The Higher Education Institution and the Construction Industry are yet to define the most appropriate and effective design parameters for E-learning spaces. Those which exist, focus mainly on cost, budget and timely delivery i.e. the process only not the product. An effective approach to E-learning space design is needed to address the problems of space efficiency, effectiveness, quality, innovativeness, performance and client satisfaction. This study aimed to develop a novel methodology for e-learning space design, by investigating: the impact of e-learning on facilities and design; the impact of e-learning on the design of future spaces; the impact of blended learning on space design; designing for the learn anytime, anywhere paradigm; security issues of e-learning and e-learning space design, the levels of design risk in an e-learning infrastructure and inclusive design issues. A Grounded theory approach was used during initial desk studies, synchronized with a three part forum and pilot survey of 33participants. From this process, two hypotheses emerged; firstly, e-learning space design could affect users‘ learning outcomes and secondly that; user‘s learning requirements were different and varied. To investigate further, site based analyses of 11 HEI‘s, 10 interviews and subsequently a questionnaire survey was administered. Users‘ and stakeholders requirements and good examples of e-learning space design were identified. Data were analysed using a mixed-method research design approach. Three main constructs, Space design, Technology and the E-learning Space Design research focus (ELSD focus), emerged as significant components in the development of a novel framework for the design of e-learning spaces. The relationship between the components is such that the design of spaces with consideration of the ELSD research focus would ensure the effective identification, interpretation and delivery of users‘ requirement while maximising the benefits of the adoption of appropriate technology within HEI facilities. This was therefore proposed as the realistic framework/model for future design of E- learning Spaces in HEI campuses. The framework was adapted into a conceptual design guide to provide guidance for future space design. It is expected the study will support the HEI sector globally as it moves towards achieving best practice solutions to future E-learning space design in HEI campuses.

在本篇論文中，我們主要是探討有邊界值的二次微分一積分方程式的解的存在性及唯 一性的問題。在LAKSHRNIKANTHAN 和KHAVANIN的“二次微分一積分方程式及單調法“ （THE METHOD OF MIXED MONOTONY AND SECOND ORDER INTEGRO-DIFFERENTIAL SYSTE M, ANAL.２８（１９８８），１９９－２０６）中，他們利用到混合單調法的技巧： 將不具有任何單調性質的函數擴充到一混合單調函數（亦即此函數對某些變數是單調 非遞減，而對另外某些變數是單調非遞增），然後利用其上解及下解（UPPER, LOWER SOLUTION）來生成兩個單調數列，而此二單調數列具有同時均勻的收斂到原方程式的 解的性質，而完成其存在性，其唯一性則是利用最大原則法（MAXIMUM PRINCIPLE ） ，而完成了他們對二次微分一積分方程式的解的探討。 在上述中，我們認為作者給予擴充函數的性質太強了，故我們對條件放寬，允許它不 是混合單調函數，而另外給了較弱的限制條件，此時我們與證明方法有了改變，我們 用到了SCHAUDER的定點定理（FIXED POINT THEOREM ）：若Ｔ是一區間映到相同區間 的緊緻運算子（COMPACT OPERATOR），則存在一點Ｘ使得Ｔ（Ｘ）＝Ｘ。於是解便可 得到，其唯一性亦是利用最大原則法得到。 最後，我們必須確定我們所使用的擴充函數確實存在，所以我們給了一個關於擴充函 數存在的充分條件來保證它的確存在，而不只是一種理想函數而已。到此，再加上一 些數值結果，我們就完成了整篇的論文。