When a page, represented by the interval $[0,1]$ , is folded right over left $n $ times, the right-hand fold contains a sequence of points. We specify these points using two different representation techniques, both involving binary signed-digit representations.

When a page, represented by the interval $[0,1],$ is folded right over left $ n$ times, the right-hand fold contains a sequence of points. We specify these points and the order in which they appear in each fold. We also determine exactly where in the folded structure any point in $[0,1]$ appears and, given any point on the bottom line of the structure, which point lies at each level above it.

Three-dimensional (3D) battery architectures have emerged as a new direction for powering microelectromechanical systems and other small autonomous devices. Although there are few examples to date of fully functioning 3D batteries, these power sources have the potential to achieve high power density and high energy density in a small footprint. This overview highlights the various architectures proposed for 3D batteries, the advances made in the fabrication of components designed for these devices, and the remaining technical challenges. Efforts directed at establishing design rules for 3D architectures and modeling are providing insight concerning the energy density and current uniformity achievable with these architectures. The significant progress made on the fabrication of electrodes and electrolytes designed for 3D batteries is an indication that a number of these battery architectures will be successfully demonstrated within the next few years.

Experimental studies of silicate glass/water reactions at low temperatures have previously identified the glass surface area-to-solution volume ratio (SA/V) as a significant rate determining parameter [1-4]. The value produced when SA/V is multiplied by reaction time, hereafter referred to as SVT, has been proposed as a scaling factor for comparing experimental results collected under different test conditions and for extrapolating short-term results to longer periods of time. Developing an understanding of the effect of SAN is needed for modeling experimental results where SA/V ranges in value or may vary during experiments. It is also useful to understand the effect of SA/V for modeling natural systems where this value almost certainly varies, such as during the hydrothermal diagenesis of natural glasses or projecting the long-term reaction of water and borosilicate nuclear waste glass in a geologic repository.

Test samples of 131 type glass that have been reacted for extended time periods in water vapor atmospheres of different relative humidities and in static leaching solution have been examined to characterize the reaction products. Analytical electron microscopy (AEM) was used to characterize the leached samples, and a complicated layer structure was revealed, consisting of phases that precipitate from solution and also form within the residual glass layer. The precipitated phases include birnessite, saponite, and an iron species, while the intralayer phases include the U-TI containing phase brannerite distributed within a matrix consisting of bands of an Fe rich montmorillonite clay. Comparison is made between samples leached at 40°C for 4 years with those leached at 90°C for 3-1/2 years. The samples reacted in water vapor were examined with scanning electron microscopy and show increasing reaction as both the relative humidity and time of reaction increases. These samples also contain a layered structure with reaction products on the glass surface.