A note on oscillation criteria for second-order neutral dynamic equations on isolated time scales

The principal goal of this paper is to amend oscillation results obtained in the recent paper by Saker and O’Regan (2011) [9].     

Nonlinear pumping in oscillatory diffusive processes: The impact on the oceanic deep layers and lakes

We discuss a significant mathematical property of the nonlinear diffusion equation, so-called, the pumping effect, which of great importance in many natural diffusion processes. An oscillatory boundary value problem is considered for the nonlinear diffusive equation of thermal conductivity. We demonstrate that pure periodical oscillations of temperature at the boundary result in a nonlinear pumping of the heat implying that the heat is pumped out or into the inner regions depending on the change in the temperature oscillation amplitude. As an example, the residual effect in temperature of the World Ocean’s deep layers and lakes due to the oscillatory processes at the surface is presented and analyzed. As is generally known, the sea surface temperature (SST) profiles indicate long-term oscillations, and, therefore, according to the pumping effect when the SST oscillation amplitudes increase, the heat comes up to the surface while the deep layers become rather cooler, otherwise, as the amplitudes decrease, the heat transfers into the deep layers.     

Some oscillation results for second-order nonlinear delay dynamic equations

This paper is concerned with oscillatory behavior of a class of second-order delay dynamic equations on a time scale. Two new oscillation criteria are presented that improve some known results in the literature. The results obtained are sharp even for the second-order ordinary differential equations.     

Oscillation of higher order nonlinear dynamic equations with a nonlinear neutral term

This study introduces the oscillation of higher order nonlinear dynamic equations with a nonlinear neutral term. The findings are obtained via utilising an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. We propose novel oscillation criteria that improve, extend and simplify existing ones in the literature. The results are associated with several numerical examples.     

二阶时标非线性中立型动力学方程的振动性

运用广义Riccati变换给出时标上二阶非线性中立型动力学方程振动的充分条件,进一步研究了具扰动项的动力学方程解的性态.所得结论推广和改进了已知文献的部分结果.     

Numerical approach for solving fractional relaxation–oscillation equation

In this study, we will obtain the approximate solutions of relaxation–oscillation equation by developing the Taylor matrix method. A relaxation oscillator is a kind of oscillator based on a behavior of physical system’s return to equilibrium after being disturbed. The relaxation–oscillation equation is the primary equation of relaxation and oscillation processes. The relaxation–oscillation equation is a fractional differential equation with initial conditions. For this propose, generalized Taylor matrix method is introduced. This method is based on first taking the truncated fractional Taylor expansions of the functions in the relaxation–oscillation equation and then substituting their matrix forms into the equation. Hence, the result matrix equation can be solved and the unknown fractional Taylor coefficients can be found approximately. The reliability and efficiency of the proposed approach are demonstrated in the numerical examples with aid of symbolic algebra program, Maple.     

基于CCAPM框架的财富不平等与房价关系研究

运用含有房屋的CCAPM模型,在同时考虑房屋的消费属性与投资属性基础上分析了财富(或收入)分配对房价的影响;并通过数值模拟解释了我国房价高企的根源.结论表明,我国房价高企是财富分配不均所致,财富不均等程度加剧致使房屋从消费属性向投资属性转变进而推高了房价.文章也分析了财富分配对居民消费结构的影响,财富分配不均等程度加剧使得贫穷阶层的房屋消费比重下降而富裕阶层的投资性购房比重增加,进而拉高房价.文章最后指出,要调控我国当前房地产市场价格,必须从财富(或收入)分配入手,明晰产权.     

Fite–Hille–Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments

We study oscillatory behavior of solutions to a class of second-order half-linear dynamic equations with deviating arguments under the assumptions that allow applications to dynamic equations with delayed and advanced arguments. Several improved Fite–Hille–Wintner-type criteria are obtained that do not need some restrictive assumptions required in related results. Illustrative examples and conclusions are presented to show that these criteria are sharp for differential equations and provide sharper estimates for oscillation of corresponding $q$-difference equations.     

Oscillation of second order nonlinear dynamic equations with a nonlinear neutral term on time scales

In this article, we consider the oscillation of second order nonlinear dynamic equations with a nonlinear neutral term on time scales. Some new sufficient conditions which insure that any solution of the equation oscillates are established by means of an inequality technique and Riccati transformation. This paper improves and generalizes some known results. Several illustrative examples are given throughout.     

Nonlinear oscillation of second‐order neutral dynamic equations with distributed delay

In this paper, we consider the nonlinear oscillation of the following second‐order neutral delay dynamic equations with distributed delay on a time scale , where Z(t) = x(t) + p(t)x(τ(t)),α,β > 0 are constants. By using some new techniques, we obtain oscillation criteria for the equation when β > α,β = α, and β < α, respectively. Those results established here complete and develop the oscillation criteria in the literature. Also, our main results are illustrated with some examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Integral operators on BMO and Campanato spaces

This paper establishes the mapping properties of integral operators on space of bounded mean oscillation and Campanato spaces. In particular, we have the Hardy’s inequality and the boundedness of the Hadamard fractional integrals on space of bounded mean oscillation and Campanato spaces.     

具有可变时滞的非线性非自治差分方程的振动性及其应用

本文获得了一类具有可变时滞的非线性非自治差分方程的振动准则,建立了这类差分方程的几个线性化振动性定理,并得到了具有可变时滞的离散型非自治广义Logistic方程关于其正平衡点振动的一系列充分条件.     

带次线性中立项的二阶广义Emden-Fowler微分方程的Philos型振动准则

研究一类带次线性中立项的二阶非线性广义Emden-Fowler时滞微分方程的振动性.利用Riccati变换和不等式技巧,在非正则条件下建立了该类方程多个简便的Philos型和Kamenev型新振动准则.所得定理也适应于包括经典Euler方程等线性非中立型方程,推广和改进了已有文献中的相应结果.最后还给出应用实例展示了所...     

Solutions to stochastic fractional oscillation equations

We formulate a fractional stochastic oscillation equation as a generalization of Bagley’s fractional differential equation. We do this in analogy with the case for Basset’s equation, which gives rise to fractional stochastic relaxation equations. We analyze solutions under some conditions of spatial regularity of the operators considered.     

一阶中立型时滞差分方程振动的充分必要条件

研究了一阶常系数中立型时滞差分方程A[x(n)-px(n-τ)]+qx(n-σ)=0的振动性.通过构造若干适当的函数,分别得到了在01两种情况下该方程的一切解振动的充分必要条件.     

如何调控经济金融化？——基于中国经济的三方演化博弈视角

十九大以来,中国的改革开放进程不断加快,在金融领域体制改革也是不断深化,开放程度不断提高,期间实体经济金融化的问题在我国日益凸显,经济“脱实向虚”的现象愈发严重,而实体经济能否健康发展将决定一个国家综合国力的强弱。因此,通过研究实体企业金融化问题来探讨中国防范产业“空心化”的策略非常必要。运用演化博弈和模拟仿真的方法,构建基于政府监管部门、实体企业和金融企业金融化的三方演化博弈分析框架,重点分析政府监管对企业策略选择的影响,并对演化均衡过程进行模拟仿真。研究表明,政府对企业所采取措施譬如加大处罚、提高减税幅度或补贴等对促进实体企业和金融企业达成合作关系有积极作用,实体企业和金融企业对分利技术水平和社会禀赋倍增率的变化敏感。     

Yan’s oscillation theorem revisited

Yan’s contribution [J. Yan, Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc. 98 (1986) 276–282] was an important breakthrough in the development of the Theory of Oscillation. This frequently cited paper has stimulated extensive investigations in the field. During the last decade, an integral oscillation technique has been developed to such an extent as to allow us to revisit Yan’s fundamental oscillation theorem and remove one of the conditions, leaving the other assumptions and the conclusion intact, thus enhancing this keystone result.     

Stability of the Equilibrium State of a Rigid Body with Multilayer Ideal Liquid Separated by Elastic Plates

Ukrainian Mathematical Journal - L. N. Sretenskii’s problem and the problem of oscillation of physical pendulum are generalized to the case of multilayer ideal liquid separated by elastic...     

周期线性微分方程解的一个关键性质

周期线性微分方程某解f(z)和f(z qω）的线性相关性是方程复振研究的起步关键,其中ω是方程系数的周期,q是某正整数。S.Bank和J.Langley于1992年证明了重要结果,但其优势条件有时不适用。本文提出“组合优势条件”产用其发展了这一结果,大大扩充了其适用性。