Computation and construction of vault geometry prototypes

Physical models and scaled prototypes of architecture play an important role in design. They enable architects and designers to investigate the formal, functional, and material attributes of the design. Understanding digital processes of realizing scaled prototypes is a significant problem confronting design practice. This paper reports on three approaches to the translation of Gaussian surface models into scaled physical prototype models. Based on the geometry of Eladio Dieste’s Gaussian Vaults, the paper reports on the aspects encountered in the process of digital to physical construction using scaled prototypes. The primary focus of the paper is on computing the design geometry, investigating methods for preparing the geometry for fabrication and physical construction. Three different approaches in the translation from digital to physical models are investigated: rapid prototyping, two-dimensional surface models in paper and structural component models using CNC fabrication. The three approaches identify a body of knowledge in the design and prototyping of Gaussian vaults. Finally the paper discusses the digital to fabrication translation processes with regards to the characteristics, benefits and limitations of the three approaches of prototyping the ruled surface geometry of Gaussian Vaults. The results of each of three fabrication processes allowed for a better understanding of the digital to physical translation process. The use of rapid prototyping permits the production of form models that provide a representation of the physical characteristics such as size, shape and proportion of the Gaussian Vault.

First of all, I split the 24 : strategies for mental computation

In this article, the author sets out some goals and classroom activities for the teaching of mental computation. The author also discusses the importance of allowing children to help each other and explains that there is benefit in children listening to mathematical strategies given by other children.

First of all I split the 24 : strategies for mental computation

Goals for mental computation are presented along with some ideas for teaching mental computation in the classroom. The understanding of number and the operations that come from developing mental computation strategies are useful for algebra and children should be encouraged to use more efficient and diverse mental strategies.

A monotonicity index for the monotone fuzzy modeling problem

In this paper, the problem of maintaining the (global) monotonicity and local monotonicity properties between the input(s) and the output of an FIS model is addressed. This is known as the monotone fuzzy modeling problem. In our previous work, this problem has been tackled by developing some mathematical conditions for an FIS model to observe the monotonicity property. These mathematical conditions are used as a set of governing equations for undertaking FIS modeling problems, and have been extended to some advanced FIS modeling techniques. Here, we examine an alternative to the monotone fuzzy modeling problem by introducing a monotonicity index. The monotonicity index is employed as an approximate indicator to measure the fulfillment of an FIS model to the monotonicity property. It allows the FIS model to be constructed using an optimization method, or be tuned to achieve a better performance, without knowing the exact mathematical conditions of the FIS model to satisfy the monotonicity property. Besides, the monotonicity index can be extended to FIS modeling that involves the local monotonicity problem. We also analyze the relationship between the FIS model and its monotonicity property fulfillment, as well as derived mathematical conditions, using the Monte Carlo method.

The mechanics of computation and human thought

Thousands of students are preparing for chemistry examinations in June. An unresolved debate is whether they should be permitted to use graphics and programmable calculators in those examinations. Some educators have not only advocated the use of graphics calculators, but have also pointed to the Danish system in which students are permitted to use computers in senior school examinations.

In some Australian jurisdictions, graphics calculators are permitted in year 12 mathematics examinations, but not in chemistry examinations. The reasoning is that information or methods of solving numerical chemical problems can be stored in the memory of graphics calculators, giving some students an unfair advantage. This means that chemistry students either have to learn how to use (and buy!) two types of calculators or, if they only have one calculator, are disadvantaged in using non-programmable calculators in mathematics examinations.

The use of technology (or its lack thereof) can limit how and what students learn. “The mechanics of computation and human thought” is an allusion to Asimov’s short story, “A Feeling of Power” in which, overuse of technology has caused people to forget how to do simple arithmetic. In our current assessment system, the insistence that students must be able to do simple chemical calculations has lead to underuse of available technology. The misperception is that the ability to do calculations is linked to understanding of concepts.

Graphics calculators, programmable calculators and computers are tools. Instead of banning or limiting technology, we should take the opportunity to rethink what is being assessed and how it is assessed. It is the proper use of technology, by combining the mechanics of computation and human thought to deepen understanding and to ask probing questions that truly leads to a feeling of power.

Minimizing bounded uncertainty impact on scheduling with earliest start and due-date constraints via interval computation

Bounded uncertainty is a major challenge to real life scheduling as it increases the risk and cost depending on the objective function. Bounded uncertainty provides limited information about its nature. It provides only the upper and the lower bounds without information in between, in contrast to probability distributions and fuzzymembership functions. Bratley algorithm is usually used for scheduling with the constraints of earliest start and due-date. It is formulated as . The proposed research uses interval computation to minimize the impact of bounded uncertainty of processing times on Bratley’s algorithm. It minimizes the uncertainty of the estimate of the objective function. The proposed concept is to do the calculations on the interval values and approximate the end result instead of approximating each interval then doing numerical calculations. This methodology gives a more certain estimate of the objective function.

Multi-objective image segmentation with an interactive evolutionary computation approach

In this paper, a multi-objective image segmentation approach with an Interactive Evolutionary Computation (IEC)-based framework is presented. Two objectives, i.e., the overall deviation and the connectivity measure, are optimized simultaneously using a mu

Exact-estimator-based terminal sliding mode control system design

This paper investigates an estimator-based terminal sliding mode control system. An exact estimator is proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic levitation system to implement the control performance.

FracSym: automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented. © 2013 Elsevier B.V. All rights reserved.