The normative ontology of the law - Peter Cane's responsibility in law and morality

Implications of Peter Cane's analysis of responsibility in 'Responsibility in Law and Morality' - Cane's preconceptualisation of the 'symbiotic' relationship between law and morality - a principal criticism is that Cane does not develop his seven methodological principles into a more ambitious argument.

Learning mathematics in a classroom community of inquiry

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

A conceptual model of personalized virtual learning environments

The Virtual Learning Environment (VLE) is one of the fastest growing areas in educational technology research and development. In order to achieve learning effectiveness, ideal VLEs should be able to identify learning needs and customize solutions, with or without an instructor to supplement instruction. They are called Personalized VLEs (PVLEs). In order to achieve PVLEs success, comprehensive conceptual models corresponding to PVLEs are essential. Such conceptual modeling development is important because it facilitates early detection and correction of system development errors. Therefore, in order to capture the PVLEs knowledge explicitly, this paper focuses on the development of conceptual models for PVLEs, including models of knowledge primitives in terms of learner, curriculum, and situational models, models of VLEs in general pedagogical bases, and particularly, the definition of the ontology of PVLEs on the constructivist pedagogical principle. Based on those comprehensive conceptual models, a prototyped multiagent-based PVLE has been implemented. A field experiment was conducted to investigate the learning achievements by comparing personalized and non-personalized systems. The result indicates that the PVLE we developed under our comprehensive ontology successfully provides significant learning achievements. These comprehensive models also provide a solid knowledge representation framework for PVLEs development practice, guiding the analysis, design, and development of PVLEs. (c) 2005 Elsevier Ltd. All rights reserved.

Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.