Effect of the Noise Correlation Time on the Stationary Current of Brownian Particle in a Spatially Symmetric Periodic Potential

We investigate the noise-induced transport of Brownian particle in a deterministic spatial symmetrical periodic potential driven by colored cross correlation between a multiplicative white noise and an additive white noise. We derive the general formula of the stationary current. Based on numerical computation, we found that directed motion of the Brownian particles can be induced by the correlation time τ of cross correlation between the multiplicative noise and the additive noise and the current reversal and the direction of the current is controlled by the τ.     

An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.     

脉冲中立型单种群模型的正周期解

利用拓扑度理论讨论了一类具有脉冲的中立型单种群生态模型,得到了该系统的正周期解存在的充分条件.     

Rotating an interval and a circle

We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the Black Sea.

     

Moderate deviations for randomly perturbed dynamical systems

A Moderate Deviation Principle is established for random processes arising as small random perturbations of one-dimensional dynamical systems of the form X_n=f(X_n−1). Unlike in the Large Deviations Theory the resulting rate function is independent of the underlying noise distribution, and is always quadratic. This allows one to obtain explicit formulae for the asymptotics of probabilities of the process staying in a small tube around the deterministic system. Using these, explicit formulae for the asymptotics of exit times are obtained. Results are specified for the case when the dynamical system is periodic, and imply stability of such systems. Finally, results are applied to the model of density-dependent branching processes.     

Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

Computation of periodic solutions of Hamiltonian systems

This paper attempts to give a practical method to compute global periodic solutions of autonomous Hamiltonian systems of arbitrary finite order. The proposed numerical method is based on continuation of solutions branching from equlibrium points and requires no iterations. Moreover, during computation of one-parameter families of periodic orbits, their possible bifurcations are determined as well.     

How Nature Adapts Chemical Structures to Curved Surfaces

Guided by the symmetry in a natural way, periodic potential surfaces partition the space in solid crystalline compounds. The arrangement of atoms, clusters and molecules obviously follows the (in general) curved shape of these ‘space partitioners’. In structures, the atoms therefore choose only a very limited subset of the infinite set of possible positions. In collective structures the periodic surfaces separate areas of different interactions between atoms, clusters, and molecules. In a certain sense, they can be considered as inner surfaces, a knowledge of which reveals insights into the organization of crystalline matter. There are many good indications that the weakly bonded electrons in the highest occupied orbitals are preferably localized in the region of the space partitioners. Dynamic processes as well can be correlated to the shape of the periodic surfaces. Moreover, the surfaces are didactically very helpful in making accessible the complicated three-dimensional relations in collective structures because the main features are projected onto (although curved) two-dimensional creations. The application of periodic potential surfaces to such a variety of compounds as quartz, brass and alpha-amylose underscores their general significance. Simple qualitative considerations already reveal the manifold relations to animate and inanimate nature through to mathematics, art and architecture. It appears that, in a very universal sense, the adaption of structures to a collective order finds a natural solution through curvature.     

A one-pot direct regioselective iodination of Fischer-Borsche product using periodic acid in PEG-400

A metal-free and greener approach for the one-pot direct iodination and dehydrogenation of dihydrobenzo[a]carbazoles has been developed using periodic acid in polyethylene glycol-400 (PEG-400) under mild condition. This method has been proven to be tolerate to a broad range of functional groups, with good to excellent yields include metal-free inexpensive catalyst, easy work-up, benign reaction condition and high regioselectivity. The solvent has been successfully recycled up to 5 times without any loss of activity in an aqueous medium.