On improvements of the Rozanova's inequality

<p>Abstract</p> <p>In the present paper, we establish some new Rozanova's type integral inequalities involving higher-order partial derivatives. The results in special cases yield some of the interrelated results on Rozanova's inequality and provide new estimates on inequalities of this type.</p> <p> <b>MS (2000) Subject Classifiication: </b>26D15.</p

Some new nonlinear retarded sum-difference inequalities with applications

<p>Abstract</p> <p>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.</p> <p> <b>2000 Mathematics Subject Classification</b>: 26D10; 26D15; 26D20.</p

Pre-primary education in Hong Kong : the evolution of governance and policy tools

published_or_final_versionPolitics and Public AdministrationMasterMaster of Public Administratio

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. Introduction In the last few years, mobile handheld devices have emerged as a tool for teachers and students to use in K-12 and higher education settings. In this article, we adapted Becta&apos;s definition (cited in One of the promises that mobile handheld devices hold is that of a one device to student ratio The purpose of this article is to review the empirical literature pertaining to the use of mobile handheld devices in K-12 and higher education settings. In this article, we limit our review of handhelds to devices such as personal digital assistants (PDAs), 154 Australasian Journal of Educational Technology, 2009, 25(2) palmtops, and mobile phones. PDAs are shirt pocket sized devices equipped with computer capabilities Significance of this review This review of research not only helps researchers and educators identify the contemporary research topics, research methodologies, and usage of mobile handheld devices in K-12 and higher education settings, but also suggests directions for future research as well as some guidelines for the nature of that research. Method Searching and selection procedures The search for relevant literature was completed in two stages. First, we examined peer reviewed articles that we found in electronic databases using keyword searches including mobile learning, wireless learning, and handheld devices. We used Academic Search Premier, Business Source Premier, Communication and Mass Media Complete, ERIC, Library, Information Science and Technology Abstracts, and PsycARTICLES. In the second stage, we used the &quot;snowball&quot; method by searching for journal articles, as well as articles presented in peer reviewed conferences that are cited in some of the articles that we had read. Altogether, as at 28 December, 2008, we read 136 articles and deleted 92. The 92 articles were discarded because they were opinion papers, conceptual articles, non-empirical descriptions of program implementations, and literature reviews. The Appendix includes the remaining articles (n=44) which we included in our review of research. The 44 articles are listed according to the authors, year of publication, purpose, research method, data collection method, and context. Data analysis The basic unit of analysis was the individual empirical article. To answer the first research question, &quot;How are mobile handheld devices such as PDAs, palmtops, and mobile phones used by students and teachers?&quot;, we used Churchill and Churchill&apos;s (2007) framework to guide our initial analysis and coding. This framework originally explicates a set of five ways in which PDAs may be used, namely as: (a) multimedia access tools, (b) communication tools, (c) capture tools, (d) representational tools, and (e) analytical tools. (See the Results section for a fuller description.) Although Churchill and Churchill&apos;s framework was used a priori, we did not forcefully impose any of the coding categories onto our data corpus. During the course of our analysis, we also allowed for new categories (if any) to emerge inductively. To address the second, third, and fourth research questions, &quot;What types of research methods have been applied using these handheld devices?&quot;, &quot;What data collection methods are used in the research?&quot;, and &quot;What research topics have been conducted on these mobile handheld devices?&quot;, we employed the constant-comparative or grounded approach espoused by 156 Australasian Journal of Educational Technology, 2009, 25(2) Results Uses of mobile handheld devices At the conclusion of our analysis, we had seven major categories of the uses of handheld devices such as PDAs, palmtops, and mobile phones in education. The seven categories include: (a) multimedia access tool, (b) communication tool, (c) capture tool, (d) representational tool, (e) analytical tool, (f) assessment tool, and (g) task managing tool. The first five categories originated from Churchill and Churchill&apos;s Multimedia access tools This refers to employing the PDAs, palmtops, or mobile phones as tools for accessing multimedia resources such as e-books, databases, web pages, PowerPoint presentations, audio files and video clips Communication tools This refers to employing the handheld devices to communicate information from one person to others Capture tools This refers to utilising the devices to capture various data and media Representational tools PDAs, palmtops, or mobile phones may also be used by students to create representations that demonstrate or showcase their thinking, ideas, experiences and knowledge Analytical tools This refers to employing the devices to manipulate certain data or variables such as graphic calculators Assessment tools This refers to the employment of handhelds for students to answer examination questions, tests, or quizzes. For example, Task management tools This refers to utilising the devices as personal information managers which store and organise a user&apos;s address book, contact information, calendar, task lists (i.e. &apos;to-do-list&apos;), documenting or recording student grades, attendance rates, or submission of homework (e.g. Further analysis suggested that the three most frequent uses of the handhelds centered on utilising the devices as communication (21.8%), multimedia access (20.5%), and task management (17.9%) tools. These were followed by the use of handhelds as assessment (14.1%), capture tools (12.8%), representational (6.4%), and analytical tools (6.4%) (Se

Note on weighted Carleman-type inequality

A double inequality involving the constant e is proved by using an inequality between the logarithmic mean and arithmetic mean. As an application, we generalize the weighted Carleman-type inequality