I discuss a novel technique for periodically extending by reflection an ordered series of phase-difference {xk.} to yield estimation of new frequency and time variances having improved longterm confidence and the same mean as the Allan variance. In addition, I describe a correction to a negative bias in the sample variance based on the actual number of observations in the measurements at long t...

Between-day variance is an ambiguous term representing either total variance or pure between-day variance. In either case, it is often incorrectly calculated even though analysis of variance (ANOVA) and other excellent methods of estimation are available. We used statistical theory to predict the magnitude of error expected from using several intuitive approaches to estimation of variance compo...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

During the process of adding links, we find that the synchronizability of the classical Barabási-Albert (BA) scale-free or Watts-Strogatz (WS) small-world networks can be statistically quantified by three essentially structural quantities of these networks, i.e., the eccentricity, variance of the degree distribution, and clustering coefficients. The results indicate that both the eccentricity a...

This paper deals with the search for reliable efficient finite difference methods numerical solution of random heterogeneous diffusion reaction models a degree randomness. Efficiency appeals to computational challenge in framework that requires not only approximating stochastic process but also its expectation and variance. After studying positivity conditional mean square stability, computatio...

In this paper, we show how to exactly sample from the distribution of the maximum of a random walk with negative drift. We also explore related variance reduction methods.