Smoothing and differentiation of thermogravimetric data of biomass materials

Due to the experimental errors, the chemical effect of minor reactions, and some physical effects of heat and mass transfer, there usually exists much noise in the mass loss data resulted from thermal decomposition experiments, and thus high quality smoothing algorithm plays an important role in obtaining reliable derivative thermogravimetric (DTG) curves required for differential kinetic analysis. In this paper three smoothing methods, i.e. Moving Average smoothing, Gaussian smoothing, and Vondrak smoothing, are investigated in detail for pre-treatment of biomass decomposition data to obtain the DTG curves, and the smoothing results are compared. It is concluded that by choosing reasonable smoothing parameters based on the spectrum analysis of the data, the Gaussian smoothing and Vondrak smoothing can be reliably used to obtain DTG curves. The kinetic parameters calculated from the original TG curves and smoothed DTG curves have excellent agreement, and thus the Gaussian and Vondrak smoothing algorithms can be used directly and accurately in kinetic analysis.This work was sponsored by National Natural Science Foundation of China under Grants 50346038 and 50323005, the China NKBRSF project (No. 2001CB409600), the Anhui Excellent Youth Scientist Fundation (2004–2005), the Specialized Research Fund for the Doctoral Program of Higher Education and the National Key Technologies R&D Programme (2001BA510B09-03).     

On Gaussian Processes Equivalent in Law to Fractional Brownian Motion

We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H1/2. For the case H>1/2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the Hitsuda representation we consider a certain special kind of Gaussian stochastic equation with fractional Brownian motion as noise.     

On the elliptic equation on

In this paper we consider the existence problem for the elliptic equation on , which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.

     

Dependence Between Extreme Values of Discrete and Continuous Time Locally Stationary Gaussian Processes

The maximum of a continuous, locally stationary Gaussian process which satisfies Bermans condition on the long range dependence is compared with the maximum of this process sampled at discrete time points. These two extreme values are asymptotically totally dependent if the grid of the discrete time points is sufficiently dense, and asymptotically independent if the the grid points are sparse.AMS 2000 Subject Classification. Primary—60F05, Secondary—60G15     

An Isometric Embedding of Moebius Band with Positive Gaussian Curvature

The main purpose of this paper is to show that there is an isometric embedding from Moebius band to R4 with positive Gaussian curvature.     

Extended Classical Asymptotic Expansions in the Case of Gaussian Limit Distribution

Let X, X ₁, X ₂,... be a sequence of independent and identically distributed random variables with common distribution function F. Denote by F _n the distribution function of centered and normed sum S _n . Let F belong to the domain of attraction of the standard normal law , that is, lim F _n (x)= (x), as n , uniformly in x . We obtain extended asymptotic expansions for the particular case where the distribution function F has the density p(x) = cx ^––1 ln(x), x > r, where 2, , c > 0, and r > 1. We write the classical asymptotic expansion (in powers of n ^–1/2) and then add new terms of orders n ^–/2 ln n, n ^–/2 ln^-1 n, etc., where 0.     

A problem of prescribing Gaussian curvature on

A class of functions and the corresponding solutions of

are obtained as a special case of the solutions of

where is defined as .

     

修正高斯模型在制备液相色谱收集区间优化中的应用

近年来制备液相色谱得到了越来越广泛的应用。制备液相色谱操作条件的优化对提高其效率及节约成本非常重要。对制备高效液相色谱而言,其样品收集区间的确定及优化是其操作条件优化的重要步骤。该文以修正高斯模型(EMG模型)为理论基础,编写了一个小软件,可有效地帮助用户确定合理的样品收集区间。此软件对制备液相色谱实际应用有积极的指导及参考意义。     

Noise-Induced Transition in a Voltage-Controlled Oscillator Neuron Model

In the presence of Gaussian white noise, we study the properties of voltage-controlled oscillator neuron model and discuss the effects of the additive and multiplicative noise. It is found that the additive noise can accelerate and counterwork the firing of neuron, which depends on the value of central frequency of neuron itself, while multiplicative noise can induce the continuous change or mutation of membrane potential.     

Gaussian Integral Formula for Quaternions Based on Class Operator's Formula of Rotation Group

There exists rare integration formulas over quaternions due to the noncommutativity of quarternions multplication. Based on the class operator's formula of rotation group we derive a Gaussian integral formula for quaternions, which is similar in form to the integration for coherent state's completeness relation.