A-level Mathematics Options – Views of Secondary-level Teachers

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules with the pure maths representing two thirds of the assessment. The applied maths section includes mechanics, statistics and (sometimes) decision maths. A combination of mechanics and statistics tends to be the most popular choice by far. The current study aims to understand how maths teachers in secondary education make decisions regarding the curriculum options and offers useful insight to those currently designing the new A-level specifications.

Semi-structured interviews were conducted with A-level maths teachers representing 27 grammar schools across Northern Ireland. Teachers were generally in agreement regarding the importance of pure maths and the balance between pure and applied within the A-level maths curriculum. A wide variety of opinions existed concerning the applied options. While many believe that the basic mechanics-statistics (M1-S1) combination is most accessible, it was also noted that the M1-M2 combination fits neatly alongside A-level physics. Lack of resources, timetabling constraints and competition with other subjects in the curriculum hinder uptake of A-level Further Maths.

Teachers are very conscious of the need to obtain high grades to benefit both their pupils and the school’s reputation. The move to a linear assessment system in England while Northern Ireland retains the modular system is likely to cause some schools to review their choice of exam board although there is disagreement as to whether a modular or linear system is more advantageous for pupils. The upcoming change in the specification offers an opportunity to refresh the assessment also and reduce the number of leading questions. However, teachers note that there are serious issues with GCSE maths and these have implications for A-level.

Suppression of the high affinity phosphate uptake system:A mechanism of arsenate tolerance in Holcus lanatus L.

In Holcus lanatus L. phosphate and arsenate are taken up by the same transport system. Short-term uptake kinetics of the high affinity arsenate transport system were determined in excised roots of arsenate-tolerant and non-tolerant genotypes. In tolerant plants the V_max of ion uptake in plants grown in phosphate-free media was decreased compared to non-tolerant plants, and the affinity of the uptake system was lower than in the non-tolerant plants. Both the reduction in V_max and the increase in K_m led to reduced arsenate influx into tolerant roots. When the two genotypes were grown in nutrient solution containing high levels of phosphate, there was little change in the uptake kinetics in tolerant plants. In non-tolerant plants, however, there was a marked decrease in the V_max to the level of the tolerant plants but with little change in the K_m. This suggests that the low rate of arsenate uptake over a wide range of differing root phosphate status is due to loss of induction of the synthesis of the arsenate (phosphate) carrier. © 1992 Oxford University Press.

Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Effect of fractional orders in the velocity control of a servo system

The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system's performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

The Erasure of Sex and Gender Minorities in the Healthcare System

Étude de cas / Case study

OPTIMAL UTILIZATION OF SERVICE FACILITY FOR A k-OUT-OF-n SYSTEM WITH REPAIR BY EXTENDING SERVICE TO EXTERNAL CUSTOMERS IN A RETRIAL QUEUE

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability and with probability 1− leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability (< 1) and with probability 1 − leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

Monte Carlo Study of the Growth of L12 ordered domains in fcc A3B binary alloys

A Monte Carlo study of the late time growth of L12-ordered domains in a fcc A3B binary alloy is presented. The energy of the alloy has been modeled by a nearest-neighbor interaction Ising Hamiltonian. The system exhibits a fourfold degenerated ground state and two kinds of interfaces separating ordered domains: flat and curved antiphase boundaries. Two different dynamics are used in the simulations: the standard atom-atom exchange mechanism and the more realistic vacancy-atom exchange mechanism. The results obtained by both methods are compared. In particular we study the time evolution of the excess energy, the structure factor and the mean distance between walls. In the case of atom-atom exchange mechanism anisotropic growth has been found: two characteristic lengths are needed in order to describe the evolution. Contrarily, with the vacancyatom exchange mechanism scaling with a single length holds. Results are contrasted with existing experiments in Cu3Au and theories for anisotropic growth.

Vacancy-assisted domain-growth in asymmetric binary alloys: A Monte Carlo Study

A Monte Carlo simulation study of the vacancy-assisted domain growth in asymmetric binary alloys is presented. The system is modeled using a three-state ABV Hamiltonian which includes an asymmetry term. Our simulated system is a stoichiometric two-dimensional binary alloy with a single vacancy which evolves according to the vacancy-atom exchange mechanism. We obtain that, compared to the symmetric case, the ordering process slows down dramatically. Concerning the asymptotic behavior it is algebraic and characterized by the Allen-Cahn growth exponent x51/2. The late stages of the evolution are preceded by a transient regime strongly affected by both the temperature and the degree of asymmetry of the alloy. The results are discussed and compared to those obtained for the symmetric case.

Comparison between molecular dynamics abd Monte Carlo simulations of an ordering process in a binary alloy

Ordering in a binary alloy is studied by means of a molecular-dynamics (MD) algorithm which allows to reach the domain growth regime. Results are compared with Monte Carlo simulations using a realistic vacancy-atom (MC-VA) mechanism. At low temperatures fast growth with a dynamical exponent x>1/2 is found for MD and MC-VA. The study of a nonequilibrium ordering process with the two methods shows the importance of the nonhomogeneity of the excitations in the system for determining its macroscopic kinetics.

On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

New accelerator system for low temperature curing of elastomers with special reference to NR, NBR and NR/BR blends

The primary objective of this work is to develop an efficient accelerator system for low temperature vulcanization of rubbers. Although xanthates are known to act as accelerators for low temperature vulcanization, a systematic study on the mechanism of vulcanization, the mechanical properties of the vulcanizates at varying temperatures of vulcanization, cure characteristics etc are not reported. Further. xanthate based curing systems are not commonly used because of their chance for premature vulcanization during processing. The proposed study is to develop a novel accelerator system for the low temperature vulcanization of rubbers having enough processing safely. lt is also proposed to develop a method for the prevulcanisation of natural rubber latex at room temperature. As already mentioned the manufacture of rubber products at low temperature will improve its quality and appearance. Also, energy consumption can be reduced by low temperature vulcanization. in addition, low temperature vulcanization will be extremely useful in the area of repair of defective products, since subjecting finished products to high temperatures during the process of repair will adversely affect the quality of the product. Further. room temperature curing accelerator systems will find extensive applications in surface coating industries.

Content Based Image Retrieval System for Malayalam Handwritten Characters

Content Based Image Retrieval is one of the prominent areas in Computer Vision and Image Processing. Recognition of handwritten characters has been a popular area of research for many years and still remains an open problem. The proposed system uses visual image queries for retrieving similar images from database of Malayalam handwritten characters. Local Binary Pattern (LBP) descriptors of the query images are extracted and those features are compared with the features of the images in database for retrieving desired characters. This system with local binary pattern gives excellent retrieval performance

Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G subset R^2, where the second part consists of three steps: In a first step the unknown potential density is replaced by a linear combination of exponentially decreasing basis functions concentrated near the boundary points. In a second step, integration over the boundary partial G is replaced by integration over the tangents at the boundary points such that even analytical expressions for the potential approximations can be obtained. In a third step, finally, the linear algebraic system is solved to determine an approximate density function and the resulting solution of the Stokes boundary value problem. Even not convergent the method leads to an efficient approximation of the form O(h^2) + epsilon, where epsilon can be chosen arbitrarily small.

A molecular and cellular analysis of the circadian system of the cockroach Rhyparobia (Leucophaea) maderae

Circadiane Schrittmacher koordinieren die täglichen Rhythmen in Physiologie und Verhalten in lebenden Organismen. Die Madeira Schabe Rhyparobia maderae (Synonym: Leucophaea maderae) ist ein gut etabliertes Modell, um die neuronalen Mechanismen der circadianen Rhythmen bei Insekten zu studieren. Die akzessorische Medulla (AME) in den optischen Loben des Gehirns wurde als das circadiane Schrittmacherzentrum der Madeira Schabe identifiziert, das circadiane Rhythmen in der Laufaktivität steuert. Über die Neurotransmitter der Eingangswege in das circadiane System der Madeira Schabe ist noch nicht viel bekannt. Das Hauptziel dieser Arbeit war es, mögliche Eingangssignale in die innere Uhr der Madeira Schabe zu bestimmen. An primären Zellkulturen von AME-Neuronen wurden Calcium-Imaging Experimente durchgeführt, um die Neurotransmitter-abhängigen Veränderungen in der intrazellulären Calcium-Konzentration zu messen. Darüber hinaus wurde die Signalkaskade des Neuropeptids Pigment Dispersing Factor (PDF), dem wichtigsten Kopplungsfaktor in circadianen Schrittmachern von Insekten, in Calcium-Imaging und Förster-Resonanzenergietransfer (FRET) Experimenten untersucht. Acetylcholin (ACh) erhöht die intrazelluläre Calcium-Konzentration in der Mehrzahl der circadianen Schrittmacherneurone der Madeiraschabe. Applikation von GABA, Serotonin und Octopamin erhöhten oder reduzierten die intrazelluläre Calcium-Konzentration in den AME-Neuronen, während Histamin und Glutamat die intrazelluläre Calcium-Konzentration ausschließlich reduzierten. Pharmakologische Experimente zeigten, dass die AME-Neurone ACh über ionotrope nikotinische ACh-Rezeptoren detektierten, während GABA über ionotrope GABAA-Rezeptoren und metabotrope GABAB-Rezeptoren detektiert wurde. Diese Ergebnisse deuten darauf hin, dass die circadiane Aktivität der Schabe durch verschiedene Eingänge, einschließlich ACh, GABA, Glutamat, Histamin, Octopamin und Serotonin, moduliert wird. Bei den FRET Studien wurde ein Proteinkinase A (PKA)-basierter FRET Sensor zur Detektion von cyclischem AMP (cAMP) verwendet. Es wurde gezeigt, dass PDF über Adenylylcyclase-abhängige und -unabhängige Signalwege wirken kann. Zusätzlich wurden Laufrad-Assays durchgeführt, um Phasenverschiebungen im Rhythmus der circadianen Laufaktivität zu detektieren, nachdem der Neurotransmitter Histamin zu verschiedenen circadianen Zeiten injiziert wurde. Histamin-Injektionen durch die Komplexaugen der Schabe ergaben eine biphasische Phasenantwortkurve (phase response curve) mit Phasenverzögerungen in der Laufaktivität am späten subjektiven Tag und am Beginn der subjektiven Nacht und Phasenbeschleunigungen in der späten subjektiven Nacht. Schließlich wurde eine extrazelluläre Ableittechnik an lebenden Schaben etabliert, die gleichzeitige Langzeit-Ableitungen von der AME, des Komplexauges (Elektroretinogramm = ERG), und der Beinmuskulatur (Elektromyogramm = EMG) für mehrere Tage ermöglichte. Diese Methode bietet einen Ausgangspunkt für weitere elektrophysiologische Untersuchungen des circadianen Systems der Schabe, in denen Substanzen (z.B. Neurotransmitter und Neuropeptide) analysiert werden können, die einen Einfluss auf den circadianen Rhythmus in der Laufaktivität haben