Abstract. Fix a number field K. For each nonzero α ∈ ZK , let ν(α) denote the number of distinct, nonassociate irreducible divisors of α. We show that ν(α) is normally distributed with mean proportional to (log log |N(α)|)D and standard deviation proportional to (log log |N(α)|)D−1/2. Here D, as well as the constants of proportionality, depend only on the class group of K. For example, for each...

In this paper we introduce a concept of asymptotic log-likelihood ratio as a measure of deviation of the joint distribution from the product of their margins, we give the generalized strong law of large numbers (strong law expressed by inequalities, i.e. strong deviation theorems) for stochastic process indexed by a tree. As corollaries, we obtain some known results.

This study measured the precision of a quantitative laboratory-developed real-time PCR test for cytomegalovirus performed at three different clinical laboratories that use the same methodology. The overall standard deviation (adjusted for analyte level) was 0.18 log(10) copies/ml, and there was no significant relationship between standard deviation and analytical measuring range.

In this paper we refine the notion of tree-decomposition by introducing acyclic (R,D)-clustering, where clusters are subsets of vertices of a graph and R and D are the maximum radius and the maximum diameter of these subsets. We design a routing scheme for graphs admitting induced acyclic (R,D)-clustering where the induced radius and the induced diameter of each cluster are at most 2. We show t...

An approach to the Shannon and Rényi entropy maximization problems with constraints on the mean and law invariant deviation measure for a random variable has been developed. The approach is based on the representation of law invariant deviation measures through corresponding convex compact sets of nonnegative concave functions. A solution to the problem has been shown to have an alpha-concave d...

Water saturation determination is one of the most important tasks in reservoir studies to predict oil and gas in place needed to be calculated with more accuracy. The estimation of this important reservoir parameter is commonly determined by various well logs data and by applying some correlations that may not be so accurate in some real practical cases, especially for carbonate reservoirs. Sin...

The multiple inert-gas elimination technique (MIGET) is a complex mathematical model and experimental technique for understanding pulmonary gas exchange. Simpler mathematical models have been proposed that have a limited view compared with MIGET but may be applicable for use in clinical practice. This study examined the use of a simple model of gas exchange to describe MIGET retention and excre...

We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the 1+1-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dim...