Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅲ: A New Multiple Entanglement Model to Predict the Dependence of Linear Viscoelastic Function (η_0, Ψ_(10)~0,η_(ext)~0) on the Ranges of Primary Molecular Weights and th

It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers

The Dependence Problem for a Class of Polynomial Maps in Dimension Four

Let h be a polynomial in four variables with the singular Hessian Hh and the gradient ▽h and R be a nonzero relation of ▽h. Set H = ▽R（▽h）. We prove that the components of H are linearly dependent when rkHh ≤ 2 and give a necessary and sufficient condition for the components of H to be linearly dependent when rkHh = 3.

A Production Inventory Model of Constant Production Rate and Demand of Level Dependent Linear Trend

The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constant production rate which stops attaining a desired level of inventories and that is the highest level of inventories. Production starts with a buffer stock and without any sort of backlogs. Due to the market demand and product’s decay, the inventory reduces to the level of buffer stock where again the production cycle starts. With a numerical search procedure the proof of the proposed model has been shown. The objective of the model is to obtain the total average optimum inventory cost and optimum ordering cycle.

Estimation of Maximal Dimensions of Commutable Matrix Spaces

In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.

ON THE DEPENDENT PROPERTY OF SOLUTIONS FOR HIGHER ORDER PERIODIC DIFFERENTIAL EQUATIONS

This article investigates the property of linearly dependence of solutions f（z） and f（z ＋ 2πi） for higher order linear differential equations with entire periodic coefficients.

Denoising of X-ray pulsar observed profile using biorthogonal lifting wavelet transform

In X-ray pulsar-based navigation, strong X-ray background noise leads to a low signal-to-noise ratio（SNR） of the observed profile, which consequently makes it very difficult to obtain an accurate pulse phase that directly determines the navigation precision. This signifies the necessity of denoising of the observed profile. Considering that the ultimate goal of denoising is to enhance the pulse phase estimation, a profile denoising algorithm is proposed by fusing the biorthogonal lifting wavelet transform of the linear phase characteristic with the thresholding technique. The statistical properties of X-ray background noise after epoch folding are studied. Then a wavelet-scale dependent threshold is introduced to overcome correlations between wavelet coefficients. Moreover, a modified hyperbola shrinking function is presented to remove the impulsive oscillations of the observed profile. The results of numerical simulations and real data experiments indicate that the proposed method can effectively improve SNR of the observed profile and pulse phase estimation accuracy, especially in short observation durations. And it also outperforms the Donoho thresholding strategy normally used in combination with the orthogonal discrete wavelet transform.

The optimum linear data fusion for dependent observations

Data fusion is one of the attractive topic in sonar signal processing. Decision level data fusion of multi-sensor (multi-array) system is described in this paper. Follow the discussion in Ref. [1], the optimum linear data fusion algorithm for N dependent observations is derived. It is proved that the estimation error of data fusion is not greater than that of individual components. The expression of estimation error and weight coefficients are presented. The results of numerical calculation and some examples are illustrated. The effect of dependence of observation data for the final estimation error is presented.

Central Limit Theorems for Asymptotically Negatively Associated Random Fields

The aim of this paper is to investigate the central limit theorems for asymptotically negatively dependent random fields under lower moment conditions or the Lindeberg condition. Results obtained improve a central limit theorem of Roussas[11]for negatively associated fields and the main results of Su and Chi [18]. and also include a central limit theorem for weakly negatively associated random variables similar to that of Burton et al.[20].