is called the discrepancy of (xn)n=1. In 1954 Roth (see [DrTi], [KN]) proved that for any sequence in [0, 1) limN→∞ND(N)/ log N > 0. (2) Let A be an s × s invertible matrix with integer entries. A matrix A is said to be ergodic if for almost all α ∈ R the sequence {αA}n≥1 is uniformly distributed. A vector α ∈ R is said to be normal (A normal) if the sequence {αA}n≥1 is uniformly distributed. L...

In this issue of Blood, Kassebaum et al estimate that the global anemia prevalence in 2010 was 32.9%, resulting in 68.4 million years lived with disability (YLD). The results emphasize the important contribution made by anemia to the overall global burden of disease and should help focus attention and resources toward this problem.

a brief background to the development of the rock engineering design process is given, showing that since the development of the science of mathematics, deterministic methods have been used to perform various calculations. the variability of rock properties and support characteristics have always been known. however, they were not explicitly used in design but compensated for by the use of a sa...

Using the gauge/gravity duality, we calculate the electromagnetic contributions to hadron masses, where mass generates dynamically by strong QCD interactions. Based on the Sakai-Sugimoto model of holographic QCD we find that the electromagnetic mass of proton is 0.48 MeV larger than that of neutron, which is in agreement with recent lattice results. Similarly for pions we obtain mπ± −mπ0 = 1.8 ...

Nonlinear multiscale algorithms often involve nonlinear perturbations of linear coarse-to-fine prediction operators S (also called subdivision operators). In order to control these perturbations, estimates of the “commutator” SF − FS of S with a sufficiently smooth map F are needed. Such estimates in terms of bounds on higher-order differences of the underlying mesh sequences have already appea...

We show variational estimates for paraproducts, Theorems 1.2 and 1.3, which can be viewed as bilinear generalizations of Lépingle’s variational estimates for martingale averages or scaled families of convolution operators. The heart of the matter is the case of low variation exponents, 1 < r ≤ 2.

We have obtained empirical relations between the p-mode frequency shift and the change in solar activity indices. The empirical relations are determined on the basis of frequencies obtained from BBSO and GONG stations during solar cycle 22. These relations are applied to estimate the change in mean frequency for the cycle 21 and 23. A remarkable agreement between the calculated and observed fre...

For the Gaussian sequence model Xi = μi + σZi, i = 1, 2, · · · , n, where Zi are iid standard normal, and σ is considered known, we give three equivalent exact formulas for the posterior mean of the mean vector μ = (μ1, · · · , μn) when μ has a uniform prior distribution in an n-dimensional solid ball of a general radius c. The exact formulas have interesting and even curious connections to non...

by the examiner in obtaining some special information about retarded children. The two subjects specially described are pupils in the high sixth grade of a large public school. The teacher of their class gave a detailed account of difficulties concerning a number of backward children and was particularly perplexed regarding Anna and Roy. In her opinion neither one could accomplish the work of t...

We should not have to look at the entire corpus (e.g., the Web) to know if two words are associated or not.1 A powerful sampling technique called Sketches was originally introduced to remove duplicate Web pages. We generalize sketches to estimate contingency tables and associations, using a maximum likelihood estimator to find the most likely contingency table given the sample, the margins (doc...