Deterministic derivation of non-equilibrium free energy theorems for natural isothermal isobaric systems

The non-equilibrium free energy theorems show how distributions of work along non-equilibrium paths are related to free energy differences between the equilibrium states at the end points of these paths. In this paper we develop a natural way of barostatting a system and give the first deterministic derivation of the Crooks and Jarzynski relations for these isothermal isobaric systems. We illustrate these relations by applying them to molecular dynamics simulations of a model polymer undergoing stretching.     

The A-integral and restricted Ahlfors–Beurling transform

In this paper we prove that the restricted Ahlfors–Beurling transform of a Lebesgue integrable function is A-integrable and derive an analogue of Riesz's equality holds.     

Mathematical justification of viscoelastic beam models by asymptotic methods

The authors derive and justify two models for the bending-stretching of a viscoelastic rod by using the asymptotic expansion method.     

Global Nonparametric Sufficient Optimality Conditions for Semi-Infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η, ρ)-Invex Functions

In this paper, we establish a set of necessary optimality conditions and discuss a fairly large number of sets of global nonparametric sufficient optimality criteria under various generalized (η, ρ)-invexity assumptions for a minmax fractional programming problem with infinitely many nonlinear inequality and equality constraints.     

高阶常微分算子特征值的重数关系

本文借助于边条件空间的几何结构,证明了自伴的高阶常微分算子特征值的解析重数等于几何重数,这是对常型Sturm-Liouville问题相关结果的一个推广.     

Simultaneous iterative methods of asymptotically quasi‐nonexpansive semigroups for split equality common fixed point problem in Banach spaces

In this paper, we present iteration methods to find a solution of asymptotically quasi‐nonexpansive semigroups for a split equality common fixed point in Banach spaces. The results show weak and strong convergence theorem of iteration that improve and extend some recent results.     

解读“微积分算术”

2011年在科学网博客上出现的微积分算术,把抽象而高深的微积分看作函数的算术,只用几步高中代数,就能避开极限而又不失严格讲解微积分.首先,用等式讲解多项式的微积分;然后用不等式讲解显式初等函数的微积分.但是,某些读者可能会存在疑问:真的能让微积分的门槛降低,而又不失严格?它到底具备什么样的特点?对学生群体的定位如何?需要进一步的解读,这就是本文的目的.     

Fluctuation theorems and orbital magnetism in nonequilibrium state

We study Langevin dynamics of a driven charged particle in the presence as well as in the absence of magnetic field. We discuss the validity of various work fluctuation theorems using different model potentials and external drives. We also show that one can generate an orbital magnetic moment in a nonequilibrium state which is absent in equilibrium.      

Some properties of the equations governing a two-dimensional quasi-gasdynamic model of traffic flows

A recently proposed two-dimensional quasi-gasdynamic model of traffic flows is considered. Its Petrovskii parabolicity is analyzed, and the stability of small perturbations against a constant background is investigated. In a nonlinear setting, an energy equality is derived and an energy estimate of the solution is obtained.     

A Possible Generalized Form of Jarzynski Equality

The crucial condition in the derivation of the Jarzynski equality (JE) from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three Gedanken experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.