浅谈电子天平的选择和使用

针对电子天平的选择、使用和维护中容易忽视的问题进行分析和阐述,并提出了解决办法和正确的操作规程。     

Fluctuations in nonequilibrium systems and broken supersymmetry

The fluctuation-dissipation theorem is not expected to hold for systems that either violate detailed balance or have time-dependent or nonpotential forces. Therefore the relation between response and correlation functions should have contributions due to the nonequilibrium nature. An explicit formula for such a contribution is calculated, which in the present derivation appears as a historydependent term. These relations are the Ward-Takahashi identities of a supersymmetric formulation of the Langevin models, and the new term results from a broken supersymmetry.     

Remarks on the Balance Relations for the Two-Dimensional Navier–Stokes Equation with Random Forcing

We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ξ(t,x) of a stationary solution has a finite exponential moment, and that for any the expectation of the integral of over the level-set , up to a constant factor equals the expectation of the integral of over the same set.     

Note on Monte Carlo methods without necessary detailed balance

Simple criteria for convergence of Monte Carlo algorithms not necessarily requiring detailed balance for any specified transition probability are derived and it is shown that it is possible to view the algorithm as a superimposition of a Brownian motion on configurational space coupled to the transition probabilities. As such, the error contributions due to a particular Monte Carlo algorithm and the integration limits in configuration space must be distinguished from those due to the nonuniform sampling of the Brownian motion, and criteria related to the number of steps required to distinguish these errors are provided for the simplest cases involving one dimension and symmetrical probability distributions.     

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.     

Guaranteeing total balance in Metropolis algorithm Monte Carlo simulations

The condition of detailed balance has long been used as a proxy for the more difficult-to-prove condition of total balance, which along with ergodicity is required to guarantee convergence of a Markov Chain Monte Carlo (MCMC) simulation to the correct probability distribution. However, some simple-to-program update schemes such as the sequential and checkerboard Metropolis algorithms are known not to satisfy detailed balance for such common systems as the Ising model.     

Key steps and intermediates in the catalytic mechanism for the reduction of peroxides by the antioxidant ebselen

Hydrogen peroxide and lipid hydroperoxides are formed during aerobic metabolism and contribute to oxidative stress, a major factor in many diseases and degenerative conditions. Although the selenoenzyme glutathione peroxidase (GPx) affords antioxidant protection in vivo by catalytically reducing harmful peroxides with glutathione, certain conditions benefit from the administration of small-molecule GPx mimetics for additional protection. To date, ebselen has been the most widely studied such compound, but its catalytic mechanism is complex and highly variable with conditions. Progress in elucidating the mechanistic details of its antioxidant activity is described in this review.