Quantum Ion-Acoustic Waves in Single-Walled Carbon Nanotubes Studied with a Quantum Hydrodynamic Model

The quantum ion-acoustic waves in single-wall carbon nanotubes are studied with the quantum hydrodynamic model, in which the electron and ion components of the nanotubes are regarded as a two-species quantum plasma system. An analytical expression of the dispersion relation is obtained for the linear disturbance. Numerical results show that the frequency of the ion-acoustic wave strongly depends on the nanotube’s radius in the long-wavelength cases

Oscillation Properties for Systems of Hyperbolic Differential Equations of Neutral Type

AbstractSufficient conditions are established for the oscillations of systems of hyperbolic differential equations of the form∂2∂t2ptuix,t+∑r=1dλrtuix,t−τr =aitΔuix,t+∑j=1m∑k=1saijktΔujx,ρkt −qix,tuix,t−∑j=1m∑h=1lqijhx,tujx,σht, x,t∈Ω×0,∞≡G,i=1,2,…,m,where Ω is a bounded domain in Rn with a piecewise smooth boundary ∂Ω, and Δ is the Laplacian in Euclidean n-space Rn

Some Nonlinear Integral Inequalities in Two Independent Variables

We investigate some new nonlinear integral inequalities in two independent variables. The inequalities given here can be used as tools in the qualitative theory of certain nonlinear partial differential equations

Some Pachpatte type inequalities on time scales

AbstractIn this paper, using the comparison theorem, we investigate some Pachpatte type integral inequalities on time scales, which provide explicit bounds on unknown functions. Our results extend some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Some applications of the main results are given in the end of this paper

Some delay integral inequalities on time scales

AbstractIn this paper, using Gronwall’s inequality, we investigate some delay integral inequalities on time scales, which provide explicit bounds on unknown functions. Our results unify and extend some delay integral inequalities and their corresponding discrete analogues. The inequalities given here can be used as tools in the qualitative theory of certain classes of delay dynamic equations on time scales

Dynamic Polarization Effects in Ion Channeling Through Single-Well Carbon Nanotubs

Ion channeling through a single-wall carbon nanotube is simulated by solving Newton’s equations for ion motion at intermediate energies, under the action of both the surface-atom repulsive forces and the polarization forces due to the dynamic perturbation of the nanotube electrons. The atomic repulsion is described by a continuum potential based on the Thomas-Fermi-Moliere model, whereas the dynamic polarization of the nanotube electrons is described by a two-dimensional hydrodynamic model, giving rise to the transverse dynamic image force and the longitudinal stopping force. In the absence of centrifugal forces, a balance between the image force and the atomic repulsion is found to give rise to ion trajectories which oscillate over peripheral radial regions in the nanotube, provided the ion impact position is not too close to the nanotube wall, the impact angle is sufficiently small, and the incident speed is not too high. Otherwise, the ion is found to oscillate between the nanotube walls, passing over a local maximum of the potential in the center of the nanotube, which results from the image interaction. The full statistical analysis of 103 ion trajectories has been made to further demonstrate the actual effect of dynamic polarization on the ion channeling

A new Pachpatte type dynamic inequality on time scales

In this paper, using the comparison theorem, we investigate a new Pachpatte type dynamic inequality on time scales, which provides explicit bounds on unknown functions. Our result unifies and extends a continuous inequality and its corresponding discrete analogues

Influence of Visual Cues of E-WOM on Consumers\u27 Purchase Intention

E-WOM is considered to be an important factor affecting consumers\u27 purchasing decisions. Now many scholars focus on the specific presentation of e-WOM to study consumer behavior, and the research on the influence mechanism of the form-based characteristics of e-WOM information on consumers is relatively lacking. Based on clue utilization theory and the perspective of consumer psychology processing, we explores the impact of visual cues of e-WOM on consumer perception and purchase intention. The experimental results show that the visual cues of e-WOM promote the mental imagery of consumers, and then have a significant impact on their perceptual diagnosis and purchase intention. Finally, the corresponding marketing management inspiration is proposed

On Some Nonlinear Integral Inequalities with an Advanced Argument

In this paper, we investigate some nonlinear integral inequalities with an advanced argument which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain advanced nonlinear differential equations. In the end of this paper, an illustrated example is given