The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied w...The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.展开更多
This paper has been addressed to the well-known problem of energy in gravitational waves. We have investigated the energy of cylindrical gravitational waves in the context of General Relativity and teleparallel theory...This paper has been addressed to the well-known problem of energy in gravitational waves. We have investigated the energy of cylindrical gravitational waves in the context of General Relativity and teleparallel theory of gravity. For this purpose, the prescriptions of Einstein, Landau-Lifshitz, Bergmann-Thomson, and Moeller are used in both the theories. It is shown that these energy-momentum complexes do not provide equivalent results in the two theories. However, these turn out to be constant for all the prescriptions except Moeller in both the theories at large distances.展开更多
Heterogeneous networks(HetNets)consisting of macro cells with very large antenna arrays and a secondary tier of small cells with a few antennas each can well tackle the contradiction of large coverage of the network a...Heterogeneous networks(HetNets)consisting of macro cells with very large antenna arrays and a secondary tier of small cells with a few antennas each can well tackle the contradiction of large coverage of the network and high data rate at the hot spots.However,it is not permissible to assign orthogonal pilot sequences for all the supported users due to the large number.Hence,we propose a pilot reduction scheme based on the heterogeneous system configurations and the unique topology of this HetNet.The reusing of pilot sequences causes the presence of the contaminated channel state information(CSI) and results in receivers' Quality of Service(QoS) outage.With the contaminated CSI,we provide an energy-efficient beamforming based on minimizing the total power consumption while keeping the QoS constraints satisfied and restricting the QoS outage probability below a given specification.By applying the approach of Bernstein approximation and semi-definite relaxation,we transform the original intractable chance constrained program to a convex problem conservatively.Numerical results show that the average power consumption of the proposed beamforming for our pilot reduction scheme is close to that of the perfect CSI case.Since our scheme will greatly compress the length of pilot sequence especially for those highly densified network with large number of small cells,it will be crucially helpful to put such two-tier massive multiple-input and multiple-output(MIMO) systems into practice.展开更多
Using the extended Blonder-Tinkham-Klapwijk formalism, we investigate the conductance spectra of graphene ferromagnet/p wave superconductor junctions. It is found that the conductance spectra are affected by the p wav...Using the extended Blonder-Tinkham-Klapwijk formalism, we investigate the conductance spectra of graphene ferromagnet/p wave superconductor junctions. It is found that the conductance spectra are affected by the p wave pairing symmetry. The ferromagnetic exchange energy in the ferromagnet can suppress Andreev retroreflection but enhance the specular Andreev reflection in graphene ferromagnet/p wave superconductor junctions. The conductance decreases with increasing exchange energy Eh for Eh〈Er （the Fermi energy in the ferromagnet region）, but the conductance increases with increasing exchange energy Eh for Eh〉EF.展开更多
We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy le...We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy levels and the corresponding eigenfunction in dosed form. We also compute the energy eigenvalues numerically.展开更多
文摘The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.
文摘This paper has been addressed to the well-known problem of energy in gravitational waves. We have investigated the energy of cylindrical gravitational waves in the context of General Relativity and teleparallel theory of gravity. For this purpose, the prescriptions of Einstein, Landau-Lifshitz, Bergmann-Thomson, and Moeller are used in both the theories. It is shown that these energy-momentum complexes do not provide equivalent results in the two theories. However, these turn out to be constant for all the prescriptions except Moeller in both the theories at large distances.
基金supported in part by the "863" Program of China No. 2014AA01A704National Natural Science Foundation of China No.61171080
文摘Heterogeneous networks(HetNets)consisting of macro cells with very large antenna arrays and a secondary tier of small cells with a few antennas each can well tackle the contradiction of large coverage of the network and high data rate at the hot spots.However,it is not permissible to assign orthogonal pilot sequences for all the supported users due to the large number.Hence,we propose a pilot reduction scheme based on the heterogeneous system configurations and the unique topology of this HetNet.The reusing of pilot sequences causes the presence of the contaminated channel state information(CSI) and results in receivers' Quality of Service(QoS) outage.With the contaminated CSI,we provide an energy-efficient beamforming based on minimizing the total power consumption while keeping the QoS constraints satisfied and restricting the QoS outage probability below a given specification.By applying the approach of Bernstein approximation and semi-definite relaxation,we transform the original intractable chance constrained program to a convex problem conservatively.Numerical results show that the average power consumption of the proposed beamforming for our pilot reduction scheme is close to that of the perfect CSI case.Since our scheme will greatly compress the length of pilot sequence especially for those highly densified network with large number of small cells,it will be crucially helpful to put such two-tier massive multiple-input and multiple-output(MIMO) systems into practice.
基金supported by the National Natural Science Foundation of China (Grant No. 11074088)
文摘Using the extended Blonder-Tinkham-Klapwijk formalism, we investigate the conductance spectra of graphene ferromagnet/p wave superconductor junctions. It is found that the conductance spectra are affected by the p wave pairing symmetry. The ferromagnetic exchange energy in the ferromagnet can suppress Andreev retroreflection but enhance the specular Andreev reflection in graphene ferromagnet/p wave superconductor junctions. The conductance decreases with increasing exchange energy Eh for Eh〈Er （the Fermi energy in the ferromagnet region）, but the conductance increases with increasing exchange energy Eh for Eh〉EF.
文摘We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy levels and the corresponding eigenfunction in dosed form. We also compute the energy eigenvalues numerically.
