The sums of three trigonometric series with logarithmic coefficients are derived by extending an approach first utilized Lerch. By applying Frullani's theorem to two these series, non-trivial integrals involving hyperbolic functions evaluated in terms the digamma function.

Time series models of serially correlated variables yield biased fitted values and forecasts. Antithetic time series can be created so as to be negatively correlated with the original time series. The original and antithetic time series can be combined so as to eliminate said bias. A system of equations that define the optimal combining parameters is derived. 2010 Mathematics Subject Classifica...

To ensure the delineated boundaries of a series of 2-D images closely following the visually perceivable edges with high boundary coherence between consecutive slices, a cell-based two-region competition algorithm based on a maximum a posteriori (MAP) framework is proposed. It deforms the region boundary in a cell-by-cell fashion through a cell-based two-region competition process. The cell-bas...

The series-connected lossy Josephson transmission line (JTL), constructed basically from junctions, capacitors, and resistors, is considered. continuum approximation equation describing the JTL derived. From latter, equations pump, signal, idler interaction are derived, thresholds for parametric amplification calculated.