The interfacial conformation of polypropylene glycols and foam behaviour

The foam behaviour of low molecular weight polypropylene glycols (PPG) was investigated as a function of concentration and molecular weight (190–2000 g mol⁻¹). For each polypropylene glycol, foam stability increases with concentration and passes through a maximum, beyond which foamability is suppressed as the solubility limit of the glycol is exceeded and droplets of glycol form. Light-scattering data as well as static and dynamic surface tension results provide the key information leading to these interpretations. A maximum in foamability was observed for the PPG molecules with increasing molecular weight (caused by a change in molecular conformation at the interface). This suppresses the Marangoni effect and leads to a decrease in foam stability.     

The Effects of a Study‐Group Process on the Implementation of Reform in Mathematics Education

In each of three consecutive years, 16 teachers were admitted to a program in which they participated in a study group to reform their teaching practices in mathematics. The 48 (total) elementary school teachers in this program were selected to ensure diversity of setting— urban and suburban, as well as public and parochial. Teachers routinely met with the study group for 1 year, engaging in follow‐up activities after that year. Surveys, interviews, and site visits showed that teachers underwent significant changes in their knowledge, beliefs, and teaching practices and were attempting to implement reform consistent with current standards. Teachers with 11 to 25 years of experience demonstrated the greatest changes. Long‐term effects of the program and its impact on colleagues within the building and district have yet to be studied.     

Control of the block copolymer morphology in templated epoxy thermosets

It has been found that by the addition of low concentrations of an amphiphilic block copolymer to an epoxy resin, novel disordered morphologies can be formed and preserved through curing. This article will focus on characterizing the influence of the block copolymer and casting solvent on the templated morphology achieved in the thermoset sample. The ultimate goal of this work is to determine the parameters that would control the microphase morphology produced. Epoxy resins blended with a series of amphiphilic block copolymers based on hydrogenated polyisoprene (polyethylene-alt-propylene or PEP) and polyethylene oxide (PEO), specifically, were investigated. In this article, the cure-induced order–order phase transition from the spherical to wormlike micelle morphology will also be discussed. It is proposed that the formation of the wormlike micelle structure from the spherical micelle structure is similar to the phase transition behavior that occurs in dilute block copolymer solutions as a function of the influence of the solvent on micelle morphology. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3338–3348, 2007     

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.     

A Penrose-like inequality for maximal asymptotically flat spin initial data sets

We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary, dimensionless geometric constants and some normalized Sobolev ratio.     

Element Pools and Numeric Coprocessors for Linear Programming on Personal Computers

This note discusses the need to use various data-compaction schemes in the implementation of sophisticated large-scale linear programming codes on modest personal computers. It demonstrates a method whereby the overhead of using these schemes is significantly reduced on Intel 80 x 86 processors.     

Expert Rule Versus Majority Rule Under Partial Information, II

The main purpose of this paper is clarifying the connection between some characteristics of a deciding body and the probability of its making correct decisions. In our model a group of decision makers is required to select one of two alternatives. We assume the probabilities of the decision makers being correct are independent random variables distributed according to the same given distribution rule. This distribution belongs to a general family, containing the uniform distribution as a particular case. We investigate the behavior of the probability of the expert rule being optimal, as well as that of the majority rule, both as functions of the distribution parameter and the group size. The main result is that for any value of the distribution parameter the expert rule is far more likely to be optimal than the majority rule, especially as the deciding body becomes larger.     

Positive and Nontrivial Solutions for the Urysohn Integral Equation

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.     

Estimates for transition probabilities on a compact manifold

The purpose of this note is to describe a procedure for transferring familiar estimates for transition probabilities on RN to transition probabilities on compact manifolds.