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
This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on t...This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on the propagation theory of edge guided modes, the analysis procedure of this structure is introduced. The numerical results demonstrate the tunability of the resonant frequency by changing the DC bias magnetic field applied to the ferrite. In contrast to previous work, the proposed structure is easy to design and fabricate and does not require a chip component.展开更多
A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal syste...A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.As a consequence,the extremal hexagonal systems with minimum or maximum zeroth-order general Randic index were completely characterized.Moreover,by using the least-square fit method and regression analysis,a new and close relation was found between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.So the zeroth-order general Randic index is a good measure of the π-electronic energies for benzenoid hydrocarbons.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
The zeroth law of thermodynamics,the Nernst-Simon and Planck statements of the third law of thermodynamics and the unattainability statement of the absolute temperature,T=0,are discussed by thermomechanical dynamics(T...The zeroth law of thermodynamics,the Nernst-Simon and Planck statements of the third law of thermodynamics and the unattainability statement of the absolute temperature,T=0,are discussed by thermomechanical dynamics(TMD)which is a classical theory of thermodynamics extended to study ther-mal transitions from thermodynamic equilibrium to nonequilibrium irre-versible states(NISs).The method of TMD has been successfully applied to mechanisms of heat engines(a drinking bird,a low temperature Stirling en-gine and thermoelectric energy conversion technologies).The TMD is applied to the thermal phase transitions from thermodynamic equilibrium to NISs,and dissipative equations of motion for phase transition mechanism of heat engines in general are studied.The results are thermodynamically consistent and have produced new technical applications on a thermoelectric power-con-version method and devices for sustainable environmental goals.The method of TMD is applied to understand consistent thermodynamic concepts of the zeroth and the third law of thermodynamics and the unattainability statement,T=0.The analyses help extend thermodynamics to NISs.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
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
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This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on the propagation theory of edge guided modes, the analysis procedure of this structure is introduced. The numerical results demonstrate the tunability of the resonant frequency by changing the DC bias magnetic field applied to the ferrite. In contrast to previous work, the proposed structure is easy to design and fabricate and does not require a chip component.
基金National Natural Science Foundation of China (No. 10901034)Chenguang Program of Shanghai Education Development Foundation,China (No. 2008CG40)
文摘A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.As a consequence,the extremal hexagonal systems with minimum or maximum zeroth-order general Randic index were completely characterized.Moreover,by using the least-square fit method and regression analysis,a new and close relation was found between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.So the zeroth-order general Randic index is a good measure of the π-electronic energies for benzenoid hydrocarbons.
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the research is supported by Japan Keirin Autorace(JKA)Foundation,Grant No.2024M-423.
文摘The zeroth law of thermodynamics,the Nernst-Simon and Planck statements of the third law of thermodynamics and the unattainability statement of the absolute temperature,T=0,are discussed by thermomechanical dynamics(TMD)which is a classical theory of thermodynamics extended to study ther-mal transitions from thermodynamic equilibrium to nonequilibrium irre-versible states(NISs).The method of TMD has been successfully applied to mechanisms of heat engines(a drinking bird,a low temperature Stirling en-gine and thermoelectric energy conversion technologies).The TMD is applied to the thermal phase transitions from thermodynamic equilibrium to NISs,and dissipative equations of motion for phase transition mechanism of heat engines in general are studied.The results are thermodynamically consistent and have produced new technical applications on a thermoelectric power-con-version method and devices for sustainable environmental goals.The method of TMD is applied to understand consistent thermodynamic concepts of the zeroth and the third law of thermodynamics and the unattainability statement,T=0.The analyses help extend thermodynamics to NISs.
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.
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
