Let G be an abelian group. The Polynomial Freiman-Ruzsa conjecture (PFR) concerns the structure of sets A ⊆ G for which |A + A| 6 K|A|. These notes provide proofs for the statements made in §10 of [8], and as such constitute a reasonably detailed discussion of the PFR in the case G = F2 . Although the purpose of these notes is to furnish proofs for the statements in §10 of [8], they are reasona...

the objective of this study was to determine the relationship between body weight (bw) and heart girth (hg) in sardi and timahdite sheep in order to develop a prediction equation of bw from hg. the data used for this study included 476 records on bw and hg (227 in sardi and 249 in timahdite) collected on males and females of different ages in 33 private farms. the bw and the hg averaged 34.8 ± ...

in this research, the spatial distribution of fe, cu, zn and mn on agricultural lands of golestan province were evaluated using different interpolation methods such as, kriging, inverse distance weighted, local polynomial, inverse multiquadric and radial basis function. thus, 505 soil samples were provided from fields during 2008 and micronutrients rates were measured for each sample. the perfo...

Random regression models (RRM) have become common for the analysis of longitudinal data or repeated records on individual over time. The goal of this paper was to explore the use of random regression models with orthogonal / Legendre polynomials (RRL) to analyze new repeated measures called clutch size (CS) as a meristic trait for Iranian native fowl. Legendre polynomial functions of increasing...

Deterioration models are important and essential part of any Pavement Management System (PMS). These models are used to predict future pavement situation based on existence condition, parameters causing deterioration and implications of various maintenance and rehabilitation policies on pavement. The majority of these models are based on roughness which is one of the most important indices in p...