Stochastic integrators indexed by a multi-dimensional parameter

Summary Multi-parameter stochastic integrators are described and classified according to directions of integrability. Sets of directions are distinguished precisely by the combinatorial dimension of corresponding fractional Cartesian products. The main theorem establishes existence of stochastic processes which are integrators in prescribed directions but not others.     

The spin-S Blume-Capel RG flow diagram

Using the finite-size scaling renormalization group, we obtain the two-dimensional flow diagram of the Blume-Capel model forS=1 andS=3/2. In the first case our results are similar to those of mean-field theory, which predicts the existence of first- and second-order transitions with a tricritical point. In the second case, however, our results are different. While we obtain in theS=1 case a phase diagram presenting a multicritical point, the mean-field approach predicts only a second-order transition and a critical endpoint.     

Looking at Fokker-Planck dynamics with a noisy instrument

We consider the class of experiments which can be characterized by a Fokker-PIanck dynamics corresponding to the overdamped motion of a state point in a suitable stochastic potential. We assume that the general form of the potential is known (or can be guessed with reasonable accuracy), but that its parameters are to be determined experimentally by measurements made with a noisy instrument. This possible method for determining the potential parameters, which exploits the system's own internal stochastic motion in order to explore rapidly its available parameter space, is substantially more efficient than traditional methods involving time averages of single point measurements, and yet does not appear to have been previously considered. The method could be important when, for example, the experiment must be completed in a limited time owing either to the expense of the experimental materials or to the temporary stationarity of the preparation, situations which are commonly encountered in experimental biochemistry and biology.     

Quantitative Impact of a Cognitive Modeling Intelligent Tutoring System on Student Performance in Balancing Chemical Equations

The need for improved interactive tutoring capabilities in educational software for chemistry problem solving is an important one clearly articulated by teachers and students. To deliver the next generation of individualized interactive capabilities users demand, it is necessary to go beyond the conventional computer-assisted instruction methodology. The focus of this paper is the assessment with first-semester general chemistry students of a recently developed artificial intelligence (AI) tutor for balancing chemical equations. This is the first such assessment of an AI-based learning tool in chemistry. Students in CHEM 121 in the Fall 2001 semester at Duquesne University (N = 273) participated in the study. Students were divided into a test group that used the AI tutor as part of their study activities and a control group that did not use the tutor. It was found that the tutor improved the performance of the test group students to a statistically significant degree, helping the weakest students the most. This study establishes the feasibility of an AI-based approach to creating advanced new tutoring software for chemistry problem solving. Access to a Web-based demonstration of the equation-balancing tutor may be obtained by emailing the corresponding author.     

A Diepoxide Belonging to the Rare C1 Point Group

2,6- and 2,7-Dimethylanthracenes were reduced seriatim with lithium in liquid ammonia and lithium in methylamine to their 1,4,5,8,9,10-hexahydro derivatives. Two-fold epoxidation of these tetraenes provided the cis and trans diepoxides resulting from electrophilic attack at the inner double bonds. Trans diepoxide 1 has the very unusual characteristic of lacking a σ plane of symmetry but possessing an inversion center. As a consequence, the ¹H NMR spectrum of C₁-symmetric 1 is simplified relative to those of its isomers 5, 9, and 10.