefan-Maxwell equation in binary gas systems and explores the necessary conditions for definite solution of concentration profiles and pertinent component fluxes. It is found that there are multiple solutions for component fluxes in contradiction to what specified by the Graham's law of diffusion.The theorem of minimum entropy production in the non-equilibrium thermodynamics is believed instructive in determining the stable steady state solution out of infinite multiple solutions possible under the specified conditions.It is suggested that only when the boundary condition of component concentration is symmetrical in an isothermal binary system, the counter-diffusion becomes equimolar. The Graham's law of diffusion seems not generally valid for the case of isothermal ordinary diffusion.展开更多
文摘A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.
基金Supported by the National Natural Science Foundation of China under Grant No.10573004
文摘We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brick-wall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bekenstein-Hawking＇s area-entropy formula. Then, by comparing with the original brick-wall method, we find that the result obtained by the thin film method is more reasonable avoiding some drawbacks, such as little mass approximation, neglecting logarithm term, and taking the term L^3 as a contribution of the vacuum surrounding the black hole, and the physical meaning of the entropy is more clearer.
文摘The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predict the droplet size distribution. This paper presents a new sub-model based on the deterministic aspects of liquid atomization process independent of the experimental data to provide the mean droplets diameter for using in the maximum entropy formulation(MEF). For this purpose, a theoretical model based on the approach of energy conservation law entitled energy-based model(EBM) is presented. Based on this approach, atomization occurs due to the kinetic energy loss. Prediction of the combined model(MEF/EBM) is in good agreement with the available experimental data. The energy-based model can be used as a fast and reliable enough model to obtain a good estimation of the mean droplets diameter of a spray and the combined model(MEF/EBM) can be used to well predict the droplet size distribution at the primary breakup.
基金Supported by the Program for New Century Excellent Talents in Universitythe National Natural Science Foundation of China under Grant No. 11075065+1 种基金the Fundamental Research Funds for the Central Universities under Grant Nos. lzujbky-2009-54, lzujbky-2009-163, and lzujbky-2009-122the Fundamental Research Fund for Physics and Mathematics of Lanzhou University under Grant No. LZULL200912
文摘With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann Robertson-Walker universe for the deformed Hofava-Lifshitz gravity. It is shown that, when the parameter of Hofava-Lifshitz gravity ω →∞, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Hofava-Lifshitz gravity.
基金Supported by the National Natural Science Foundation of China(No.29792074)and SINOPEC.
文摘Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorted for this purpose. This article addresses solution of the Stefan-Maxwell equation in binary gas systems and explores the necessary conditions for definite solution of concentration profiles and pertinent component fluxes. It is found that there are multiple solutions for component fluxes in contradiction to what specified by the Graham's law of diffusion.The theorem of minimum entropy production in the non-equilibrium thermodynamics is believed instructive in determining the stable steady state solution out of infinite multiple solutions possible under the specified conditions.It is suggested that only when the boundary condition of component concentration is symmetrical in an isothermal binary system, the counter-diffusion becomes equimolar. The Graham's law of diffusion seems not generally valid for the case of isothermal ordinary diffusion.
