On the hyperbolic order

We define the hyperbolic order of any locally injective holomorphic function between arbitrary hyperbolic domains of the complex plane and study the relation between the hyperbolic order and the Schwarzian derivative for locally injective holomorphic functions from the unit disk into itself.     

Invariance for stochastic differential systems with time-dependent constraining sets

The first part of this article presents invariance criteria for a stochastic differential equation whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain.     

A new size extensive multireference perturbation theory

A new multireference perturbation series is derived based on the Rayleigh–Schrödinger perturbation theory. It is orbitally invariant. Its computational cost is comparable to the single reference Møller–Plesset perturbation theory. It is demonstrated numerically that the present multireference second‐ and third‐order energies are size extensive by two types of supermolecules composed of H₂ and BH monomers. Spectroscopic constants of as well as the ground state energies of H₂O, NH₂, and CH₂ at three bond lengths have been calculated with the second multireference perturbation theory. The dissociation behaviors of CH₄ and HF have also been investigated. Comparisons with other approximate theoretical models as well as the experimental data have been carried out to show their relative performances. © 2013 Wiley Periodicals, Inc.     

五阶势MKdV方程的一个不变性

§1Introduction Asweknow,Backlundtransformation[1-3]isaverypowerfulwayforfindingnonline evolutionequations.Inrecentdecades,Painlevéanalysis[4]hasbecomeaverypopu methodtoobtainBacklundtransformation.Inreference[5],fordevelopingthetheory Painlevéanalysis,AndrewPickeringintroduceanewexpansionvariableZwhichsatisf thefollowingRicattiSystem:Zx=1-AZ-BZ2,Zt=-C+(AC+Cx)Z-(D-BC)Z2.(1.Astheapplicationofthenewexpansionvaraible,thepotentialfifth-orderMKd equation(PMKdV5)-vxt+(vxxxxx-10k2v2…     

基于交比不变性的投影仪标定

提出了一种新的投影仪标定方法以提高数字光栅投影三维测量中投影仪标定的准确性.该方法结合二次投影技术和交比不变性进行投影仪标定.采用二次投影技术解决投射图案与标定板图案互相干扰的问题;采用交比不变性以避免引入相机的标定误差.接着进行了对比实验,以验证所提方法的有效性.选取需要相机参数的传统投影仪标定方法以及根据全局单应性...     

Gauge functions and Galilean invariance of Lagrangians

A novel method to make Lagrangians Galilean invariant is developed. The method, based on null Lagrangians and their gauge functions, is used to demonstrate the Galilean invariance of the Lagrangian for Newton's law of inertia. It is suggested that this new solution of an old physics problem may have implications and potential applications to all gauge-based theories of physics.     

一类多因素HIV模型的研究

研究了一类多因素HIV模型.建立了一个标准型的DI模型,证明了无病平衡点的局部渐近稳定性和全局渐近稳定性.     

Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system

Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relyingon the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.     

Traveling waves for a reaction–diffusion–advection predator–prey model

In this paper we study a reaction–diffusion–advection predator–prey model in a river. The existence of predator-invasion traveling wave solutions and prey-spread traveling wave solutions in the upstream and downstream directions is established and the corresponding minimal wave speeds are obtained. While some crucial improvements in theoretical methods have been established, the proofs of the existence and nonexistence of such traveling waves are based on Schauder’s fixed-point theorem, LaSalle’s invariance principle and Laplace transform. Based on theoretical results, we investigate the effect of the hydrological and biological factors on minimal wave speeds and hence on the spread of the prey and the invasion of the predator in the river. The linear determinacy of the predator–prey Lotka–Volterra system is compared with nonlinear determinacy of the competitive Lotka–Volterra system to investigate the mechanics of linear and nonlinear determinacy.