Global hysteresis in ferroelectrics with incommensurate phases

A review of the basic experimental results connected with the formation of long-living metastable states in the incommensurate phases of ferroelectric crystals and related phenomena is given. The interpretation and appropriate physical mechanisms underlying the global hysteresis phenomena associated with these states are considered.     

Two optimal Dai–Liao conjugate gradient methods

Two adaptive choices for the parameter of Dai–Liao conjugate gradient (CG) method are suggested. One of which is obtained by minimizing the distance between search directions of Dai–Liao method and a three-term CG method proposed by Zhang et al. and the other one is obtained by minimizing Frobenius condition number of the search direction matrix. Global convergence analyses are made briefly. Numerical results are reported; they demonstrate effectiveness of the suggested adaptive choices.     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

On global stability of a nonresident computer virus model

In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.     

Hydroxyl Radical Generation and DNA Nuclease Activity: A Mechanistic Study Based on a Surface‐Immobilized Copper Thioether Clip‐Phen Derivative

Coordination compounds of copper have been invoked as major actors in processes involving the reduction of molecular oxygen, mostly with the generation of radical species the assignment for which has, so far, not been fully addressed. In the present work, we have carried out studies in solution and on surfaces to gain insights into the nature of the radical oxygen species (ROS) generated by a copper(II) coordination compound containing a thioether clip‐phen derivative, 1,3‐bis(1,10‐phenanthrolin‐2‐yloxy)‐N‐(4‐(methylthio)benzylidene)propan‐2‐amine (2CP‐Bz‐SMe), enabling its adsorption/immobilization to gold surfaces. Whereas surface plasmon resonance (SPR) and electrochemistry of the adsorbed complex indicated the formation of a dimeric Cu^I intermediate containing molecular oxygen as a bridging ligand, scanning electrochemical microscopy (SECM) and nuclease assays pointed to the generation of a ROS species. Electron paramagnetic resonance (EPR) data reinforced such conclusions, indicating that radical production was dependent on the amount of oxygen and H₂O₂, thus pointing to a mechanism involving a Fenton‐like reaction that results in the production of OH^..     

Exactly solvable chain of interacting electrons with correlated hopping and pairing

A generalization of the Mattis-Nam model Mattis and Nam (1972) [7], which takes into account a correlated hopping and pairing of electrons, is proposed, its exact solution is obtained. In the framework of the model the stability of the zero energy Majorana fermions localized at the boundaries is studied in the chain in which electrons interact through both the on-site Hubbard interaction and the correlated hopping and pairing. The ground-state phase diagram of the model is calculated, the region of existence of topological states is determined. It is shown that low-energy excitations destroy bonds between electrons in the chain, leading to an insulator state.     

带有媒体影响上限的传染病模型研究

媒体报道对传染病的传播有着一定的影响,但它并不是影响其传播的本质因素.通过建立一个具有分段感染率的传染病模型来刻画媒体报道对传染病传播影响的饱和性.分析了系统各平衡态的局部稳定性,同时利用排除极限环的存在性证明了各平衡态的全局稳定性.最后,通过模拟来验证我们的理论分析.     

二维胶体玻璃中玻色峰与结构无序度的关联

本文从实验上研究了胶体玻璃在相同面密度下随着体系结构无序程度的增加, 振动态密度和玻色峰的变化规律. 通过调制两种不同粒径的温敏性水凝胶的数量比来改变体系的无序程度. 通过分析无序体系的声子模式得到体系的振动特性. 研究发现, 随着无序度的增加, 态密度在低频区域增强、玻色峰增高、玻色峰的峰值向低频区域移动. 不同无序程度的样品引起玻色峰的低频声子模式都表现出准局域的特点, 且低频准局域声子模式与样品中无序结构存在关联.     

Approximation by an iterative method of a low‐Mach model with temperature dependent viscosity

In this work, we prove the existence and the uniqueness of the strong solution of a low‐Mach model, for which the dynamic viscosity of the fluid is a given function of its temperature. The method is based on the convergence study of a sequence towards the solution, for which the rates are also given. The originality of the approach is to consider the system in terms of the temperature and the velocity, leading to a nonlinear temperature equation and the development of some specific tools and results.     

A fast iterative method to find the matrix geometric mean of two HPD matrices

The purpose of this research is to present a novel scheme based on a quick iterative scheme for calculating the matrix geometric mean of two Hermitian positive definite (HPD) matrices. To do this, an iterative scheme with global convergence is constructed for the sign function using a novel three‐step root‐solver. It is proved that the new scheme is convergent and shown to have global convergence behavior for this target, when square matrices having no pure imaginary eigenvalues. Next, the constructed scheme is used and extended through a well‐known identity for the calculation of the matrix geometric mean of two HPD matrices. Ultimately, several experiments are collected to show its usefulness.