We study the dispersion properties of surface plasmon（SP） oscillations in a semi-bounded semiconductor plasma with the effects of the Coulomb exchange（CE） force associated with the spin polarization of electrons a...We study the dispersion properties of surface plasmon（SP） oscillations in a semi-bounded semiconductor plasma with the effects of the Coulomb exchange（CE） force associated with the spin polarization of electrons and holes as well as the effects of the Fermi degenerate pressure and the quantum Bohm potential.Starting from a quantum hydrodynamic model coupled to the Poisson equation,we derive the general dispersion relation for surface plasma waves.Previous results in this context are recovered.The dispersion properties of the surface waves are analyzed in some particular cases of interest and the relative influence of the quantum forces on these waves are also studied for a nano-sized Ga As semiconductor plasma.It is found that the CE effects significantly modify the behaviors of the SP waves.The present results are applicable to understand the propagation characteristics of surface waves in solid density plasmas.展开更多
Plasma echo theory is revisited to apply it to a semi-bounded plasma. Spatial echoes associated with plasma surface wave propagating in a semi-bounded plasma are investigated by calculating the second order electric f...Plasma echo theory is revisited to apply it to a semi-bounded plasma. Spatial echoes associated with plasma surface wave propagating in a semi-bounded plasma are investigated by calculating the second order electric field produced by external charges and satisfying the boundary conditions at the interface. The boundary conditions are two-fold: the specular reflection condition and the electric boundary condition. The echo spots are determined in terms of the perpendicular coordinate to the interface and the parallel coordinate along which the wave propagates. This improves the earlier works in which only the perpendicular coordinate is determined. In contrast with the echo in an infinite medium, echoes in a bounded plasma can occur at various spots. The diversity of echo occurrence spots is due to the discontinuity of the electric field at the interface that satisfies the specular reflection boundary condition. Physically, the diversity appears to be owing to the reflections of the waves from the interface.展开更多
In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on th...In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.展开更多
Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（...Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（ε） N L（E; m）, we have the following Pukushima＇s decomposition u（Xt）-u（X0） --- Mut ＋ Nut. Define Pu f（x） = Ex[eNT f（Xt）]. Let Qu（f,g） = ε（f,g）＋ε（u, fg） for f, g E D（ε）b. In the first part, under some assumptions we show that （Qu, D（ε）b） is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then （Put〉0is strongly continuous on L2（E;m）. If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J（E x E - d） 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf（x） = Ex[eAtf（Xt）] to be strongly continuous.展开更多
The local and global behavior of the positive solutions of the difference equation was investigated, where the parametersα,βandγand the initial conditions are arbitrary positive numbers. Furthermore, the characteri...The local and global behavior of the positive solutions of the difference equation was investigated, where the parametersα,βandγand the initial conditions are arbitrary positive numbers. Furthermore, the characterization of the stability was studied with a basin that depends on the conditions of the coefficients. The analysis about the semi-cycle of positive solutions has end the study of this work.展开更多
By using Gerstewitz functions, we establish a new equilibrium version of Ekeland varia- tional principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the...By using Gerstewitz functions, we establish a new equilibrium version of Ekeland varia- tional principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the objective bimaps. Applying the new version of Ekeland principle, we obtain some existence theorems on solutions for set-valued vector equilibrium problems, where the most used assumption on compactness of domains is weakened. In the setting of X complete metric spaces （Z, d）, we present an existence result of solutions for set-valued vector equilibrium problems, which only requires that the domain X C Z is countably compact in any Hausdorff topology weaker than that induced by d. When （Z, d） is a Fechet space （i.e., a complete metrizable locally convex space）, our existence result only requires that the domain C Z is weakly compact. Furthermore, in the setting of non-compact domains, we deduce several existence theorems on solutions for set-valued vector equilibrium problems, which extend and improve the related known results.展开更多
基金financial support of Arak University under research Project No.96/5834UGC-SAP(DRS,Phase Ⅲ)[with Sanction order No.F.510/3/DRS-III/2015(SAPI)]UGC-MRP[with F.No.43-539/2014(SR) and FD Diary No.3668] for support
文摘We study the dispersion properties of surface plasmon（SP） oscillations in a semi-bounded semiconductor plasma with the effects of the Coulomb exchange（CE） force associated with the spin polarization of electrons and holes as well as the effects of the Fermi degenerate pressure and the quantum Bohm potential.Starting from a quantum hydrodynamic model coupled to the Poisson equation,we derive the general dispersion relation for surface plasma waves.Previous results in this context are recovered.The dispersion properties of the surface waves are analyzed in some particular cases of interest and the relative influence of the quantum forces on these waves are also studied for a nano-sized Ga As semiconductor plasma.It is found that the CE effects significantly modify the behaviors of the SP waves.The present results are applicable to understand the propagation characteristics of surface waves in solid density plasmas.
文摘Plasma echo theory is revisited to apply it to a semi-bounded plasma. Spatial echoes associated with plasma surface wave propagating in a semi-bounded plasma are investigated by calculating the second order electric field produced by external charges and satisfying the boundary conditions at the interface. The boundary conditions are two-fold: the specular reflection condition and the electric boundary condition. The echo spots are determined in terms of the perpendicular coordinate to the interface and the parallel coordinate along which the wave propagates. This improves the earlier works in which only the perpendicular coordinate is determined. In contrast with the echo in an infinite medium, echoes in a bounded plasma can occur at various spots. The diversity of echo occurrence spots is due to the discontinuity of the electric field at the interface that satisfies the specular reflection boundary condition. Physically, the diversity appears to be owing to the reflections of the waves from the interface.
基金Supported by the National Natural Science Foundation of China (Grant No.10771038)
文摘In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.
基金supported by NSFC(11201102,11326169,11361021)Natural Science Foundation of Hainan Province(112002,113007)
文摘Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（ε） N L（E; m）, we have the following Pukushima＇s decomposition u（Xt）-u（X0） --- Mut ＋ Nut. Define Pu f（x） = Ex[eNT f（Xt）]. Let Qu（f,g） = ε（f,g）＋ε（u, fg） for f, g E D（ε）b. In the first part, under some assumptions we show that （Qu, D（ε）b） is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then （Put〉0is strongly continuous on L2（E;m）. If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J（E x E - d） 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf（x） = Ex[eAtf（Xt）] to be strongly continuous.
文摘The local and global behavior of the positive solutions of the difference equation was investigated, where the parametersα,βandγand the initial conditions are arbitrary positive numbers. Furthermore, the characterization of the stability was studied with a basin that depends on the conditions of the coefficients. The analysis about the semi-cycle of positive solutions has end the study of this work.
基金Supported by National Natural Science Foundation of China(Grant Nos.11471236 and 11561049)
文摘By using Gerstewitz functions, we establish a new equilibrium version of Ekeland varia- tional principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the objective bimaps. Applying the new version of Ekeland principle, we obtain some existence theorems on solutions for set-valued vector equilibrium problems, where the most used assumption on compactness of domains is weakened. In the setting of X complete metric spaces （Z, d）, we present an existence result of solutions for set-valued vector equilibrium problems, which only requires that the domain X C Z is countably compact in any Hausdorff topology weaker than that induced by d. When （Z, d） is a Fechet space （i.e., a complete metrizable locally convex space）, our existence result only requires that the domain C Z is weakly compact. Furthermore, in the setting of non-compact domains, we deduce several existence theorems on solutions for set-valued vector equilibrium problems, which extend and improve the related known results.
