Design,Synthesis, and Characterization of Photolabeling Probes for the Study of the Mechanisms of the Antiviral Effects of Ribavirin

Ribavirin, the only small molecule available so far for treating hepatitis‐C‐virus infection, was recently used in an emergency context to treat patients with severe acute respiratory syndrome (SARS) in the early stages of the disease. To study the mechanisms responsible for the antiviral effects of ribavirin by using a photolabeling approach, we designed, synthesized, and characterized the azidotriazole nucleosides 1 and 2 as photolabeling probes of ribavirin. These probes were synthesized either by performing nucleophilic substitution of the corresponding bromotriazole nucleoside with NaN₃ (Scheme 2) or by directly coupling the azidotriazole with the protected ribose sugar (Scheme 4). The azidotriazole nucleosides 1 and 2 showed a fast, clear‐cut photochemical reaction, which suggests that they are promising candidates for use in photolabeling studies.     

Self-Assembly of Highly Stable Zirconium(IV) Coordination Cages with Aggregation Induced Emission Molecular Rotors for Live-Cell Imaging

The self-assembly of highly stable zirconium(IV)-based coordination cages with aggregation induced emission (AIE) molecular rotors for in vitro bio-imaging is reported. The two coordination cages, NUS-100 and NUS-101, are assembled from the highly stable trinuclear zirconium vertices and two flexible carboxyl-decorated tetraphenylethylene (TPE) spacers. Extensive experimental and theoretical results show that the emissive intensity of the coordination cages can be controlled by restricting the dynamics of AIE-active molecular rotors though multiple external stimuli. Because the two coordination cages have excellent chemical stability in aqueous solutions (pH stability: 2–10) and impressive AIE characteristics contributed by the molecular rotors, they can be employed as novel biological fluorescent probes for in vitro live-cell imaging.     

EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.     

Large deviations for the Boussinesq equations under random influences

A Boussinesq model for the Bénard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier–Stokes equations and the transport equation for temperature. Large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion.     

关于一个扰动非线性薛定谔方程的注记

本文讨论了一个扰动非线性薛定谔方程对于Ｓｔｏｋｅｓ波的一类同宿轨道，证明了这类轨道是不存在的。     

A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions

Nonlinear partial differential equation with random Neumann boundary conditions are considered. A stochastic Taylor expansion method is derived to simulate these stochastic systems numerically. As examples, a nonlinear parabolic equation (the real Ginzburg-Landau equation) and a nonlinear hyperbolic equation (the sine-Gordon equation) with random Neumann boundary conditions are solved numerically using a stochastic Taylor expansion method. The impact of boundary noise on the system evolution is also discussed.     

Stochastic modeling of unresolved scales in complex systems

Model uncertainties or simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., ‘unresolved’) due to a lack in our understanding of these mechanisms or limitations in computational power. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. A stochastic scheme is devised to take the effects of unresolved scales into account, in the context of solving nonlinear partial differential equations. An example is presented to demonstrate this strategy. Dedicated to Professor Peter E. Kloeden on the occasion of his 60th birthday