The transitive property of thermal equilibrium is shown to be equivalent to the transitiveproperty of synchronization of rates of coordinate clocks. A necessary and sufficient condi-tion for the validity of the zeroth...The transitive property of thermal equilibrium is shown to be equivalent to the transitiveproperty of synchronization of rates of coordinate clocks. A necessary and sufficient condi-tion for the validity of the zeroth law of thermodynamics in Riemann space time is obtained.It is pointed out that the validation of the zeroth law is a necessary condition to construct"simultaneity surfaces", but not a sufficient condition. The reason why one has to use the"dragged system" in the study of Hawking radiation in Kerr spacetime has been explained.展开更多
It is known as the zeroth law of black hole physics that the surface gravity, k of a stationary black hole is constant over the event horizon. It is analogous to the property in thermodynamics: temperature is uniform ...It is known as the zeroth law of black hole physics that the surface gravity, k of a stationary black hole is constant over the event horizon. It is analogous to the property in thermodynamics: temperature is uniform over an equilibrium system. However, this is not the real representation of the zeroth law of thermodynamics. The real and perfect representation of the law is that two bodies, each in thermal equilibrium with a third system, are展开更多
A two⁃port encapsulated low⁃contrast grating with suppressed zeroth order under normal incidence is described in this paper.Based on such grating configuration,the improved efficiency and spectral bandwidth of the fir...A two⁃port encapsulated low⁃contrast grating with suppressed zeroth order under normal incidence is described in this paper.Based on such grating configuration,the improved efficiency and spectral bandwidth of the first order for TE and TM polarizations with a designed period of 1860 nm can be obtained.On the one hand,some of the accurate grating parameters were numerically optimized utilizing a rigorous coupled⁃wave analysis;on the other hand,the inherent physical mechanism suppressing the zeroth order through an encapsulated fused⁃silica grating was adequately interpreted on account of a simplified modal method.Encapsulated grating with a cover layer cannot be simply considered as adding a coating on it.Compared with reported surface⁃relief grating,all parameters of encapsulated grating should be re⁃optimized and the optimized performances of encapsulated grating were greatly improved.Therefore,the encapsulated grating can be potentially applied in writing fiber Bragg gratings.展开更多
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of ed...Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of edges incident with a vertex of minimum degree. Define the zeroth-order general Randic index R_α-0（G） =Σ x∈V（G） d_G-α（x）, where dG（x） denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super edge-connected in terms of the zeroth-order general Randic index for -1 ≤α 〈 0, respectively.展开更多
文摘The transitive property of thermal equilibrium is shown to be equivalent to the transitiveproperty of synchronization of rates of coordinate clocks. A necessary and sufficient condi-tion for the validity of the zeroth law of thermodynamics in Riemann space time is obtained.It is pointed out that the validation of the zeroth law is a necessary condition to construct"simultaneity surfaces", but not a sufficient condition. The reason why one has to use the"dragged system" in the study of Hawking radiation in Kerr spacetime has been explained.
基金Project supported by the National Natural Science Foundation of China.
文摘It is known as the zeroth law of black hole physics that the surface gravity, k of a stationary black hole is constant over the event horizon. It is analogous to the property in thermodynamics: temperature is uniform over an equilibrium system. However, this is not the real representation of the zeroth law of thermodynamics. The real and perfect representation of the law is that two bodies, each in thermal equilibrium with a third system, are
基金Sponsored by the National Natural Science Foundation of China(Grant No.51578247).
文摘A two⁃port encapsulated low⁃contrast grating with suppressed zeroth order under normal incidence is described in this paper.Based on such grating configuration,the improved efficiency and spectral bandwidth of the first order for TE and TM polarizations with a designed period of 1860 nm can be obtained.On the one hand,some of the accurate grating parameters were numerically optimized utilizing a rigorous coupled⁃wave analysis;on the other hand,the inherent physical mechanism suppressing the zeroth order through an encapsulated fused⁃silica grating was adequately interpreted on account of a simplified modal method.Encapsulated grating with a cover layer cannot be simply considered as adding a coating on it.Compared with reported surface⁃relief grating,all parameters of encapsulated grating should be re⁃optimized and the optimized performances of encapsulated grating were greatly improved.Therefore,the encapsulated grating can be potentially applied in writing fiber Bragg gratings.
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
基金supported by the National Natural Science Foundation of China(No.11501490,61373019,11371307)by the Natural Science Foundation of Shandong Province(No.ZR2015AM006)
文摘Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of edges incident with a vertex of minimum degree. Define the zeroth-order general Randic index R_α-0（G） =Σ x∈V（G） d_G-α（x）, where dG（x） denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super edge-connected in terms of the zeroth-order general Randic index for -1 ≤α 〈 0, respectively.
