Behavior and process of background signal formation of hydrogen,carbon, nitrogen,and oxygen in silicon wafers during depth profiling using dual-beam TOF-SIMS

The behavior and mechanism of background signals during depth profiling of atmospheric elements using dual-beam time-of-flight secondary ion mass spectrometry (TOF-SIMS) have been experimentally investigated for silicon wafers. The background signals of atmospheric elements were found to be inversely proportional to the sputtering rate. Most of the background signals are largely attributable to the accumulation of components through adsorption and ion bombardment in the pre-equilibrium state. On the other hand, the contribution of real-time adsorption during the instant after the last sputtering in the equilibrium state is negligible under the present experimental conditions. H₂O is dominant in the background formation process of hydrogen and oxygen, which is supported by the higher adsorption coefficients. The background levels of carbon and nitrogen are lower than those of hydrogen and oxygen. Furthermore, the background signal of carbon with respect to the sputtering rate shows a different trend than the other elements. This could be attributed to accumulation in the pre-equilibrium state. These results indicate that the background levels can be lowered close to those of dynamic-SIMS by using an extremely high sputtering rate in dual-beam TOF-SIMS.     

Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.     

Blow-up of solution for beam equation with delay and dynamic boundary conditions

In this paper, we consider an elastic beam equation with delay, source term, and boundary conditions together with some suitable initial data. Using the Faedo-Galerkin approximation and some estimates, we get the local existence of solution. Moreover, we obtain the finite time blow-up of solution by constructing suitable Lyapunov functionals.     

Periodic solutions of a periodic stochastic human immunodeficiency virus model with distributed delay and cytotoxic T lymphocytes immune response

In this paper, a periodic stochastic human immunodeficiency virus (HIV) model with distributed delay and cytotoxic T lymphocytes (CTL) immune response is investigated. First, by It $ô$'s formula, we show that the solution with any positive initial value is global and positive. Then, by the stochastic comparison theorem, we obtain the sufficient conditions guaranteeing the existence and global attractivity of infection-free periodic solution. Furthermore, we discuss the existence of the infective periodic solution by Has'minskii theory. Finally, numerical examples are given to illustrate the results.     

Kinetics studies of 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol,and 2,4,4-trimethyl-1-pentanol with chlorine atoms: Photooxidation mechanism of 2,4,4-trimethyl-1-pentanol

The rate constants for the reaction between chlorine atoms and either 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol, or 2,4,4-trimethyl-1-pentanol at 298 K were determined using the relative method with 2-butanol and 1-pentanol as reference compounds. The values obtained for 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol, and 2,4,4-trimethyl-1-pentanol (k × 10¹⁰ cm³ molec⁻¹ s⁻¹) were, respectively, (2.64 ± 0.5), (2.72 ± 0.5), and (2.50 ± 0.4), in agreement with the values of the rate constants reported in bibliography for similar alcohols and the values estimated by structure activity relationship methods. The photooxidation products of 2,4,4-trimethyl-1-pentanol initiated by chlorine atoms were identified (formaldehyde, 2-propanone, 2,2-dimethyl propanal, 4,4,-dimethyl-2-pentanone, and 3,3-dimethylbutanal), and the reaction mechanism was determined.     

Delay driven Hopf bifurcation and chaos in a diffusive toxin producing phytoplankton‐zooplankton model

This paper deals with a diffusive toxin producing phytoplankton‐zooplankton model with maturation delay. By analyzing eigenvalues of the characteristic equation associated with delay parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are studied. Explicit results are derived for the properties of bifurcating periodic solutions by means of the normal form theory and the center manifold reduction for partial functional differential equations. Numerical simulations not only agree with the theoretical analysis but also exhibit the complex behaviors such as the period‐3, 5, 6, 7, 8, 11, and 12 solutions, cascade of period‐doubling bifurcation in period‐2, 4, quasi‐periodic solutions, and chaos. The key observation is that time delay may control harmful algae blooms (HABs). Moreover, numerical simulations show that the chaotic states induced by the period‐doubling bifurcation are purely temporal, which is stationary in space and oscillatory in time. The investigations may provide some new insights on harmful phytoplankton blooms.     

Periodic Solutions of Third-order Differential Equations with Finite Delay in Vector-valued Functional Spaces

In this paper, we study the well-posedness of the third-order differential equation with finite delay(P_3): αu'"(t) + u"(t) = Au(t) + Bu'(t) + Fut +f(t)(t ∈ T := [0,2π]) with periodic boundary conditions u(0) = u(2π), u'(0) = u"(2π),u"(0)=u"(2π) in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces B_(p,q)~s(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠ {0}, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp([-2π, 0]; X)(resp. Bp,qs([-2π, 0]; X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. B_(p,q)~s-well-posedness)of(P_3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.     

时间延迟扩散-波动分数阶微分方程有限差分方法

本文提出求解时间延迟扩散-波动分数阶微分方程有限差分方法，方程中对时间的一阶导函数用α阶（0 < α < 1） Caputo分数阶导数代替.文章中利用Lubich线性多步法对分数阶微分进行差分离散，且文章利用分段区间证明该方法是稳定的，且利用数值实验加以验证.