Global existence of solutions of the critical semilinear wave equations with variable coefficients outside obstacles

In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coefficients case, we show that the energy cannot concentrate at any point (t, x) ∈ (0, ∞) ×Ω. For that purpose, following Ibrahim and Majdoub's paper in 2003, we use a geometric multiplier similar to the well-known Morawetz multiplier used in the constant coefficients case. We then use the compari...     

Approximation for counts of head runs

In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein’s method and coupling.     

Markov branching processes with immigration-migration and resurrection

We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are...     

Homoclinic solutions in periodic difference equations with saturable nonlinearity

In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases.     

On anti-pluricanonical systems of Q-Fano 3-folds

We investigate birationality of the anti-pluricanonical map Φ-m,the rational map defined by the anti-pluricanonical system |-mKX|,on weak Q-Fano 3-folds.     

Implementing two optimal economical quantum cloning with superconducting quantum interference devices in a cavity

We propose a unified scheme to implement the optimal 1→ 3economical phase-covariant quantum cloning and optimal 1→3 economical real state cloning with superconducting quantum interference devices (SQUIDs) in a cavity.During this process,no transfer of quantum information between the SQUIDs and cavity is required.The cavity field is only virtually excited.The scheme is insensitive to cavity decay.Therefore,the scheme can be experimentally realized in the range of current cavity QED techniques.     

Investigation of morphology selection for CBr_4-C_2Cl_6 alloy in three dimensions with multi-phase field method

With the multi-phase field model, the unidirectional solidification with constant velocity growth and variable velocity growth of the CBr4-C2Cl6 eutectic alloy is simulated in three dimensions. The simulated results with constant velocity growth show that with the increase of pulling velocity, the morphology of the CBr4-C2Cl6 alloy evolves in the sequence of lamellar merging →lamellar-rod transition→stable lamellar growth→oscillating growth→lamellar branching. A morphology selection map is established with ...     

Properties of the 3/2~-[521] band in the odd-N rare-earth nuclei

High-spin states in 161Er have been studied experimentally via the 150Nd(16O, 5n) reaction at a beam energy of 86 MeV. Three rotational bands built on the 5/2+[642], 3/2-[521], and 11/2-[505] configurations have been extended up to high-spin states, and particularly, the α = -1/2 branch of the ground state 3/2-[521] band has been revised significantly. It is found that signature inversion occurs in the 3/2-[521] band after the band crossing in 161Er. The systematics of the signature inversion associated wit...     

Microstructure and magnetic properties of CoFe_2O_4 thin films deposited on Si substrates with an Fe_3O_4 under-layer

The microstructure and magnetic properties of cobalt ferrite thin films deposited by the sputtering method on an Fe3O4 under-layer were investigated at different post-annealing temperatures.Results show that the Fe3O4 under-layer can accelerate the grain growth of cobalt ferrite films due to the phase transformation of the Fe3O4 under-layer at about 400°C-500°C.By introducing the Fe3O4 under-layer,cobalt ferrite nanocrystalline thin films with high coercivity can be obtained at lower post-annealing temperat...     

Modelling of multi-bodies in close proximity under water waves——Fluid resonance in narrow gaps

Viscous fluid model and potential flow model with and without artificial damping force(f=-μV,μ the damping coefficient and V the local averaging flow velocity) are employed in this work to investigate the phenomenon of fluid resonance in narrow gaps between multi-bodies in close proximity under water waves.The numerical results are compared with experimental data available in the literature.The comparison demonstrates that both the viscous fluid model and the potential flow model are able to predict the res...