an extended peng-robinson equation of state (epr-eos) is used to model the vapor-liquid equilibrium (vle) in systems containing (water + nacl + co2), (water + methanol + nacl + co2), (water + na2so4 + co2) and (water + nh4cl + co2). the binary and ternary interaction parameters between salt and solvent are adjusted to experimental mean solvent activity of salts (nacl and na2so4). for the system...

In this note we present a proof of the combinatorial nullstellensatz using simple arguments from linear algebra. The combinatorial nullstellensatz [1] is an elegant tool which has many applications in combinatorial number theory, graph theory and combinatorics (see [1] and [2]). In this note we present a proof of this result using simple arguments from linear algebra. In Theorem 1, we recall th...

We investigate the equilibrium state of the model of Peng, et al. for molecular breeding. In the model, a population of DNA sequences is successively culled by removing the sequences with the lowest binding affinity to a particular target sequence. The remaining sequences are then amplified to restore the original population size, undergoing some degree of point-substitution of nucleotides in t...

BosonSampling, which we proposed three years ago, is a scheme for using linear-optical networks to solve sampling problems that appear to be intractable for a classical computer. In a recent manuscript, Gogolin et al. claimed that even an ideal BosonSampling device’s output would be “operationally indistinguishable” from a uniform random outcome, at least “without detailed a priori knowledge”; ...

The aim of this paper is to improve a theorem of János Kollár by a different method. For a given smooth Complex projective threefold X of general type, suppose the plurigenus Pk(X) ≥ 2, Kollár proved that the (11k + 5)-canonical map is birational. Here we show that either the (7k+3)-canonical map or the (7k+5)-canonical map is birational and the (13k+6)-canonical map is stably birational onto i...

BosonSampling, which we proposed three years ago, is a scheme for using linear-optical networks to solve sampling problems that appear to be intractable for a classical computer. In a recent manuscript, Gogolin et al. claimed that even an ideal BosonSampling device’s output would be “operationally indistinguishable” from a uniform random outcome, at least “without detailed a priori knowledge”; ...