monte carlo simulation is widely used in calculations involing transport of photons through different materials of different shapes. the method consists of randomly generating a finite set of photon histories over which the quantities of interest are averaged. in photon transport calculations, sampling the photon scattering angle from the klein-nishina probability distribution is of special imp...

Let [NB]1 denote the ideal generated by nonbounding c.e. degrees and NCup the ideal of noncuppable c.e. degrees. We show that both [NB]1 ∩ NCup and the ideal generated by nonbounding and noncuppable degrees are new, in the sense that they are different from M, [NB]1 and NCup — the only three known definable ideals so far.

We give exact formulas for the growth of the ideal Aλ for λ a quadratic element of the algebra of Boolean functions over the Galois field GF (2). That is, we calculate dimAkλ where Ak is the subspace of elements of degree less than or equal to k. These results clarify some of the assertions made in the article of Yang and Chen [YC] concerning the efficiency of the XL algorithm in cryptography.

This paper uses the weighted L$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. When all variables are integer it finds the whole set of efficient solutions. In each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...