COMPLEXATION BEHAVIOR OF POLY(ACRYLIC ACID) AND POLY(ETHYLENE OXIDE) IN WATER AND WATER-METHANOL

To investigate the effects of solvent type and temperature on the interpolymer complexation via hydrogen bonding, a study was made on the complex system of poly(acrylic acid) (PAA) and poly(ethylene oxide) (PEO) in two kinds of solvent systems, pure water and water-MeOH (30 wt%) mixed solvent, at various temperatures using the Ubbelohde viscometer, pH-meter, and UV spectrophotometer. The repeating unit mole ratio at the most optimum complexation as confirmed by the reduced viscosity measurement was shifted from [PEO]/[PAA] ≈ 1.25:1 to 1.5:1 by the addition of methanol to water. From the UV measurement, the deviation from the “isosbestic point” (where the absorbance of the solution remains constant) has presented another evidence for the solvent effect on complexation. In addition, the analysis of the changes in thermodynamic properties upon complexation as well as the fraction of carboxyls associated with PEO oxygens and the complex stability constant as estimated by potentiometric titration at several temperatures reveals that the complex formation in mixed solvent became more unfavorable compared to that in pure solvent at high temperatures above 30°C. This could be explained by considering that in water the hydrophobic interaction as well as the hydrogen bonding may greatly contribute to the stabilization of the polymer complex formed, while in water-methanol the main stabilizing force would be the hydrogen bonding alone.     

A research on the grey prediction model GM(1,n)

The grey theory can be applied in the research of prediction, decision-making and control, especially in prediction. The primary characteristic of a grey system is the incompleteness of information. A grey system could be whitened by way of inserting more messages in itself and its accuracy of prediction could be raised. The solution to the existing grey prediction model GM(1,n) is inaccurate and then its prediction accuracy cannot be expected. To solve the existing GM(1,n) by assuming step by step the first order accumulated generating operation data of the associated series to be constants is incorrect. The existing model GM(1,n) is seriously wrong even for a system having a nonnegative associated series with constant entries. There are currently only a few wrong papers based on the existing GM(1,n) model to be published. Almost all the improved prediction models based on the existing GM(1,n) model are correct. For example, the improved models are correct by convolution integral or fitting their forcing terms by several elementary functions. The algorithm of GMC(1,n) is applied to explain why the existing GM(1,n) model is incorrect in this article.     

Diffusiophoresis in a concentrated suspension of colloidal spheres in nonelectrolyte gradients

The diffusiophoretic motion of a homogeneous suspension of identical spherical particles is considered under conditions of small Reynolds and Peclet numbers. The effects of interaction of the individual particles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of mass and momentum are solved for each cell, in which a spherical particle is envisaged to be surrounded by a concentric shell of suspending fluid, and the diffusiophoretic velocity of the particle is calculated for various cases. Analytical expressions of this mean particle velocity are obtained in closed form as functions of the volume fraction of the particles. Comparisons between the ensemble-averaged diffusiophoretic velocity of a test particle in a dilute suspension and our cell-model results are made. Received: 30 June 1999 Accepted: 8 December 1999     

The birth of the X-ray refractive lens

In the X-ray region, no optics based on the principle of refraction existed since the discovery of the X-rays by Röentgen in November 1985, although mirrors and zone-plates that use the principle of reflection and diffraction have been employed. The idea of a practical X-ray refractive lens was first disclosed in February 1994, i.e., just one year before the centenary of the discovery of X-rays. The present paper reviews why the X-ray lens did not appear for so many years, and how the design was born. The paper also discusses technologies to be developed for high performance X-ray lenses, and advantages of refractive X-ray lenses over other X-ray optics.     

2013 unit vectors in the plane

Given a norm in the plane and 2013 unit vectors in this norm, there is a signed sum of these vectors whose norm is at most one.     

The MacLane class and complex differential equations in the unit disk

The interaction between the coefficients and solutions for linear differential equations and for Riccati differential equations is investigated in the unit disk in terms of their asymptotic values as described by the MacLane class. This interaction is further explored within the context of a meromorphic version of the MacLane class.     

Scheduling unit time jobs with integer release dates to minimize the weighted number of tardy jobs

Consider a set of n unit time jobs, each one having a release date, a due date, both nonnegative integers, and a weight, a positive real number. Given a set of m parallel machines, we describe an algorithm for finding schedules with minimum weighted number of tardy jobs. The complexity of the proposed algorithm is O(n²\frac(1+logm)m)O(n^{2}\frac{(1+\log m)}{m}) . The best previous algorithm for this problem has complexity O(mn ³) and employs network flow techniques. Our method is based on a characterization for schedules of this type and employs graph theoretic tools.     

On minimum rank and zero forcing sets of a graph

For a graph G on n vertices and a field F, the minimum rank of G over F, written as mr^F(G), is the smallest possible rank over all n×n symmetric matrices over F whose (i,j)th entry (for ) is nonzero whenever ij is an edge in G and is zero otherwise. The maximum nullity of G over F is M^F(G)=n-mr^F(G). The minimum rank problem of a graph G is to determine mr^F(G) (or equivalently, M^F(G)). This problem has received considerable attention over the years. In [F. Barioli, W. Barrett, S. Butler, S.M. Cioab?, D. Cvetkovi?, S.M. Fallat, C. Godsil, W. Haemers, L. Hogben, R. Mikkelson, S. Narayan, O. Pryporova, I. Sciriha, W. So, D. Stevanovi?, H. van der Holst, K.V. Meulen, A.W. Wehe, AIM Minimum Rank-Special Graphs Work Group, Zero forcing sets and the minimum rank of graphs, Linear Algebra Appl. 428 (2008) 1628-1648], a new graph parameter Z(G), the zero forcing number, was introduced to bound M^F(G) from above. The authors posted an attractive question: What is the class of graphs G for which Z(G)=M^F(G) for some field F? This paper focuses on exploring the above question.