Periodic Solutions for a Prescribed Mean Curvature Equation with Multiple Delays

We study the existence of periodic solutions for the one-dimensional prescribed mean curvature delay equation (d/dt)(x'(t)/1+x't2) +∑i=1naitgxt-τit=pt. By using Mawhin's continuation theorem, a new result is obtained. Furthermore, the nonexistence of periodic solution for the equation is investigated as well

Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument

AbstractBy means of Mawhin's continuation theorem, we study some second order differential equations with a deviating argument: x″(t)=f(t,x(t),x(t−τ(t)),x′(t))+e(t). Some new results on the existence of periodic solutions are obtained. The interest is that we allow the degree with respect to the variables x0,x1,x2 of f(t,x0,x1,x2) to be greater than 1; and also the result (Theorem 3.2) is related to the deviating argument τ(t). Meanwhile, we give an example to demonstrate our result

Disorder effects on the quantum coherence of a many-boson system

The effects of disorders on the quantum coherence for many-bosons are studied in a double well model. For the ground state, the disorder enhances the quantum coherence. In the deep Mott regime, dynamical evolution reveals periodical collapses and revivals of the quantum coherence which is robust against the disorder. The average over variations in both the on-site energy and the interaction reveals a beat phenomenon of the coherence-decoherence oscillation in the temporal evolution.Comment: 4 figure

Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay

AbstractIn this paper, we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd) which denotes the family of bounded continuous Rd-value functions ϕ defined on (-∞,0] with norm ∥ϕ∥=sup-∞<θ⩽0|ϕ(θ)| under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition. The solution is constructed by the successive approximation

On the existence of m-point boundary value problem at resonance for higher order differential equation

AbstractBy means of Mawhin's continuation theorem, we study m-point boundary value problem at resonance in the following form: x(k)(t)=f(t,x(t),x′(t),…,x(k−1)(t))+e(t),t∈(0,1),x′(0)=0,x″(0)=0,…,x(k−1)(0)=0,x(1)=∑i=1m−2aix(ξi), where m⩾3, k⩾2 are two integers, ai∈R, ξi∈(0,1) (i=1,2,…,m−2) are constants satisfying ∑i=1m−1ai=1 and 0<ξ1<ξ2<⋯<ξm−2. A new result on the existence of solutions is obtained. The interesting is that we do not need all the ai's (1⩽i⩽m−2) have the same sign, and also the degrees of some variables among x0,x1,…,xk−1 in the function f(t,x0,x1,…,xk−1) are allowable to be greater than 1. Meanwhile, we give some examples to demonstrate our result

Analysis of Environmental Data with Censored Observations

The potential threats to humans and to terrestrial and aquatic ecosystems from environmental contamination could depend on the sum of the concentrations of different chemicals. However, direct summation of environmental data is not generally feasible because it is common for some chemical concentrations to be recorded as being below the analytical reporting limit. This creates special problems in the analysis of the data. A new model selection procedure, named forward censored regression, is introduced for selecting an appropriate model for environmental data with censored observations. The procedure is demonstrated using concentrations of atrazine (2-chloro- 4-ethylamino-6-isopropylamino-s-triazine), deethylatrazine (DEA, 2-amino-4-chloro-6-isopropylamino-s-triazine), and deisopropylatrazine (DIA, 2-amino-4-chloro-6-ethylamino-striazine) in groundwater in the midwestern United States by using the data derived from a previous study conducted by the U.S. Geological Survey. More than 80% of the observations for each compound for this study were left censored at 0.05 μg/L. The values for censored observations of atrazine, DEA, and DIA are imputed with the selected models. The summation of atrazine residue (atrazine + DEA + DIA) can then be calculated using the combination of observed and imputed values to generate a pseudo-complete data set. The all-subsets regression procedure is applied to the pseudo-complete data to select the final model for atrazine residue. The methodology presented can be used to analyze similar cases of environmental contamination involving censored data