Bouncing universe models in an extended gravity theory

Some bouncing models are investigated in the framework of an extended theory of gravity. The extended gravity model is a simple extension of the General Relativity where an additional matter geometry coupling is introduced to account for the late time cosmic speed up phenomena. The dynamics of the models are discussed in the background of a flat FRW universe. Some viable models are reconstructed for specifically assumed bouncing scale factors. The behavior of the models are found to be decided mostly by the parameters of the respective models. The extended gravity based minimal matter-geometry coupling parameter has a role to remove the omega singularity occurring at the bouncing epoch. It is noted that the constructed models violate the energy conditions, however, in some cases this violation leads to the evolution of the models in phantom phase. The stability of the models are analyzed under linear homogeneous perturbations and it is found that, near the bounce, the models show instability but the perturbations decay out smoothly to provide stable models at late times.     

Exponential Stability for Time-changed Stochastic Differential Equations

Acta Mathematicae Applicatae Sinica, English Series - So far there have been few results presented on the exponential stability for time-changed stochastic differential equations. The main aim of...     

Weak dissipation of electrostatic solitary structures in warm collisional pair-ion plasmas with non-Maxwellian electron population

The localized electrostatic structures with dissipation due to ion-neutral collisions in a symmetric warm pair-ion plasma in the presence of non-Maxwellian population of electrons are studied. The analytical model for ion dynamics is based on fluid equations and the evolution equation is derived by using the reductive perturbation scheme in the form of a damped Korteweg-de Vries equation. The parameter regime relevant to space-based observations and laboratory plasmas is considered and time evolution of the propagating ion-acoustic soliton is discussed. The energetic-particles-driven properties of soliton for various spectral indices, dissipation, ion temperature, and density are illustrated with comparison to the thermal mode for Boltzmann distribution of electrons.     

Interfacial instability of ferrofluid flow under the influence of a vacuum magnetic field

This study is to numerically test the interfacial instability of ferrofluid flow under the presence of a vacuum magnetic field. The ferrofluid parabolized stability equations(PSEs) are derived from the ferrofluid stability equations and the Rosensweig equations, and the characteristic values of the ferrofluid PSEs are given to describe the ellipticity of ferrofluid flow. Three numerical models representing specific cases considering with/without a vacuum magnetic field or viscosity are created to mathematically examine the interfacial instability by the computation of characteristic values. Numerical investigation shows strong dependence of the basic characteristic of ferrofluid Rayleigh-Taylor instability(RTI) on viscosity of ferrofluid and independence of the vacuum magnetic field.For the shock wave striking helium bubble, the magnetic field is not able to trigger the symmetry breaking of bubble but change the speed of the bubble movement. In the process of droplet formation from a submerged orifice, the collision between the droplet and the liquid surface causes symmetry breaking. Both the viscosity and the magnetic field exacerbate symmetry breaking. The computational results agree with the published experimental results.     

“Quad-band flexible magnesium zinc ferrite (MgZnFe2O4)-based double negative metamaterial for microwave applications”

This article presents vertically coupled, rectangular complementary split-ring resonator-shaped quad-band double-negative (DNG) metamaterial unit cells, that is, having both negative permittivity and permeability, which redirect negative refractive and also are not found in nature. The metamaterial is fabricated on magnesium zinc ferrite-based flexible microwave substrates, and the flexible substrates are chosen with two different concentrations of magnesium (Mg) denoted by Mg₃₀ and Mg₅₀ for 30% and 50% of Mg, which possess dielectric constants of 4.32 and 3.15 and loss tangents of 0.003 and 0.005, respectively. The proposed metamaterials are demonstrated by utilizing the CST microwave simulator, and their effective parameters are extracted according to the Nicolson-Ross-Wire method. With Mg_30, the prepared, flexible metamaterial shows measured resonances at 3.70 GHz, 7 GHz, 8.60 GHz, and 9.78 GHz, whereas with Mg₅₀ it shows the measured resonances at 4.10 GHz, 7.70 GHz, 9.33 GHz, and 10.62 GHz. Very good effective medium ratios (EMR) along with DNG properties are obtained, namely 6.5 and 5.85 for Mg₃₀ and Mg_50, respectively, with a physical dimension of 12.5 × 9.5 mm² for both of the unit cells_. Also, the electric field, magnetic field, and surface current distribution at different resonances and the polarization insensitivity at different polarization angles were observed. Thus, the designed new flexible substrate microwave materials based on DNG metamaterials are potential candidates for S-, C- and X-band applications, as well as for flexible microwave technologies.     

从双层规划的角度看道德风险理论的一阶条件方法

本文首先对双层规划的一个特殊例子即道德风险模型中使用的一阶条件方法（FOA）做简要的梳理，然后提出一种更为一般的使FOA有效的原则与方法。新方法主要依赖于代理人对委托人设置的目标的最优反应映射是否存在不动点，这个性质不要求原问题与用一阶条件放松以后的问题之间的约束集等价，从而也不要求代理人的期望效用对行动具有全局凹性。在新方法下，可以用较为简单的方法证明FOA在以下两种情形之一有效，即如果分布函数是概率分布的凸组合或者分布函数来自某些特殊的指数族分布。     

Embedded exponential-type low-regularity integrators for KdV equation under rough data

BIT Numerical Mathematics - In this paper, we introduce a novel class of embedded exponential-type low-regularity integrators (ELRIs) for solving the KdV equation and establish their optimal...