In this paper we study recurrences concerning the combinatorial sum k≡r (mod m) n k and the alternate sum k≡r (mod m) (−1) (k−r)/m n k , where m > 0, n 0 and r are integers. For example, we show that if n m − 1 then

The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals built with algebraic functions.

Using a direct approach the return map near a focus of a planar vector field with nilpotent linear part is found as a convergent power series which is a perturbation of the identity and whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals.

BACKGROUND Previous studies of the reproducibility of self-reported age at menarche have been limited because of small study samples, short follow-up and the limited age span of the women included. METHODS The present study assessed the reproducibility of age at menarche in 6731 women with a wide variation of age when giving the information about age at menarche. The women reported age at men...

AIM To investigate and compare the analytical and clinical performance of TianLong automatic hypersensitive hepatitis B virus (HBV) DNA quantification system and Roche CAP/CTM system. METHODS Two hundred blood samples for HBV DNA testing, HBV-DNA negative samples and high-titer HBV-DNA mixture samples were collected and prepared. National standard materials for serum HBV and a worldwide HBV D...

We propose a simple and efficient way to calculate trivariate normal probabilities. The algorithm is based on a formula for the partial derivative of the trivariate probability with respect to a correlation coefficient.

Based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. Further...

To test whether electromyogram (EMG) is nonlinear deterministic signal or just random noise, we comprehensively analyze four EMGs of an adult woman. At first, we calculate the correlation time, L-Z complexity, approximate entropy (ApEn), maximum Lyapunov exponent (Ly1) and correlation dimension (Dcorr) of each EMG data and its ten surrogate data. We find that all the results are quite different...

In this paper, we introduce and study the concepts of correlation and correlation coefficient of neutrosophic data in probability spaces. In the case of finite spaces, these results give the results due to Salama et al. [16, 17, 18] and study some of their properties.

Recent advances in LiDAR (Light Detection and Ranging) technology have allowed for the remote sensing of important forest characteristics to be more reliable and commercially available. Studies have shown that this technology can adequately estimate forest characteristics such as individual tree locations, tree heights, and crown diameters. These values are then used to estimate biophysical pro...