高阶变系数函数方程的非振动解

给出一类高阶非线性函数方程的一些新的非振动准则,并且给出了在差分方程中的若干应用,结果改进和推广了近期文献的某些结果.     

Oscillation criteria and asymptotic properties of solutions of third‐order nonlinear neutral differential equations

The main goal of this article is to study the asymptotic properties and oscillation of the third‐order neutral differential equations with discrete and distributed delay. We give several theorems and related examples to illustrate the applicability of these theorems. Copyright © 2014 John Wiley & Sons, Ltd.     

Change of the short-range scattering in the graphene covered with Bi2O3 clusters

In this work, we have studied the oxidation process of the bismuth doped graphene in the ambient air. Complete oxidation of the bismuth clusters and that of the graphene are firmly confirmed. The influence of oxygen on the graphene is characterized by means of Hall measurement and SdH oscillation. All transport measurements demonstrate a hole-type doping behavior. Our work also demonstrates that the short-range scattering mechanism is enhanced in doped graphene due to accumulated O-species adsorbates after being exposed in the atmosphere for 40 days and is suppressed after annealing. This investigation may open a new perspective for fabricating the graphene metal oxide devices.     

Fabrication of Self‐Oscillating Micelles with a Built‐In Oxidizing Agent

Various biological behaviors are fueled by “respiration”, which is an example of catabolism. So far, we have reported various self‐oscillating soft materials exhibiting bioinspired dynamic movements. These autonomous polymer systems are driven by the Belousov–Zhabotinsky (BZ) reaction, which is analogous to the tricarboxylic acid (TCA) cycle that is an integral part of respiration. However, in the BZ reaction, the external addition of an oxidizing agent is necessary to initiate the oxidation process, which is realized by intracellular moieties such as ubiquinone in living systems. Herein, we realized self‐oscillating micelles that are driven without the external addition of an oxidizing agent. This was achieved by embedding the oxidizing source into the structure of the self‐oscillating AB diblock copolymers. This strategy introduces a new function equivalent to intracellular oxidizing moieties, and is useful for the design of completely autonomous bioinspired materials.     

DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES

In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.     

Ocean internal waves interpreted as oscillation travelling waves in consideration of ocean dissipation

Most studies of the synthetic aperture radar remote sensing of ocean internal waves are based on the solitary wave solutions of the Korteweg-de Vries （KdV） equation, and the dissipative term in the KdV equation is not taken into account. However, the dissipative term is very important, both in the synthetic aperture radar images and in ocean models. In this paper, the traveling-wave structure to characterize the ocean internal wave phenomenon is modeled, the results of numerical experiments are advanced, and a theoretical hypothesis of the traveling wave to retrieve the ocean internal wave parameters in the synthetic aperture radar images is introduced.     

具有时滞的非线性强迫微分方程振动的充分必要条件

对于一类特殊的具有时滞的二阶次线性强迫微分方程x"(t) +a (t)|x(τ(t))|γsgnx(τ(t)) =g(t)(0＜τ＜1),给出了它的所有解振动的一个充要条件.     

Oscillation and Nonoscillation of Higher Order Self-Adjoint Differential Equations

Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation (-1)ⁿ(t^alphay⁽ⁿ⁾)⁽ⁿ⁾+q(t)y = 0 (*) are established. In these criteria, equation (*) is viewed as a perturbation of the conditionally oscillatory equation (-1)ⁿ(t^alphay⁽ⁿ⁾)⁽ⁿ⁾ - µ,t^2n-y = 0, where _n, is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.