Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence

Densities and viscosities of propylene carbonate with aromatic hydrocarbons (benzene, 1,4-dimethylbenzene and ethylbenzene) at 288.15, 298.15 and 308.15 K

Densities and viscosities of the binary mixtures of propylene carbonate with benzene, 1,4-dimethylbenzene and ethylbenzene were measured over the entire mole fraction range at 288.15, 298.15 and 308.15?K. Using the experimental values of densities and viscosities the excess molar volumes and viscosity deviations were calculated. The results were fitted by Redlich–Kister equation. The results were discussed in terms of intermolecular interactions.     

多孔径扫描波面恢复技术的精度评定及影响因素

多孔径扫描波面恢复技术是一项新的高精度大孔径面形检测手段.本文从建立波面恢复精度的评价标准出发,结合实测结果进行讨论,并对影响精度的两个重要因素即拼接模式及拼接区大小进行分析.     

Occurrence, Repetition and Matching of Patterns in the Low-temperature Ising Model

We continue our study of the exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low-temperature plus-phase of the Ising model, we prove exponential laws with error bounds for occurrence, return, waiting and matching times. Moreover we obtain a Poisson law for the number of occurrences of large cylindrical events and a Gumbel law for the maximal overlap between two independent copies. As a by-product, we derive precise fluctuation results for the logarithm of waiting and return times. The main technical tool we use, in order to control mixing, is disagreement percolation     

A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction

We consider the propagation of a combustion front resulting from the gasless combustion of a condensed state fuel. The propagation of the front, essentially a premixed laminar flame, is supported by an exothermic reaction subject to possible heat loss through a competitive endothermic reaction. The dynamics of the endothermic process inducing the heat loss strongly depend on the temperature and the local fuel concentration. Through an analysis based on high activation energy, the steady-state values of the final burnt temperature as well as the burning velocity are obtained, and the control parameters are identified. Using a linear perturbation method, we assess the stability of the propagating front and obtain a condition for oscillatory behaviour. The critical parameter values for the transition from steady to oscillatory burning speeds are identified. The results represent a generalization of those obtained by Matkowsky and Sivashinsky to include the effects of heat loss induced by a competitive endothermic reaction.     

Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory

We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the particle microstates is then examined in the large-n limit. Using the theory of large deviations, we show that if the initial macroscopic average is constrained to be near a given value, y, then the macroscopic average at time t converges in probability as n to a value _t(y) given explicitly in terms of a canonical expectation. Some general features of the graph of _t(y) versus t are examined, particularly in regard to continuity, symmetry, and convergence.     

An exactly soluble case of the triangular ising model in a magnetic field

An anisotropic triangular Ising model in which the first- and second-order parameters and the field parameters are functionally related is solved exactly by representing the distribution of the atom patterns in terms of a suitably constructed Markov process. The probabilities of patterns, defined as the probabilities generated by this process, are a mathematically tractable alternative to the classical representation of these probabilities in terms of the partition function. The interaction and field parameters of this Ising model, its magnetization, free energy, and its nearest neighbor correlation functions, are expressed in terms of the parameters of this Markov process. Special cases are worked out in detail and numerical examples are given.     

关于多指标变量大数律尾概率级数的完全收敛性

本文对ｉｄ多指标随机变量序列｛Ｘｋ;ｋ∈Ｎｄ｝（ｄ≥２）的部分和Ｓｎ＝∑ｋ≤ｎＸｋ及Ｈ（ｔ）↑＋∞,（ｔ→＋∞）,提出并讨论了Порохоров的３个问题（ｄ≥２）,并讨论了多指标随机变量和的完全收敛性．     

On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators

Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by μ. We prove that the uniform law of large numbers holds if the class has an envelope function that is μ-integrable, or if is bounded in L _p(μ) for some p>1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of the class in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE) and to prove consistency for a class of simple M-estimators. This revised version was published online in June 2006 with corrections to the Cover Date.