Fuzzy processing in transitivity development

We review the literature on the development of transitive reasoning, and note three historical stages. Stage 1 was dominated by the Piagetian idea that transitive inference is logical reasoning in which relationships between adjacent terms figure as premises. Stage 2 was dominated by the information-processing view that memory for relationships between adjacent terms is determinative in transitivity performance. Stage 3 has produced data that are inconsistent with both the logic and memery positions, leading to a new theory that is designed to account for such findings, fuzzy-trace theory. The basic assumption of fuzzytrace theory is that reasoners rely on global patterns, or gist. We describe the tenets of fuzzytrace theory, and explore its implications for different theoretical conceptions of logical competence, concluding that young children possess transitivity competence. We discuss the connection between transitivity competence (cognition) and intransitive preferences (metacognition).     

Demystifying DEA — A Visual Interactive Approach Based on Multiple Criteria Analysis

Both Data Envelopment Analysis (DEA) and Multiple Criteria Analysis (MCA) can be used to assess the efficiency with which units perform similar tasks. This paper describes an approach derived from the integration of data envelopment analysis and a multi-attribute value function. This approach is implemented as a visual interactive decision support system, the use of which is illustrated by a practical application. The authors feel that this approach overcomes some of the limitations of the original DEA approach and, in particular, increases users' understanding of DEA. The approach is particularly well suited to the analysis of the efficiency of a small number of units.     

A posteriori error estimation for the dual mixed finite element method of the elasticity problem in a polygonal domain

In this article, we propose a residual based reliable and efficient error estimator for the new dual mixed finite element method of the elasticity problem in a polygonal domain, introduced by M. Farhloul and M. Fortin. With the help of a specific generalized Helmholtz decomposition of the error on the strain tensor and the classical decomposition of the error on the gradient of the displacements, we show that our global error estimator is reliable. Efficiency of our estimator follows by using classical inverse estimates. The lower and upper error bounds obtained are uniform with respect to the Lamé coefficient λ, in particular avoiding locking phenomena. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005.     

The Binary System Tetradecanedioic Acid–Hexadecanedioic Acid: Polymorphism of the Components and Experimental Phase Diagram

Complementary techniques had to be applied to investigate the binary system tetradecanedioic acid (C₁₄H₂₆O₄)–hexadecanedioic acid (C₁₆H₃₀O₄), because all the forms observed have the same space group (P2₁/c; Z = 2). We studied the polymorphism of the two single compounds and of their mixtures by X‐ray powder diffraction, differential‐scanning calorimetry (DSC), infrared spectroscopy (IR), scanning electron microscopy (SEM), and thermo‐optical microscopy (TOM). The two diacids were found to be isopolymorphic. At low temperature, they crystallize in the same ordered C‐form, and, on heating, adopt the ordered C_h‐form, 1° below their melting point. In contrast to similar compounds (unbranched alkanes, alkanols, and fatty acids), the solid–solid and solid–liquid phase‐transition temperatures decrease with increasing chain length. At low temperature, a new monoclinic form, C_i, appears as a result of the disorder of composition in the mixed samples. There are two [C + C_i]‐type solid–solid domains. On heating, the solid domains are related to solid–liquid domains by a peritectic invariant for compositions rich in C₁₄H₂₆O₄, and by a eutectic invariant for compositions rich in C₁₆H₃₀O₄. At higher temperature, there appears a second peritectic invariant for compositions rich in C₁₄H₂₆O₄, together with a metatectic invariant for compositions rich in C₁₆H₃₀O₄. All the solid forms observed in this binary system are isostructural. Nevertheless, the equilibrium between them is complex near the melting point, and their miscibility in the solid state is reduced.     

Entropy Maximization for Markov and Semi-Markov Processes

The literature about maximum of entropy for Markov processes deals mainly with discrete-time Markov chains. Very few papers dealing with continuous-time jump Markov processes exist and none dealing with semi-Markov processes. It is the aim of this paper to contribute to fill this lack. We recall the basics concerning entropy for Markov and semi-Markov processes and we study several problems to give an overview of the possible directions of use of maximum entropy in connection with these processes. Numeric illustrations are presented, in particular in application to reliability.     

Precise evaluation of a polynomial at a point given in staggered correction format

The problem of the evaluation in floating-point arithmetic of a polynomial with floating-point coefficients at a point which is a finite sum of floating-point numbers is studied. The solution is obtained as an infinite convergent series of floating-point numbers. The algorithm requires a precise scalar product, but this can always be implemented by software in a high-level language without assembly language routines as we indicate. A convergence result is proved under a very weak restriction on the size of the degree of the polynomial in terms of the unit roundoff u; roughly speaking, the degree should not be larger than the square root of (1 + u)(2u). Even in the particular case when the point at which to evaluate the polynomial reduces to one floating-point number, we find a new simplified algorithm among the whole family that the preceding convergence result allows.

This problem occurs, among others, in the convergence of the Newton method to some real root of the given polynomial p. If we simply use the Horner scheme to evaluate the polynomial p in a neighbourhood of the root, in some cases the evaluation will contain no correct digits and will prevent us from getting convergence even to machine accuracy. The convergence of iterative methods, among which the Newton method, with added perturbations was the central theme of my talk given at the ICCAM'92. The second part will appear in a forthcoming paper. These added perturbations can represent for example forward or backward errors occurring in finite-precision computations.

The problem discussed here appears in validating some hypotheses of these general convergence results (see the forthcoming paper).     

Isolation and Characterization of Crystalline,Neutral Diborane(4) Radicals

Diaryldihalodiboranes(4) were reacted with bis(amidinato)‐ and bis(guanidinato)silylenes to generate the first neutral diborane‐centered radicals. These formally non‐aromatic 5π electron systems are stable in the solid state as well as in solution and were characterized by solid‐state structure determination, high‐resolution mass spectrometry, and EPR spectroscopy. The reactivity of one of these radicals with the oxidant 1,4‐benzoquinone led to ring‐opening and B?O bond formation.     

Micro Raman spectroscopy used for the study of corrosion products on copper alloys: study of the chemical composition of artificial patinas used for restoration purposes

Studying the atmospheric corrosion of copper alloy artifacts is important to acquire a better knowledge about the condition of the object and its possible conservation and restoration. The nature of the formed product, e.g. sulfate, carbonate or chloride, depends on factors such as the amount of polluting elements or humidity but may also depend on the nature of the underlying aesthetic patina, applied by the artist. The composition of the patination solution and the method of patination will both influence the nature of this aesthetic patina, i.e. its chemical composition and morphology. However, although a lot of patination recipes exist, little is known about these patinas as far as composition, structure and ageing is concerned. Therefore, a combination of several surface analytical techniques is required for the complete characterization of patina layers. In this paper, Raman spectroscopy is used to study the characteristics of several patinas obtained on copper following different traditional recipes.     

One-pot synthesis of 2,4-benzodiazepin-1-ones using benzotriazole methodology

2, 4-Benzodiazepin-1-ones were prepared in moderate to good yields by reaction of bis(benzotriazolylmethyl)amines with ortho-metalated N-substituted benzamides.