1,114 research outputs found

    On Linearizing Systems of Diffusion Equations

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    We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence transformations of the second generation potential system to derive forms of this system that can be linearized. In turn, these transformations lead to nonlocal mappings that linearize the original system.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

    Continuous and discrete transformations of a one-dimensional porous medium equation

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    We consider the one-dimensional porous medium equation ut=(unux)x+μxunuxu_t=\left (u^nu_x \right )_x+\frac{\mu}{x}u^nu_x. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some cases this porous medium equation is connected with well known equations. With the introduction of a new dependent variable this partial differential equation can be equivalently written as a system of two equations. Point transformations are also sought for this auxiliary system. It turns out that in addition to the continuous point transformations that may be derived by Lie's method, a number of discrete transformations are obtained. In some cases the point transformations which are presented here for the single equation and for the auxiliary system form cyclic groups of finite order

    Development, implementation, and evaluation of an online English placement test at college level: a case study.

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    The primary purpose of the present project was to research the case study of current English placement practices at Intercollege in view of incorporating change, improvement and efficiency, within the framework of current work based learning and applied linguistics (and more particularly English online language testing) research discipline. The review of work based learning and current theories and practices in applied linguistics research discipline helped establish the characteristics of an insider researcher and the research approach and research techniques that would best serve such a project. The review of current theories and practices in second language (L2) teaching and learning in general, and in L2 testing in particular revealed that there is an extensive range of practices: these range from testing discrete points to integrative tasks. Tests are also delivered both in pen-and-paper as well as in electronic form, the latter being either computer based testing (CBT) or computer adaptive testing (CAT). The review of current English placement practices at Intercollege indicated the need for a new English placement test, developed in a scientific way, informed by current theories and practices, based on current test design models and taking advantage of more efficient methods of delivery, and placement. This review also revealed the need for more efficiency in the mode of delivery, administration, marking, reporting and test duration. Finally, this study of the current English placement practices at Intercollege established the need for a placement test that would incorporate a mechanism of continuous testing of reliability and validity as well as improvement. The detailed study of the specific context, setting, particular language programme, resources, test-takers, instructors, etc. informed by current theories and practices in second language (L2) testing online, helped in the development of the New English Placement Test Online (NEPTON) test specifications, and as a consequence, the development of the proposed test itself. The study of test delivery modes and the consideration of the specific work based conditions and requirements. For example administration, delivery, time and money efficiency, urgent need of an improved and more efficient English placement test (EPT) resulted in the selection of computer based testing delivery, with many features of the computer adaptive testing delivery mode incorporated in it such as randomized selection of test items and fewer items. The test item writing and item modération process resulted in the formation of a substantial pool of varied items in different skills, text types, topics, settings, and covering a variety of lexical and grammatical points and communicative, authentic-like situations in ali six levels. The field test which was took place in May 2004 in pen-and-paper form by almost 1200 students in ali three Intercollege campuses helped check the content and the test trial which took place in the period of August-September in its electronic form helped come up with the test cutoff points, and the fine-tuning of the test. The item analysis ensured the appropriateness of ali items. Pre-test questionnaires established test-takers' biographical data and information about test-taker computer familiarity. The test face validity (stakeholders' attitudes and feelings about the NEPTON) was established through the use of pre and post-test questionnaires. Experts in the area Coming, from the three campuses, also studied the test specifications and the test itself (both in its electronic and pen-and-paper format) and completed a questionnaire, thus contributing to the establishment of the test content and construct validity. The test reliability was established through a split half reliability index process and a series of other aspects or processes such as the size of the item bank, the instructions, the moderation process, and the item analysis, which are explained in chapter 5 in more details. The research project consists of two components: (a) The report, which describes the way work based and applied linguistics research approaches were used to investigate the case study of English placement test at college level at Intercollege in Cyprus and to what extent this has broad change, improvement and effìciency to current practices; and (b) The evidence of such a research project, which is the New English Placement Test Online (NEPTON), in other words, the test itself, developed, implemented and evaluated in order to materialize this change, improvement and efficiency aimed at by this project

    A rainfall loading response recorded at 300 meters depth: implications for geological weighing lysimeters

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    Static pore water pressures in confined aquifers vary in response to ground surface loading changes, including precipitation and evaporation. Under certain hydrogeological conditions such aquifers can function as giant natural weighing lysimeters, referenced here as ‘geological weighing lysimeters’. The extent of the land area ‘weighed’ increases with aquifer depth and it is of interest to establish at what depth it is still possible to monitor surface water budgets. An 86 mm rainfall event produced a clear loading signal in a well in western Kansas at 300 m depth. The loading effect is quantitatively consistent with elastic deformation induced by the rainfall mass and suggests that geological weighing lysimeters could operate at considerably greater depths, thereby monitoring water budgets over a significant land area