Concept image and concept definition in mathematics with particular reference to limits and continuity

The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept. This may not be globally coherent and may have aspects which are quite different from the formal concept definition. The development of limits and continuity, as taught in secondary school and university, are considered. Various investigations are reported which demonstrate individual concept images differing from the formal theory and containing factors which cause cognitive conflict

Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis

The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students’ responses, we describe students’ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis

Engineering bacteriophage encapsulation processes to improve stability and controlled release using pH responsive formulations

Enteric pathogens form a large part of infectious diseases which contribute to a bulk of the healthcare costs. Enteric infections are usually contracted via the faecal-oral route or through contact with contaminated surfaces. Treatment by antibiotics is becoming increasingly ineffective due to the growing number of antibiotic resistant strains. Anti-microbial resistance poses a serious threat to the future of healthcare worldwide and necessitates the search for alternate forms of therapy. Bacteriophages (phages), are viruses which specifically infect and lyse bacteria. To introduce phages as a viable form of therapy, route of administration needs to be considered carefully. Model phages with broad host ranges are ideal for therapy however oral delivery to the lower gastro-intestinal (GI) poses several challenges. The acidic stomach environment can be detrimental to phages, rendering them inactive during passage. To overcome this challenge and improve the stability of phage during encapsulation and storage, this PhD research has been conducted. pH responsive polymers, Eudragit and alginate were used to develop composite microparticles which protected phage from acidic pH (pH 1-3). A novel method of acidifying oil was developed for crosslinking droplets in vitro to avoid the use of harsh solvent systems that can cause phage inactivation. Platform microfluidic technology was employed for phage encapsulation for the first time. Monodispersed droplets and particles were produced, offering fine-tuning of droplet diameter to tailor the release and pH protection of encapsulated phage. Process scale-up was attempted using membrane emulsification (ME) to produce larger volumes of encapsulated phage. In vitro and in-situ models investigated the efficacy of encapsulated phage-bacterial killing. Industrial scale method of spray drying, and electrospinning were also used to demonstrate the versatility of the formulation. Tableting dry powder phage, showed an effective method for producing solid dosage forms for therapy. Additionally, electrospun phage fibres also showed the potential use of pH responsive formulations in addressing wound infections. Improvement in encapsulated phage storage stability was observed with the addition of trehalose in the formulation. This research underpins the need for testing phage encapsulation for site-specific delivery and offers insight into the potential use of commercially available technologies

AMERICA, ARGUS og Niels

Max Vinner er velkendt blandt træskibsejere blandt andet gennem sin virksomhed som redaktør for T.S.-bladet. Max Vinner har desuden i mange år været en af hovedmændene i bådlauget, der sejler med Nordlandsbåden »Rana«, hvor man gennem sejladsforsøg har indvundet nye erfaringer vedrørende sejlegenskaberne hos vikingetidens fartøjer. Christian Nielsen var meget interesseret i de 3 omtalte fartøjers fælles træk, og Max Vinner har i sin artikel samlet og udnyttet, Christians notater, optegnelser, skitser og tegninger

High precision microfluidic microencapsulation of bacteriophages for enteric delivery

A Salmonella specific bacteriophage Felix O1 (Myoviridae) was microencapsulated in a pH responsive polymer formulation. The formulation incorporated a pH responsive methacrylic acid copolymer Eudragit® S100 (10% (w/v)) with the addition of the biopolymer sodium alginate, the composition of which was varied in the range (0.5% (w/v)e2% (w/v)). The microencapsulation process employed commercially available microfluidic droplet generation devices. We have used readily available low cost microfluidic chips instead of bespoke in-house fabricated glass capillary devices which are accessible only in specialist research facilities. We show that these co-flow microfluidic devices can easily be used to prepare phage encapsulated microparticles making them suitable for use by both the phage research community and industry in order to evaluate and optimise phage compatible formulations for microencapsulation. A novelty of the work reported here is that the size of the generated monodispersed droplets could be precisely controlled in the range 50 mme200 mm by varying the flow rates of the dispersed and continuous phases. Consequently, alginate concentration and microparticle size were shown to influence the phage release profile and the degree of acid protection afforded to phages upon exposure to simulated gastric fluid (SGF). Bigger microparticles (~100 mm) showed better acid protection compared with smaller beads (~50 mm) made from the same formulation. Increasing the alginate composition resulted in improved acid protection of phages for similar particle sizes. The high viscosity formulations containing higher amounts of alginate (e.g. 2% (w/v)) negatively affected ease of droplet generation in the microfluidic device thereby posing a limitation in terms of process scale-up. Felix O1 encapsulated in the formulation containing 10% (w/v) ES100 and 1% (w/v) alginate showed excellent protection upon exposure of the gelled microparticles to SGF (pH 1 for 2 h) without the use of any antacids in the encapsulation matrix. Encapsulated phages previously exposed to SGF (pH 1 for 2 h) were released at elevated pH in simulated intestinal fluid (SIF) and were shown to arrest bacterial growth in the log growth phase. We have therefore demonstrated the microencapsulation of phages using readily available microfluidic chips to produce solid dosage microcapsule forms with a rapid pH triggered release profile suitable for targeted delivery and controlled release in the gastrointestinal tract

First year mathematics undergraduates’ settled images of tangent line

This article was published in the serial, The Journal of Mathematical Behavior [© Elsevier]. The definitive version is available at: http://www.sciencedirect.com/science/article/pii/S0732312310000556This study concerns 182 first year mathematics undergraduates’ perspectives on the tangent line of function graph in the light of a previous study on Year 12 pupils’ perspectives. The aim was the investigation of tangency images that settle after undergraduates’ distancing from the notion for a few months and after their participation in university admission examination. To this end we related the performances of the undergraduates and the pupils in the same questions of a questionnaire; we classified the undergraduates in distinct groups through Latent Class Analysis; and, we examined this classification according to the Analytical Local, Geometrical Global and Intermediate Local perspectives on tangency we had identified among pupils. The findings suggest that more undergraduates than pupils demonstrated intermediate perspectives on tangency. Also, the undergraduates’ settled images were influenced by persistent images about tangency and their prior experience in the context of preparation for and participation in the examination

Clostridium difficile specific bacteriophage microencapsulation within porous Eudragit particles and pH dependent controlled release for colon targeted delivery [Abstract]

Clostridium difficile specific bacteriophage microencapsulation within porous Eudragit particles and pH dependent controlled release for colon targeted delivery [Abstract

Microencapsulation of Clostridium difficile specific bacteriophage using glass microcapillary devices and pH dependent controlled release for colon targeted delivery [Abstract]

Microencapsulation of Clostridium difficile specific bacteriophage using glass microcapillary devices and pH dependent controlled release for colon targeted delivery [Abstract

Microencapsulation of Clostridium difficile specific bacteriophages using microfluidic glass capillary devices for colon delivery using pH triggered release

The prevalence of pathogenic bacteria acquiring multidrug antibiotic resistance is a global health threat to mankind. This has motivated a renewed interest in developing alternatives to conventional antibiotics including bacteriophages (viruses) as therapeutic agents. The bacterium Clostridium difficile causes colon infection and is particularly difficult to treat with existing antibiotics; phage therapy may offer a viable alternative. The punitive environment within the gastrointestinal tract can inactivate orally delivered phages. C. difficile specific bacteriophage, myovirus CDKM9 was encapsulated in a pH responsive polymer (Eudragit® S100 with and without alginate) using a flow focussing glass microcapillary device. Highly monodispersed core-shell microparticles containing phages trapped within the particle core were produced by in situ polymer curing using 4-aminobenzoic acid dissolved in the oil phase. The size of the generated microparticles could be precisely controlled in the range 80 μm to 160 μm through design of the microfluidic device geometry and by varying flow rates of the dispersed and continuous phase. In contrast to free `naked' phages, those encapsulated within the microparticles could withstand a 3 h exposure to simulated gastric fluid at pH 2 and then underwent a subsequent pH triggered burst release at pH 7. The significance of our research is in demonstrating that C. difficile specific phage can be formulated and encapsulated in highly uniform pH responsive microparticles using a microfluidic system. The microparticles were shown to afford significant protection to the encapsulated phage upon prolonged exposure to an acid solution mimicking the human stomach environment. Phage encapsulation and subsequent release kinetics revealed that the microparticles prepared using Eudragit® S100 formulations possess pH responsive characteristics with phage release triggered in an intestinal pH range suitable for therapeutic purposes. The results reported here provide proof-of-concept data supporting the suitability of our approach for colon targeted delivery of phages for therapeutic purposes