A technique for representing multiple-output binary functions with applications to verfication and simulation

This paper presents a technique for representing multiple output binary and word-level functions in GF(N) ($N=p^m$, p a prime number and m a nonzero positive integer) based on decision diagrams (DD). The presented DD is canonical and can be made minimal with respect to a given variable order. The DD has been tested on benchmarks including integer multiplier circuits and the results show that it can produce better node compression (more than an order of magnitude in some cases) compared to shared BDDs. The benchmark results also reflect the effect of varying the input and output field sizes on the number of nodes. Methods of graph-based representation of characteristic and encoded characteristic functions in GF(N) are also presented. Performance of the proposed representations has been studied in terms of average path lengths and the actual evaluation times with 50,000 randomly generated patterns on many benchmark circuits. All these results reflect that the proposed technique can out perform existing techniques

Synthesis and Cathodoluminescence of Undoped and Cr^3^+-Doped Sodium Titanate Nanotubes and Nanoribbons

We report on the synthesis of Cr^3^+-doped sodium titanate nanotubes and nanoribbons by a hydrothermal method. The presence of dopant ions in these nanostructures was confirmed by high angle annular dark field scanning transmission electron microscopy in combination with electron energy loss spectroscopy measurements. Luminescence properties of undoped and Cr^3^+-doped sodium titanate nanotubes and nanoribbons were investigated by cathodoluminescence in the scanning electron microscope. A broad visible band in the range 1.7−2.7 eV is observed in these nanostructures. Such emission is similar to that observed in bulk anatase TiO_2 and titanate powders, and is related to TiO_6 octahedra, which is a common feature to all the samples investigated. Near-infrared emission, sometimes attributed to Ti^3^+ interstitials, is observed in bulk powders but is absent in the titanate nanotubes and nanoribbons. Incorporation of Cr^3^+ between the titanate layers of the nanostructures is revealed by the characteristic intraionic emission line at 1.791 eV. Sodium titanate nanoribbons appear to be an effective host for optically active Cr^3^+ ions, as compared with nanotubes or bulk powder