Splines in Numerical Integration

AMS Subj. Classification: 65D07, 65D30.

Fracture properties of silicon carbide thin films by bulge test of long rectangular membrane

This paper reports the mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates. Using bulge testing combined with a refined load-deflection model of long rectangular membranes, which takes into account the bending stiffness and prestress of the membrane material, the Young's modulus, prestress, and fracture strength for the 3C-SiC thin films with thicknesses of 0.40 and 1.42 mu m were extracted. The stress distribution in the membranes under a load was calculated analytically. The prestresses for the two films were 322 +/- 47 and 201 +/- 34 MPa, respectively. The thinner 3C-SiC film with a strong (111) orientation has a plane-gstrain moduli of 415 +/- 61 GPa, whereas the thicker film with a mixture of both (111) and (110) orientations exhibited a plane-strain moduli of 329 +/- 49 GPa. The corresponding fracture strengths for the two kinds of SiC films were 6.49 +/- 0.88 and 3.16 +/- 0.38 GPa, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over edge, surface, and volume of the specimens and were fitted with Weibull distribution function. For the 0.40-mu m-thick membranes, the surface integration has a better agreement between the data and the model, implying that the surface flaws are the dominant fracture origin. For the 1.42-mu m-thick membranes, the surface integration presented only a slightly better fitting quality than the other two, and therefore, it is difficult to rule out unambiguously the effects of the volume and edge flaws.

Where is the rate in the rule?

A well-developed understanding of rate is foundational to conceptual understanding of introductory calculus. Many students achieve procedural competence with the application of rules for differentiation without developing an awareness of the connection between derivative and rate. In addition, rate-related reasoning is needed to make informed decisions in many everyday applications of rate. This paper reports on additional data collected during interviews for a project investigating the different ways rate may be experienced by pre-calculus students. Many researchers (for example Kaput, 1999) have suggested that the conceptual understanding of function may be enhanced through the presentation and exploration of multiple representations of a variety of functions. In this paper, one section of each interview is considered in detail to evaluate the participants’ understanding in a specific rate context. Participants were asked to discuss a dynamic geometry simulation of a blind on two different windows one rectangular and the other not. Detailed analysis of the video-record of each participant’s interview provides insights into their perceptions of rate in several different representations. In the sections below, the conceptual framework is described; details of the interviews and the computer-based simulation are provided; and the analysis of the data is discussed.

Rule learning and extraction using a hybrid neural network : a case study on fault detection and diagnosis

A hybrid network, based on the integration of Fuzzy ARTMAP (FAM) and the Rectangular Basis Function Network (RecBFN), is proposed for rule learning and extraction problems. The underlying idea for such integration is that FAM operates as a classifier to cluster data samples based on similarity, while the RecBFN acts as a “compressor” to extract and refine knowledge learned by the trained FAM network. The hybrid network is capable of classifying data samples incrementally as well as of acquiring rules directly from data samples for explaining its predictions. To evaluate the effectiveness of the hybrid network, it is applied to a fault detection and diagnosis task by using a set of real sensor data collected from a Circulating Water (CW) system in a power generation plant. The rules extracted from the network are analyzed and discussed, and are found to be in agreement with experts’ opinions used in maintaining the CW system.

Young children as rule makers

Young children engage in a constant process of negotiating and constructing rules, utilizing these rules as cultural resources to manage their social interactions. This paper examines how young children make sense of, and also construct, rules within one early childhood classroom. This paper draws on a recent study conducted in Australia, in which video-recorded episodes of young children’s talk-in-interaction were examined. Analysis revealed four interactional practices that the children used, including manipulating materials and places to claim ownership of resources within the play space; developing or using pre-existing rules and social orders to control the interactions of their peers; strategically using language to regulate the actions of those around them; and creating and using membership categories such as ‘car owner’ or ‘team member’ to include or exclude others and also to control and participate in the unfolding interaction. While the classroom setting was framed within adult conceptions and regulations, analysis of the children’s interaction demonstrated their co-constructions of social order and imposition of their own forms of rules. Young children negotiated both adult constructed social order and also their own peer constructed social order, drawing upon various rules within both social orders as cultural resources by which they managed their interaction.

Improvements to the design of Litesteel Beams undergoing lateral distortional buckling

An Australian manufacturer has recently developed an innovative group of cold-formed steel hollow flange sections, one of them is LiteSteel Beams (LSBs). The LSB sections are produced from thin and high strength steels by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. They have a unique geometry consisting of rectangular hollow flanges and a relatively slender web. The LSB flexural members are subjected to lateral distortional buckling effects and hence their capacities are reduced for intermediate spans. The current design rules for lateral distortional buckling were developed based on the lower bound of numerical and experimental results. The effect of LSB section geometry was not considered although it could influence the lateral distortional buckling performance. Therefore an accurate finite element model of LSB flexural members was developed and validated using experimental and finite strip analysis results. It was then used to investigate the effect of LSB geometry. The extensive moment capacity data thus developed was used to develop improved design rules for LSBs with one of them considering the LSB geometry effects through a modified slenderness parameter. The use of the new design rules gave higher lateral distortional buckling capacities for LSB sections with intermediate slenderness. The new design rule is also able to accurately predict the lateral distortional buckling moment capacities of other hollow flange beams (HFBs).

Retrospectivity and the rule of law

This book analyses and refines the arguments for and against retrospective rule making, concluding that there is one really strong argument against it: the expectation that, if an individual's actions are considered by a future court, the legal consequences of that action will be determined by the law that was discoverable at the time the action was performed. This argument, which goes to the heart of the rule of law, is generally determinative. However, in some cases the argument does not run and this book suggests that, in some areas of law, reliance should be actively discouraged by prospective warnings that the law is subject to change.