Crystallization and Melting Behavior of Polypropylene in Presence of Hydrogenated Dicyclopentadiene

A study of miscibility, morphology, crystallization, and dynamic mechanical properties of polypropylene in the presence of a low-molecular-weight compound, hydrogenated dicyclopentadiene (DCPD), is described. Differential scanning calorimetry (DSC), optical microscopy (OM), and dynamic mechanical analysis (DMA) were used for this purpose. The blends exhibit composition-dependent melting point depression and reduced degree of crystallinity. Isothermal crystallization measurements show that the crystallization takes place at a lower temperature with an increase in crystallization half time with respect to pristine PP. This indicates retardation in crystallization of PP in the blends. The observed changes in the melting and crystallization behaviors are ascribed to the miscibility of the two components. The interaction parameter estimated using the Flory–Huggins equation shows negative values, suggesting the presence of strong specific interaction between PP and DCPD.     

About some quadrature formulas

In this paper, we studied a class of quadrature formulas obtained by using the connection between the monospline functions and the quadrature formulas. For this class we obtain the optimal quadrature formula with regard to the error and we give some inequalities for the remainder term of this optimal quadrature formula.      

Asymptotic expressions for remainder terms of some quadrature rules

Asymptotic expressions for remainder terms of the mid-point, trapezoid and Simpson’s rules are given. Corresponding formulas with finite sums are also given.      

Bounds for the Entries of Matrix Functions with Applications to Preconditioning

Let A be a symmetric matrix and let f be a smooth function defined on an interval containing the spectrum of A. Generalizing a well-known result of Demko, Moss and Smith on the decay of the inverse we show that when A is banded, the entries of f(A)are bounded in an exponentially decaying manner away from the main diagonal. Bounds obtained by representing the entries of f(A)in terms of Riemann-Stieltjes integrals and by approximating such integrals by Gaussian quadrature rules are also considered. Applications of these bounds to preconditioning are suggested and illustrated by a few numerical examples.     

Numerical approximations for the steady‐state waiting times in a GI/G/1 queue

This paper focuses on easily computable numerical approximations for the distribution and moments of the steadystate waiting times in a stable GI/G/1 queue. The approximation methodology is based on the theory of Fredholm integral equations and involves solving a linear system of equations. Numerical experimentation for various M/G/1 and GI/M/1 queues reveals that the methodology results in estimates for the mean and variance of waiting times within ±1% of the corresponding exact values. Comparisons with competing approaches establish that our methodology is not only more accurate, but also more amenable to obtaining waiting time approximations from the operational data. Approximations are also obtained for the distributions of steadystate idle times and interdeparture times. The approximations presented in this paper are intended to be useful in roughcut analysis and design of manufacturing, telecommunications, and computer systems as well as in the verification of the accuracies of inequalities, bounds, and approximations.     

解高维热传导方程的一族高精度的显式差分格式

本文构造出针对三维和四维热传导方程的一族高精度的显格式,其截断误差阶达到Ｏ（τ＾２＋ｈ＾４）,并给出了稳定性条件,通过数值实例,验证了此方法较周顺兴（１９８０年）的结果提高二位以上有效数字。     

The qualitative analysis of a dynamical system of differential equations arising from the study of multilayer scales on pure metals II

We provide a qualitative analysis of the -dimensional dynamical system:

where is an arbitrary positive integer. Under mild algebraic conditions on the constant matrix , we show that every solution , , extends to a solution on , such that , for . Moreover, the difference between any two solutions approaches as . We then use this result to give a complete qualitative analysis of a 3-dimensional dynamical system introduced by F. Gesmundo and F. Viani in modeling parabolic growth of three-oxide scales on pure metals.

     

Green's function for a third-order generalized right focal problem

We determine the Green's function for the third-order three-point generalized right focal boundary value problem

     

The Asymptotic Behavior for Numerical Solution of a Volterra Equation

Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied.The methods are based on the first-second order backward difference methods.The memory term is approximated by the comvolution quadrature and the interpolant quadrature.Discretization of the spatial partial differential operators by the finite element method is also considered.