Chaotic resonance: A simulation

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding achaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.     

Geometric Knowledge of Middle School Students in a Reform-based Mathematics Curriculum

National and international studies have found U.S. elementary students to be weak in their understandings and applications of geometric concepts. The University of Chicago School Mathematics Project's (UCMSP) Everyday Mathematics Program is one of the current reform-based elementary curricula incorporating geometry throughout the K-6 curriculum, with an emphasis on hands-on and problem-solving activities. In this study, the geometric knowledge of fifth and sixth graders using the UCSMP curriculum is compared to the knowledge of students using more traditional curricula. Because UCSMP students had been in the program since kindergarten, this research attempts to measure the longitudinal effects of such an approach. Along with an overall score, a subset of test items was used to assign each student a van Hiele level for geometric thinking, as well as a reasoning score. On all measures, UCSMP students substantially outperformed their counterparts, and nearly all differences were significant. Aspects of the UCSMP curriculum and the van Hiele model for learning geometry are discussed relative to these results.     

A System for Three-Dimensional Interactive Simulation of Hand Biomechanics

A real-time interactive graphics simulation of the mechanics of the human thumb has been developed. The simulation utilizes a realistic data structure for the bones of the thumb which may be expanded to include the hand and forearm. This is coupled to a model of the kinematics of the joints in a concurrent processing arrangement in which the dynamic graphical transformations for scaling, translation, rotation, perspective, and clipping are all performed on a special-purpose display processor. The model and the control functions are distributed between this processor and a separate general-purpose superminicomputer. The resulting system presents the user with a realistic simulation of the movements of the thumb in normal and impaired states. The user may choose from a menu of options, including an interactive tendon transfer simulation for the current hand being simulated. He may control (interactively and in real time) the view, observation position, skeletal motion, and parameters for use in the model of joint mechanics. This type of computer modeling, utilizing a realistic three-dimensional data structure, models of musculoskeletal kinematics, and interactive programming, shows great potential for bringing mathematical modeling into useful clinical, research, and educational applications.     

On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

Feasibility Study of Batteryless Temperature Transponders Using Miniature Microwave Cavity Resonators

Batteryless temperature transponders have been constructed and tested. The design employs a sensing element consisting of a miniature cavity resonator loaded with a ceramic material of high dielectric constant and large temperature coefficient of resonant frequency. This is connected by thin coaxial cable to a small dipole or sector antenna. Prototypes with sensors 3 mm in diameter have been fabricated and can resolve temperature differences of 0.1°C in air. Signals have been obtained from transponders implanted in anesthetized rats, but antenna orientation is a critical and limiting factor that will require further efforts before a system is capable of operating in freely roaming animals.     

Generalized Rotation numbers

A rooted graph is a pair (G,x), where G is a simple undirected graph and x ∈ V(G). If G is rooted at x, its kth rotation number h_k (G,x) is the minimum number of edges in a graph F of order |G| + k such that for every v ∈ V(F) we can find a copy of G in F with the root vertex x at v. When k = 0, this definition reduces to that of the rotation number h(G,x), which was introduced in [“On Rotation Numbers for Complete Bipartite Graphs,” University of Victoria, Department of Mathematics Report No. DM-186-IR (1979)] by E.J. Cockayne and P.J. Lorimer and subsequently calculated for complete multipartite graphs. In this paper, we estimate the kth rotation number for complete bipartite graphs G with root x in the larger vertex class, thereby generalizing results of B. Bollobás and E.J. Cockayne [“More Rotation Numbers for Complete Bipartite Graphs,” Journal of Graph Theory, Vol. 6 (1982), pp. 403–411], J. Haviland [“Cliques and Independent Sets,” Ph. D. thesis, University of Cambridge (1989)], and J. Haviland and A. Thomason [“Rotation Numbers for Complete Bipartite Graphs,” Journal of Graph Theory, Vol. 16 (1992), pp. 61–71]. © 1993 John Wiley & Sons, Inc.