Proof Frameworks: A Way to Get Started

Many mathematics departments have instituted transition-to-proof courses for second semester sophomores to help them learn how to construct proofs and to prepare them for proof-based courses, such as abstract algebra and real analysis. We have developed a way of getting students, who often stare at a blank piece of paper not knowing what to do, to start writing proofs. This is the technique of writing proof frameworks, which is based on the logical structure of the statements of the theorems and associated definitions. Also, in order to unpack the conclusion and know what is to be proved, students need definitions to become “operable.”     

Dynamical behavior of stochastic multigroup S-DI-A epidemic models for the transmission of HIV

In this paper, we study two stochastic multigroup S-DI-A epidemic models for the transmission of HIV. For the stochastic S-DI-A epidemic model with periodic coefficients, we first obtain sufficient conditions for persistence in the mean of the disease. Then in the case of persistence, we show that the model admits a positive T-periodic solution by using Khasminskii theory of periodic solution. Moreover, we establish sufficient conditions for exponential extinction of the infectious disease. For the stochastic S-DI-A epidemic model disturbed by both white and telegraph noises, we first establish sufficient conditions for persistence in the mean of the disease. Then in the case of persistence, we obtain sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solutions by constructing a suitable stochastic Lyapunov function with regime switching and we also obtain sufficient conditions for exponential extinction of the system with regime switching.     

Calcium,a Cell Cycle Commander,Drives Colon Cancer Cell Diffpoptosis

The story of the cell commonder, calcium, reaches into all corners of the cell and controls cell proliferation, differentiation, function, and even death. The calcium-driven eukaryotic revolution is one of the great turning points in the life history, happened about two billion years later when it was converted from a dangerous killer that had to be kept out of cell into the cell master which drives the cell. This review article will take the readers to a tour of tissues chosen to best show the calcium’s many faces (proliferator, differentiator, and killer). The reader will first see calcium and its many helpers, such as the calcium-binding signaler protein calmodulin, directing the key events of the cell cycle. Then the tour will move onto the colon to show calcium driving the proliferation of progenitor cells, then the differentiation and ultimately the programmed death of their progeny. Moreover, the reader will learn of the striking disabling and bypassing of calcium-dependent control mechanisms during carcinogenesis. Finally, recommendations should be taken from the underlying mechanisms through which calcium masters the presistance, progression, and even apoptosis of colorectal cancer cells. Thus, this could be of great interest for designing of chemoprevention protocols.     

The Complexity of Disengagement with Education and Learning: A Case Study of Young Offenders in a Secure Custodial Setting in England

Abstract

This study explored the nature of disengagement in young people serving custodial sentences. This was in order to gain new theoretical insights into strategies for their reengagement with education. This is because 90% of young offenders who drop out of school prior to incarceration are reportedly disengaged (dropout being an indicator of disengagement). This paper reports on a qualitative ethnographic case study in one secure children’s home in England. Semi-structured interviews with 16 incarcerated young people were conducted from which five participated in in-depth case studies along with teachers and care staff. Data were collected as participants engaged with a learning opportunity over a period of time. Extending emerging theory of disengagement, findings showed that disengagement oscillated between both active and passive forms within the same individual and pointed to the need for a range of strategies needed for reengagement. This paper suggests that disengagement is complex where the physical and social context shapes how disengagement manifests. This has pedagogical implications for education in custodial settings and other at-risk children in alternative or mainstream education provision.     

Mathematical models for process commonality under quality and resources breakdown in multistage production

It is essential to manage customers’ diverse desires and to keep manufacturing costs as low as possible for survival in competition and eventually in production. Sharing resources in manufacturing for different products is a vital method of accomplishing this goal. The advantages of using a common process in production are stated in the literature. However, the mathematical models as well as simulation or conceptual models are not sufficient. The main objective of this paper is to develop mathematical models for multiproduct and multistage production under quality and breakdown uncertainties. The idea of the process commonality is incorporated in the proposed models. The models are validated by primary data collected from a Malaysian company and comparison of the timely requirement schedules of earlier MRP II and the proposed models under stable and perfect production environments. An appreciable convergence of the outcomes is observed. However, the proposed models are carrying additional information about the available locations of the parts in a time frame. After validation, the effects of process commonality on cost, capacity and the requirement schedule under uncertainties are examined. It is observed that the use of common processes in manufacturing is always better than the non-commonality scenario in terms of production cost. However, the increase in capacity requirement for commonality designs is higher for an ideal system, while it is less when the system suffers from breakdowns and a quality problem.     

Acceptance of mobile technologies and M-learning by university students: An empirical investigation in higher education

Education and Information Technologies - Mobile-learning (M-learning) apps have grown in popularity and demand in recent years and have become a typical occurrence in modern educational systems,...     

Enhancement of ion transport in porous media by the use of a continuously reoriented electric field

Electromigration in porous media is enhanced by a new type of electrokinetic processing. Compared with a single-oriented electric field, a continuously reoriented electric field was proven to sharply enhance mass transport of several heavy metals in kaolin. The initial concentration of the metals was: Cd: 250 mg/kg; Cu: 250 mg/kg; Ni: 250 mg/kg; Zn: 900 mg/kg. Electric field reorientation was obtained by the use of a fixed anode and a cathode that rotated at different frequencies (0, 0.25, 1.00, 1.25, 2.00, 5.00 and 10.00 r/m). Mass transport evidently increased from 0 r/m to 1.25 r/m, and then decreased as the rotation speed reached 10 r/m. From 0 r/m to 1.25 r/m, mass transport increased 2.87 times for Cd, 3.17 times for Cu, 2.11 times for Ni, and 4.13 times for Zn. We suggest that continuous reorientation of the electric field facilitates the advance of ions through kaolin pores, minimizing the retardation effect caused by media tortuosity.     

Redefining ‘community’ through collaboration and co-teaching: a case study of an ESOL specialist,a literacy specialist,and a fifth-grade teacher

This article explores the development of a professional learning community through a case study of three teachers – an ESOL specialist, a literacy specialist, and a fifth-grade teacher – who engaged in co-teaching and collaboration. The emerging community of practice offered these teachers a space to learn and problem-solve by utilizing their specialized disciplinary knowledge of students and expanding the application of reading strategies during language arts. Concurrently, opportunities for revising curriculum and instruction remained unrealized, as teachers struggled to negotiate roles and responsibilities within the top-down administratively initiated collaboration that required redefining their professional community. Implications and recommendations are discussed.     

Addressing institutional potential loss of records and knowledge in Africa: The case of the ECA institutional repository – A knowledge base on African socio-economic development

In its 50 years of existence, the United Nations Economic Commission of Africa (UNECA) has created and holds a vast quantity of information and knowledge in a variety of formats, including printed and electronic. These represent the corporate memory, providing historical evidence of its actions and decisions. The information resources include published materials such as flagship publications, journal articles, conference proceedings, technical reports, mission reports, annual reports, working papers, policy briefs, speeches and other grey literature, all which outline important research or decisions that have been made on the economic and social development in Africa. In 2009 the Library was awarded seed funding to implement the ECA Institutional Repository (IR). This paper discusses the various activities that have been undertaken to realize the project including; highly customized Dspace installation to support the MARC21 metadata, digitization, migration of metadata from the Library Integrated Management System (HORIZON) and, customization of the Dspace workflow to enable review of imported records. The paper also highlights lessons learnt, challenges and some of the best practices developed throughout the implementation and roll out of the ECA IR project. The Institutional Repository at http://repository.uneca.org/ is the first of its kind within the United Nations Secretariat and offers unique knowledge and information not available elsewhere pertaining to regional programmes, decisions and resolutions promoting social and economic development of Africa.