A primer on mathematical modelling in economics

The Commission on Graduate Education in Economics had raised several concerns regarding the role of mathematics in graduate training in economics (Krueger, 1991; Colander, 1998, 2005). This paper undertakes a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across mathematical concepts and results that are used by economists. In the process one arrives at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of Arrow's impossibility theorem. Common knowledge of the patterns in mathematical concepts and results could be effective in enhancing communication between students, teachers and researchers specializing in different sub-fields of economics.

Comments on "finite-time stability theorem of stochastic nonlinear systems" [Automatica 46 (2010) 2105-2108]

In this comment, we will point out some errors existing in Chen and Jiao (2010) from definitions to the proof of the main result, where the authors discussed the finite-time stability of stochastic nonlinear systems and proved a Lyapunov theorem on the finitetime stability.

A finite-time stability theorem of stochastic nonlinear systems and stabilization designs

This paper focuses on the finite-time stability and stabilization designs of stochastic nonlinear systems. We first present and discuss a definition on the finite-time stability in probability of stochastic nonlinear systems, then we introduce a stochastic Lyapunov theorem on the finite-time stability, which has been established by Yin et al. We also employ this theorem to design a continuous state feedback controller that makes a class of stochastic nonlinear systems to be stable in finite time. An example and a simulation are given to illustrate the theoretical analysis.

A characterization theorem for t-representable n-dimensional triangular norms

n-dimensional fuzzy sets are an extension of fuzzy sets that includes interval-valued fuzzy sets and interval-valued Atanassov intuitionistic fuzzy sets. The membership values of n-dimensional fuzzy sets are n-tuples of real numbers in the unit interval [0,1], called n-dimensional intervals, ordered in increasing order. The main idea in n-dimensional fuzzy sets is to consider several uncertainty levels in the memberships degrees. Triangular norms have played an important role in fuzzy sets theory, in the narrow as in the broad sense. So it is reasonable to extend this fundamental notion for n-dimensional intervals. In interval-valued fuzzy theory, interval-valued t-norms are related with t-norms via the notion of t-representability. A characterization of t-representable interval-valued t-norms is given in term of inclusion monotonicity. In this paper we generalize the notion of t-representability for n-dimensional t-norms and provide a characterization theorem for that class of n-dimensional t-norms. © 2011 Springer-Verlag Berlin Heidelberg.

Decompositions of finite projective planes

We consider decompositions of finite projective planes into copies of a particular structure. Our main theorem provides a connection between the existence of a proper projective subplane and the existence of a decomposition into sets of collinear points. Based on this result, we develop a connection between the existence of a projective subplane in a plane II and that of a hitting set in the dual of II.

Combinatorial aspects of jump codes

We develop an approach to jump codes concentrating on their combinatorial and symmetry properties. The main result is a generalization of a theorem previously proved in the context of isodual codes. We show that several previously constructed jump codes are instances of this theorem.

A scale-model room as a practical teaching experiment

A practical experiment is described which was used to help university students increase their understanding of the effect of construction methods and window design on passive solar heating and electrical heating. A number of one tenth scale model rooms were constructed by students and sited out-of-doors in the late autumn. The models were fabricated to mimic available commercial construction techniques with careful consideration being given to window size and placement for solar access. Each model had a thermostatically controlled electric heating element. The temperatures and electricity use of the models were recorded using data-loggers over a two week period. The performances of the models based on energy consumption and internal temperature were compared with each other and with predictions based upon thermal mass and R-values. Examples of questions used by students to facilitate this process are included. The effect of scaling on thermal properties was analysed using Buckingham’s p-theorem.

Leontief paradox and the role of factor intensity measurement

In contrast with the prediction of the Heckscher-Ohlin (HO) theorem, Leontief (1953) found that the capital-labor ratio embodied in the US exports is smaller than the capital-labor ratio embodied in the US competitive import replacements. In Leontief's analysis, the measured factor content of US imports is computed based on the assumption that all countries are using the US factor intensity techniques. This paper relaxes all assumption of identical factor intensity techniques. It uses an inferring method to infer the factor intensity techniques of different countries based on international relative factor price differences. With the inferred differentiated factor intensity techniques , the Leontief paradox is re-investigated and is found to be either disappeared or eased.

Che Vuoi? Politico-philosophical remarks on Leo Strauss' Spinoza

Rumors surrounding the Hebraic-American classical philosopher Leo Strauss’ supposed influence on leading neoconservative politicians and commentators make reconsidering Leo Strauss’ thought and legacy a philosophical task of the first political importance today. A host of articles have appeared by students and (more recently) books by Stephen Smith (2006), Heinrich Meier (2006) and Catherine and Michael Zuckert (2006). This essay is proffered as a critical contribution, by a non-Straussian student, to this literature. Its methodology and justification is to return to and reconsider Strauss’ earliest works, on the ‘political theology’ of Benedict de Spinoza. The paper argues two theses. The first is that the popular depiction of Strauss as an esoteric Nietzschean hiding behind a ‘noble’ classical or theological veneer importantly misses the mark. The second is that Strauss’ early work shows his proximity, via Jacobi, to the Heideggerian disclosure of the groundless grounds of philosophical reason, given which one must extra-rationally choose reason over faith. One striking implication of this argument, in the contemporary political climate, is to underscore the unlikely convergence between the philosophical sources of neoconservative and the ‘post-structuralist’ thought associated with much of the intellectual left in France and the Anglophone world. Yet in contrast to the widespread image of Strauss, I argue that the mature Strauss’ continuing commitment to this decisionistic framework is in fact most clear is his ‘exoteric,’ public statements on religion – i.e. it is not the ‘esoteric’ purloined letter Strauss’ critics seek out. The reason for Strauss’ continuing public advocacy of the impossibility of reason’s disproving faith, I propose, highlights the primarily political (versus philosophical) nature of this turn: in Strauss’ conservative acceptance of the political necessity of religion for social order, framed in terms of a revised commitment to the ‘medieval’ (versus modern) enlightenment of Maimonides and Farabi.

Mining inconsistent secure messages toward analyzing security protocols

Traditional approaches such as theorem proving and model checking have been successfully used to analyze security protocols. Ideally, they assume the data communication is reliable and require the user to predetermine authentication goals. However, missing and inconsistent data have been greatly ignored, and the increasingly complicated security protocol makes it difficult to predefine such goals. This paper presents a novel approach to analyze security protocols using association rule mining. It is able to not only validate the reliability of transactions but also discover potential correlations between secure messages. The algorithm and experiment demonstrate that our approaches are useful and promising.

Democracy, global transitions, and education : using speculative fictions as thought experiments in anticipatory critical inquiry

The purpose of a thought experiment, as the term was used by quantum and relativity physicists in the early part of the twentieth century, was not prediction (as is the goal of classical experimental science), but more defensible representations of present 'realities'. Indeed, one of the best-known examples of a thought experiment ('Schrodinger's cat') demonstrates the impossibility of prediction at the quantum level. Speculative fictions, from Mary Shelley's Frankenstein to the Star Wars saga, can be read as socio-technical thought experiments that can help us to apprehend and comprehend present 'realities' and uncertainties, and to anticipate and critique possible futures. In this paper I will demonstrate how two examples of popular speculative fictions, Frank Herbert's Dune (1965) and Ursula Le Guin's The Telling (2000), can be read as thought experiments that describe problematic aspects of contemporary social and cultural transformations. I will argue that critical and deconstructive readings of these novels can help us to produce anticipatory critiques of possible ways in which democratic institutions are being transformed by globalisation. I will conclude by considering the implications of such anticipatory critiques for generating questions, problems and issues in educational inquiry and for choosing appropriate methodologies for investigating them.