We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees there exists a limit graphing and thus an associated Type-II1 von Neumann algebra. The Kesten-von Neumann-Serre spectral measure of the Laplacian on the limit graphing is the weak limit of the spectral measures of the Laplacians of the finite graphs. Using this limit techniques we prove a Cheeger type ...

Graphing univariate distributions is central to both statistical graphics, in general, and Stata’s graphics, in particular. Now that Stata 8 is out, a review of official and user-written commands is timely. The emphasis here is on going beyond what is obviously and readily available, with pointers to minor and major trickery and various user-written commands. For plotting histogram-like display...

Although graphic calculators have been developed in mathematics education for nearly two decades, research on the technology’s use is not robust. Its use in secondary schools (for example, in Great Britain, France, Sweden, New Zealand, Netherlands, and United States) is not well understood, universally accepted, nor well-documented. In Malaysia, research on the usage of graphic calculators is s...

We define a class of generic CR submanifolds of C n of real codi-mension d, 1 ≤ d ≤ n − 1, called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem, for Bloom-Graham model graphs with a polynomial growth assumption on their graphing...

The original version of this article unfortunately contained a mistake. name “Susan Maruca” is now corrected in the author group.

Effective multimodal graphing tools can be beneficial to both sighted and visually impaired students and scientists. However, before this can become a reality, considerable research is required on the auditory graphing components. We suggest mappings, polarities, scaling, context, and training be studied in particular. We point to previous work in these areas and make suggestions for expanded r...

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 11 interval. Strange attractors and fractals appear in...

we describe an object oriented design and flexible implementation of a set of graphing tools implemented by using only the standard graphical user interface widgets provided by an interactive program composition system developed at Siemens Corporate R&D. The system, SX/Tools, allows for the addition of arbitrary tools (widgets) by direct composition of a set of initial objects. Using this mecha...