Rectifiable oscillations in second-order linear differential equations

We study the linear differential equation , on I=(0,1), where the coefficient f(x) is strictly positive and continuous on I, and satisfies the Hartman-Wintner condition at x=0. The four main results of the paper are: (i) a criterion for rectifiable oscillations of (P), characterized by the integrability of on I; (ii) a stability result for rectifiable and unrectifiable oscillations of (P), in terms of a perturbation on f(x); (iii) the s-dimensional fractal oscillations (for which we assume also f(x)∼cx−α when x→0, α>2, and s=max{1,3/2−2/α}); and (iv) the co-existence of rectifiable and unrectifiable oscillations in the absence of the Hartman-Wintner condition on f(x). Explicit examples related to the above results are given.     

Study on the liquid membrane oscillation of water/oil/water system containing TTAB and picric acid

The liquid membrane oscillation of a novel water （aqueous tetradecyl trimethyl ammoniumbromide, TTAB and alcohol solution）/oil （picric acid in chloroform solution）/water （aqueous glucose solution） system was investigated. By using homemade device, the curves of various liquid membranes oscillation with different concentration of TTAB and picric acid, types of alcohol and other organic solvents at different temperature were measured. The results show that the water （aqueous 7 mmol/L of TTAB and 0.5 mol/L of n-propanol solution）/oil （0.5 mmol/L of picric acid in chloroform solution）/water （aqueous glucose solution） system performed sustained and stable oscillation at 30 ℃. And the novel system can recognise added amino acid.     

Oscillation of second-order damped dynamic equations on time scales

The study of dynamic equations on time scales has been created in order to unify the study of differential and difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which may be an arbitrary closed subset of the reals. This way results not only related to the set of real numbers or set of integers but those pertaining to more general time scales are obtained. In this paper, by employing the Riccati transformation technique we will establish some oscillation criteria for second-order linear and nonlinear dynamic equations with damping terms on a time scale . Our results in the special case when and extend and improve some well-known oscillation results for second-order linear and nonlinear differential and difference equations and are essentially new on the time scales , h>0, for q>1, , etc. Some examples are considered to illustrate our main results.     

在强辐射阻尼存在下完全反转态的线型

在180°脉冲加z方向脉冲梯度场作用后,采样得到90%水样的自由感应衰减信号,其具有几乎完整的双曲正割函数特征,并通过付立叶变换得到其频谱,发现其具有强烈的震荡特征,这与通常用不完善的180°单脉冲观测到的相位畸变有所不同,并且发现这种强震荡只有在强辐射阻尼存在下以及θ₀非常接近180°时才能观测到.在辐射阻尼线型理论基础上,合理的理论计算已进行,我们得到了与实验观测相当一致的结果.     

含多滞量的非线性中立型差分方程的振动准则

本文研究了较为一般的含有多个滞量的非线性中立型差分方程的振动性,得到了该类方程振动的一个充要条件．     

Oscillation and Nonoscillation in Delay or Advanced Differential Equations and in Integrodifferential Equations

Some new oscillation and nonoscillation criteria are given for linear delay or advanced differential equations with variable coefficients and not (necessarily) constant delays or advanced arguments. Moreover, some new results on the existence and the nonexistence of positive solutions for linear integrodifferential equations are obtained.     

Necessary and Sufficient Conditions for the Oscillation of a Second Order Linear Differential Equation

In this paper we give a necessary and sufficient condition for the oscillation of the second order linear differential equation where p is a locally integrable function and either or where We give some applications which show how these results unify and imply some classical results in oscillation theory.     

Mechanism on oscillating lifted flames in nonpremixed laminar coflow jets

The oscillating lifted flame in a laminar nonpremixed nitrogen-diluted fuel jet is known to be a result of buoyancy, though the detailed physical mechanism of the initiation has not yet been properly addressed. We designed a systematic experiment to test the hypothesis that the oscillation is driven by competition between the positive buoyancy of flame and the negative buoyancy of a fuel stream heavier than the ambient air. The positive buoyancy was examined with various flame temperatures by changing fuel mole fraction, and the negative buoyancy was investigated with various fuel densities. The density of the coflow was also varied within a certain range by adding either helium or carbon dioxide to air, to study how it affected the positive and negative buoyancies at the same time. As a result, we found that the range of oscillation was well-correlated with the positive and the negative buoyancies; the former stabilized the oscillation while the latter triggered instability and became a source of the oscillation. Further measurements of the flow fields and OH radicals evidenced the important role of the negative buoyancy on the oscillation, detailing a periodic variation in the unburned flow velocity that affected the displacement of the flame.