Solid-state analysis of low-melting 1,3-dialkylimidazolium hexafluorophosphate salts (ionic liquids) by combined x-ray crystallographic and computational analyses

The interactions of ions in the solid state for a series of representative 1,3-dialkylimidazolium hexafluorophosphate salts (either ionic liquids or closely related) have been examined by crystallographic analysis, combined with the theoretical estimation of crystal-packing densities and lattice-interaction energies. Efficient close-packing of the ions in the crystalline states is observed, but there was no compelling evidence for specific directional hydrogen-bonding to the hexafluorophosphate anions or the formation of interstitial voids. The close-packing efficiency is supported by the theoretical calculation of ion volumes, crystal lattice energies, and packing densities, which correlated well with experimental data. The crystal density of the salts can be predicted accurately from the summation of free ion volumes and lattice energies calculated. Of even more importance for future work, on these and related salts, the solid-state density of 1,3-dialkylimidazolium hexafluorophosphate salts can be predicted with reasonable accuracy purely on the basis of on ab initio free ion volumes, and this allows prediction of lattice energies without necessarily requiring the crystal structures.

The absence of creativity in Feist and the computational process

The decision of the U.S. Supreme Court in 1991 in Feist Publications, Inc. v. Rural Tel. Service Co. affirmed originality as a constitutional requirement for copyright. Originality has a specific sense and is constituted by a minimal degree of creativity and independent creation. The not original is the more developed concept within the decision. It includes the absence of a minimal degree of creativity as a major constituent. Different levels of absence of creativity also are distinguished, from the extreme absence of creativity to insufficient creativity. There is a gestalt effect of analogy between the delineation of the not original and the concept of computability. More specific correlations can be found within the extreme absence of creativity. "[S]o mechanical" in the decision can be correlated with an automatic mechanical procedure and clauses with a historical resonance with understandings of computability as what would naturally be regarded as computable. The routine within the extreme absence of creativity can be regarded as the product of a computational process. The concern of this article is with rigorously establishing an understanding of the extreme absence of creativity, primarily through the correlations with aspects of computability. The understanding established is consistent with the other elements of the not original. It also revealed as testable under real-world conditions. The possibilities for understanding insufficient creativity, a minimal degree of creativity, and originality, from the understanding developed of the extreme absence of creativity, are indicated. 

A similarity measure for graphs with low computational complexity

We present and analyze an algorithm to measure the structural similarity of generalized trees, a new graph class which includes rooted trees. For this, we represent structural properties of graphs as strings and define the similarity of two Graphs as optimal alignments of the corresponding property stings. We prove that the obtained graph similarity measures are so called Backward similarity measures. From this we find that the time complexity of our algorithm is polynomial and, hence, significantly better than the time complexity of classical graph similarity methods based on isomorphic relations. (c) 2006 Elsevier Inc. All rights reserved.