The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for the existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In addition, we consider a random process for evolving directed graphs with bounded degrees. The bounds are not the same for different vertices but satisfy...

A new method for calculating average molecular weights is presented for nonlinear polymers. In contrast to the previous methods of Flory and Stockmayer which first calculate the distribution of all species and then use the distributions to calculate average properties, the new method calculates these properties directly. In contrast to the method of Gordon, probability generating functions are ...

Weibull distribution has been used widely by many researches around the world especially in the analysis of high voltage experimental data. Unfortunately, the statistical techniques used to analyse the high voltage experimental data are not highly accurate. In view of the foregoing, this paper presents a new statistical approach to analyze the tree inception voltage of silicone rubber and epoxy...

We derive an expression for the free energy of the blends of block copolymers expressed as a functional of the density distribution of the monomer of each block. The expression is a generalization of the Flory-Huggins-de Gennes theory for homo polymer blends, and also a generalization of the Ohta-Kawasaki theory for the melts of diblock copolymers. The expression can be used for any blends of h...

2014 We consider a linear polymer melt where the chains are made by condensation of bifunctional monomers. In the very large distribution of molecular weights that is obtained one may distinguish typical and very large chains with different behaviours. Screening is effective in the former, which act as a (good) solvent for the latter. The cross-over molecular weight N * between the two classes ...

A description of the Hochschild cohomology algebra for the symmetric 8-dimensional algebras found by Liu and Schulz is given in terms of generators and relations. The dimensions of the cohomology groups are calculated. §