Some new nonlinear retarded sum-difference inequalities with applications

The main objective of this paper is to establish some new retarded nonlinear sum-difference inequalities with two independent variables, which provide explicit bounds on unknown functions. These inequalities given here can be used as handy tools in the study of boundary value problems in partial difference equations. © 2011 Wang et al; licensee Springer.published_or_final_versio

Generalizations of Hölders inequality

Some generalized Hölder's inequalities for positive as well as negative exponents are obtained.published_or_final_versio

Asynchronous online discussion: Instructor facilitation vs. peer facilitation

Asynchronous online discussion forums have been widely used in schools and universities. They form an integral part of e-learning and blended learning. Many researchers and educators use asynchronous online discussion activity to develop student thinking skills, problem solving skills, and others. There are many factors that may affect student participation in asynchronous online discussion forums such as discussion topics, group size, ground rules of the discussion forums, facilitation skills, and others. We believe that facilitators play an important role in the success of asynchronous online discussion. Usually instructors or students serve as facilitators for online discussion activities. In this study, we explore participants" preference in terms of facilitator (instructor facilitator vs. peer facilitator). In addition, we also found out the reasons for their preference. © 2010 Wing Sum Cheung & Khe Foon Hew.published_or_final_versio

A review of research methodologies used in studies on mobile handheld devices in K-12 and higher education settings

Mobile handheld devices are increasingly being used in education. In this paper, we undertook a review of empirical based articles to summarise the current research regarding the use of mobile handheld devices (personal digital assistants/PDAs, palmtops, and mobile phones) in K-12 and higher education settings. This review was guided by the following four questions: (a) How are mobile handheld devices such as PDAs, palmtops, and mobile phones used by students and teachers? (b) What types of research methods have been applied using such devices? (c) What data collection methods are used in the research? and (d) What research topics have been conducted on these handheld devices in education settings, as well as their related findings? We summarise and discuss some major findings from the research, as well as several limitations of previous empirical studies. We conclude by providing some recommendations for future research related to mobile handheld devices in education settings.published_or_final_versio

Using asynchronous online discussion in education: lessons learned over the last ten years

Over the last ten years we have been exploring the educational use of asynchronous online discussion (AOD) at a university in Singapore. While the advantages of using AOD have been widely reported, the challenges or problems of using it have received lesser attention. This paper briefly reports the three main challenges we faced in actual lesson implementations of AOD in the last ten years. These challenges are “Assignment mode”, “No time for discussion”, and “lack of in-depth critical thinking”. In addition, we also made some suggestions to overcome them.postprin

On Opial's Type Inequalities for An Integral Operator with Homogeneous Kernel

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On Hardy-Pachpatte-Copson's Inequalities

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On inverse Hilbert-type inequalities

This paper deals with new inverse-type Hilbert inequalities. Our results in special cases yield some of the recent results and provide some new estimates on such types of inequalities.published_or_final_versio

An equivalence form of the Brunn-Minkowski inequality for volume differences

In this paper, we establish an equivalence form of the Brunn-Minkowski inequality for volume differences. As an application, we obtain a general and strengthened form of the dual Kneser-Süss inequality. © 2007 The Korean Mathematical Society.published_or_final_versio

Examining facilitators' habits of mind in an asynchronous online discussion environment: A two cases study

Asynchronous online discussion has been widely used by faculty members and students in schools and universities. Previous research has examined how factors such as the discussion activity, knowledge about the discussion topic, and the behaviour of other participants can affect learner participation. This study explored student facilitators' influence in promoting learners' participation in terms of their exhibited habits of mind. The following habits of mind of the facilitators were examined: (a) awareness of own thinking, (b) accurate and seeks accuracy, (c) open minded, (d) taking a position when the situation warrants it, and (e) sensitive to other. A two-cases study methodology approach was used in this study. The habits of "awareness of own thinking" and "open minded" were found to be exhibited more often by the student facilitators in the two cases. When we zoomed into the top 30% of the forums in terms of learners' participation, we also found that the frequency of habits of mind, "awareness of own thinking" and "open minded", were exhibited more often by the facilitators.published_or_final_versio