The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).     

The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.     

New formulation of restricted growth processes

We present a new formulation of a class of growth models-those which evolve according to an exclusion process. This formulation is based upon a transformation of the probability distribution function which involves Grassmann variables. This method is very general and enables one to derive an exact stochastic differential equation for the model of interest. We describe this method using the traffic model as an example.     

Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

Stimultaneous quantitative analysis using dual capillary columns of different polarities

Complex organic mixtures, such as coal liquefaction and oil shale products and by-products, are comprised of hundreds or thousands of individual components. State-of-the-art high resolution gas chromatography does not always provide sufficient resolution to allow accurate quantitation or identification of many compounds of interest. The concept of dual capillary column chromatography combines the different resolving characteristics of two capillary columns coated with different stationary phases into a single chromatographic run. In this approach, both columns are connected to the same injection port. Analysis of complex mixtures in this fashion can confirm the identification and quantitation of components on two columns of different polarity with little increased analysis time, can provide a means of obtaining quantitative data for individual components which are known to coelute on any one column, and can alert one to unknown coelution problems that would be undetected by gas chromatographic analysis on a single capillary column. Simultaneous dual column analysis was applied to three samples, the neutral polycyclic aromatic hydrocarbon (PAH) fraction of a Solvent Refined Coal-II (SRC-II) heavy distillate, the nitrogen-containing polycyclic aromatic compound (N-PAC) fraction of an SRC-II heavy distillate, and the basic fraction from a shale oil process water. Fused silica capillary columns coated with SE-54 and Durawax 3 were used for the analyses of the heavy distillate, while SE-54 an Carbowax 20M capillary columns were used for the analysis of the process water.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Fractional noise

Fractional noiseN(t),t 0, is a stochastic process for every , and is defined as the fractional derivative or fractional integral of white noise. For = 1 we recover Brownian motion and for = 1/2 we findf ^–1-noise. For 1/2 1, a superposition of fractional noise is related to the fractional diffusion equation.     

Wiener distributions and white noise analysis

The paper describes the structure of a new space of generalized Wiener functionals, , called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process:^N are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented.     

Investigation of the Curing Mechanism in the GPTS/APTS Binder System

The acid catalyzed sol-gel reaction in the mixed binder system, 3-glycidoxypropyltrimethoxysilane (GPTS)/3-aminopropyltriethoxysilane (APTS) was investigated and one step and two step synthesis process were compared. Hydrolysis product was observed using the ¹H, ¹³C NMR and Raman spectra. Especially, based on the Raman spectra, epoxy ring opening was observed, varying the ratio of GPTS to APTS. The two step process made clear sol, while the one step process resulted in a milky suspension. According to the Raman spectra, the epoxy ring opening reaction kinetics proceeded slower in the two step process than one step process. Throughout the two step process, it was possible to apply the binder for the coating of substrate.