A Short Term Step in Development of 3D Graphics Standards

Few of the arguments deployed above have been either device dependent or application area dependent. Even if further discussion leads to a resolution of these and future issues differnt from the author's, the case is made that a Transformations chapter could be written which would be naturally included in most application-oriented 3D graphics standards.     

Convergence and Consistency of Fuzzy c-means/ISODATA Algorithms

The fuzzy c-means/ISODATA algorithm is usually described in terms of clustering a finite data set. An equivalent point of view is that the algorithm clusters the support points of a finite-support probability distribution. Motivated by recent work on the hard version of the algorithm, this paper extends the definition to arbitrary distributions and considers asymptotic properties. It is shown that fixed points of the algorithm are stationary points of the fuzzy objective functional, and vice versa. When the algorithm is iteratively applied to an initial prototype set, the sequence of prototype sets produced approaches the set of fixed points. If an unknown distribution is approximated by the empirical distribution of stationary, ergodic observations, then as the number of observations grows large, fixed points of the algorithm based on the empirical distribution approach fixed points of the algorithm based on the true distribution. Furthermore, with respect to minimizing the fuzzy objective functional, the algorithm based on the empirical distribution is asymptotically at least as good as the algorithm based on the true distribution.     

Calculated molecular mean excitation energies for some small molecules

Using the random phase approximation, we have calculated the total and directional components of the mean excitation energy for stopping (I₀) and the stopping anisotropy ( ) as well as the first moment (I₁) of the dipole oscillator strength distribution for 20 small molecules and molecular ions containing 6 to 30 electrons. We find that for excitations polarized orthogonal (perpendicular) and parallel to the molecular high symmetry axis I₀^O > I₀^P for all linear molecules, while I₁^O < I₁^P for all molecules other than HF. We note that the Bloch rule holds only for small, compact molecules, and that the Bragg rule should not be used to determine the mean excitation energies of the molecules that we consider here. The stopping anisotropy is positive for all but the C_3v molecules, and is largest for the linear, rod-shaped molecules.     

On minimum distance bounds for abelian codes

This paper is an exposition of two methods of formulating a lower bound for the minimum distance of a code which is an ideal in an abelian group ring. The first, a generalization of the cyclic BCH (Bose-Chaudhuri-Hoquenghem) bound, was proposed by Camion [2]. The second method, presented by Jensen [4], allows the application of the BCH bound or any of its improvements by viewing an abelian code as a direct sum of concatenations of cyclic codes. This second method avoids the mathematical analysis required for a direct generalization of a cyclic bound to the abelian case. It can produce a lower bound that improves the generalized BCH bound. We present simple algorithms for 1) deriving the generalized BCH bound for an abelian code 2) determining direct sum decompositions of an abelian code to concatenated codes and 3) deriving a bound on an abelian code, viewed as a direct sum of concatenated codes, by applying the cyclic BCH bound to the inner and outer code of each concatenation. Finally, we point out the applicability of these methods to codes that are not ideals in abelian group rings.     

Metacyclic error-correcting codes

Error-correcting codes which are ideals in group rings where the underlying group is metacyclic and non-abelian are examined. Such a groupG(M, N,R) is the extension of a finite cyclic group _M by a finite cyclic group _N and has a presentation of the form (S, T:S ^M =1,T ^N =1, T· S=S ^R ·T) where gcd(M, R)=1, R ^N =1 modM, R 1. Group rings that are semi-simple, i.e., where the characteristic of the field does not divide the order of the group, are considered. In all cases, the field of the group ring is of characteristic 2, and the order ofG is odd.Algebraic analysis of the structure of the group ring yields a unique direct sum decomposition ofFG(M, N, R) to minimal two-sided ideals (central codes). In every case, such codes are found to be combinatorically equivalent to abelian codes and of minimum distance that is not particularly desirable. Certain minimal central codes decompose to a direct sum ofN minimal left ideals (left codes). This direct sum is not unique. A technique to vary the decomposition is described. p]Metacyclic codes that are one-sided ideals were found to display higher minimum distances than abelian codes of comparable length and dimension. In several cases, codes were found which have minimum distances equal to that of the best known linear block codes of the same length and dimension.     

Quantitative analysis of piroxicam polymorphs pharmaceutical mixtures by hyperspectral imaging and chemometrics

It has been recognized that crystal polymorphism is an important factor related to the physicochemical and biological properties of drug substances and formulations. In this work, the piroxicam polymorphic forms 1 and 2 were studied using near-infrared chemical imaging (NIR-CI) technology to map the distribution of both species in pharmaceutical formulations. In this direction, the partial least squares (PLS) method was used to construct calibration models of concentrations per pixel of the sample. The RMSEP results for both models of the polymorphic forms remained below 4% (w/w). It was also possible to distinguish local and global information of the constituents through this method. These results seem to be a suitable tool for quality process control and final product quality assurance.     

Fragmentation of water on swift He ion impact

Charge exchange and fragmentation are the usual results in ion-molecule collision systems, and the specifics of the fragmentation process determine the chemical destiny of the target system. In this paper, we report recent progress on calculations of the fragmentation patterns for the model system He²⁺ + H₂O for projectile energies of a few keV. The calculations are obtained using the electron-nuclear dynamics (END) method for solution of the time-dependent Schrödinger equation.     

Fast tripping of utility breakers and industrial load interruptions

Some industries are very sensitive to electric power interruptions and voltage sags, which are a normal consequence of the utility fault-clearing process. Typically, US utilities will try once or twice to clear faults without blowing any tap fuses, which would require dispatching a trouble crew to replace. To reduce complaints and to improve power quality for critical customers with high economic impact of interruptions, some utilities have been eliminating fuse-saving practices on feeder breakers and reclosers. The impact on overall reliability and the number of interruptions is evaluated based on distribution feeder power quality data. Some degradation in overall reliability can be expected, but this can be minimized with judicious placement of line reclosers. Critical customers can expect a significant reduction in the number of interruptions. A value-based economic analysis, including both utility and customer costs, shows that the practice has a high overall benefit-to-cost ratio. The utility experiences increased costs, but these are frequently overshadowed by the potential customer savings. However, removing fast tripping may correct for only a small portion of the utility-related events that might disrupt sensitive industrial processes. This article analyzes the impacts of removing fast tripping on reliability indices and on power system economics