Some properties of transition matrices for chain binomial models

A chain binomial model is a Markov chain with a transition matrix whose rows are binomial probabilities. Two such chains are presented and illustrated with possible applications. The paper will focus in particular on some interesting properties of the transition matrices

The influence of bulk particulate properties on pneumatic conveying performance

Interest in the use of dense phase conveying has grown considerably in recent years. However, not all products are capable of being conveyed in dense phase and it is often difficult to predict which products have dense phase capability without carrying out pilot conveying trials. The main objective of this work was to investigate the effect of bulk particular properties on pneumatic conveying performance. To achieve this, an extensive programme of conveying trials was carried out and each product tested was subjected to a series of bench scale tests to evaluate the bulk properties of the material. A phase diagram is proposed, based on the aeration properties of a material, which groups together products of similar conveying potential. The phase diagram gives a first indication on the basis of a small sample of material whether or not a product is capable of dense phase conveying. Further, it will predict the most appropriate mode of flow. For products capable of dense phase in a moving bed type flow regime, a further correlation is proposed which predicts the likely conveying performance in the pipeline in terms of mass throughput of product for given conditions based on the air retention characteristics of a product. The correlation has been generalised to extend its applicability to a range of pipeline configurations. The combination of the phase diagram and the correlation for dense phase moving bed type flow (the most commonly used form of dense phase conveying) provides a powerful design tool which will reduce the need for full conveying trials. In addition, the effect of material bulk properties on blow tank performance has also been investigated and a correlation between aeration properties and blow tank discharge characteristics is proposed

Periodic Motions in Banach Space and Applications to Functional-Differential Equations

In establishing the existence of periodic solutions for nonautonomous differential equations of the form x = g(x, t), where g is periodic in t of period for fixed x, it is often convenient to consider the translation operator T(x(t)) = x(t + ). If corresponding to each initial vector chosen in an appropriate region there corresponds a unique solution of our equation, then periodicity may be established by proving the existence of a fixed point under T. This same technique is also useful for more general functional equations and can be extended in a number of interesting ways. In this paper we shall consider a variable type of translation operator which is useful in investigating periodicity for autonomous differential and functional equations where the period involved is less obvious

The dynamics of search, impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem

The nine-dot problem is often used to demonstrate and explain mental impasse, creativity, and out of the box thinking. The present study investigated the interplay of a restricted initial search space, the likelihood of invoking a representational change, and the subsequent constraining of an unrestricted search space. In three experimental conditions, participants worked on different versions of the nine-dot problem that hinted at removing particular sources of difficulty from the standard problem. The hints were incremental such that the first suggested a possible route for a solution attempt; the second additionally indicated the dot at which lines meet on the solution path; and the final condition also provided non-dot locations that appear in the solution path. The results showed that in the experimental conditions, representational change is encountered more quickly and problems are solved more often than for the control group. We propose a cognitive model that focuses on general problem solving heuristics and representational change to explain problem difficulty

Conveying the "right" kind of message: Planning for the first language and culture within the primary classroom

Copyright @ 2008 the author. This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported License.This school-based reflective narrative explores how one inner London primary school raised their awareness of the language needs of Advanced Bilingual Learners (ABL) through an emphasis on developing and celebrating pupils’ first language skills alongside English. It stresses the central role of the teacher in planning language learning environments which empower pupils to talk confidently in their first language without feeling marginalised. In this setting, no one language is viewed as being of a lower status than the other. This paper outlines the teacher’s role in crafting this process by building on pupils’ social and cultural experiences. It further highlights the role of senior management in developing a whole-school ethos which promotes linguistic and cultural diversity, where the identities of multilingual pupils are nurtured. Evidence was collected through participant observation work conducted over a one-year period. The study was predominantly focused within a Year Six classroom (pupils aged between 10-11 years) in a multicultural school where the majority of pupils had Punjabi as their first language. At the time of the study, the school operated within the support framework and principles of a DfES (Department for Education and Skills) National Pilot Project within the UK (2004-2006). The national project was designed to promote a heightened awareness of strategies to support ABL at Key Stage Two (pupils between 7-11 years)

Explicit incidence bounds over general finite fields

Let $\mathbb{F}_{q}$ be a finite field of order $q=p^k$ where $p$ is prime. Let $P$ and $L$ be sets of points and lines respectively in $\mathbb{F}_{q} \times \mathbb{F}_{q}$ with $|P|=|L|=n$. We establish the incidence bound $I(P,L) \leq \gamma n^{3/2 - 1/12838}$, where $\gamma$ is an absolute constant, so long as $P$ satisfies the conditions of being an `antifield'. We define this to mean that the projection of $P$ onto some coordinate axis has no more than half-dimensional interaction with large subfields of $\mathbb{F}_q$. In addition, we give examples of sets satisfying these conditions in the important cases $q=p^2$ and $q=p^4$

The political economy of Russia’s economic transition problems since 1991 and their implications for Russia’s relations with the west

Copyright @ 2001, The Author