Comparison of "polynaphthalenes" prepared by two mechanistically distinct routes

The Bergman cyclization has long been known to produce polymers as side products. More recently, this attribute has been harnessed for the production of conjugated materials. However, the structures of these polymers have not been established. To resolve this question, the metal-catalyzed polymerization of 1,4-dibromonaphthalene and thermal polymerization of o-diethynylbenzene were conducted. Two distinct polymers were obtained. Comparison of IR spectroscopy, MALDI-TOF MS, solid-state NMR spectroscopy, UV-vis reflectance spectroscopy, and pyrolysis GC-MS data indicates that only one of the polymers is consistent with poly(1,4-naphthalene).     

Primal decomposition in rings, modules and lattice modules

In a work by L. Fuchs, W. Heinzer and B. Olberding, a decomposition of ideals in a commutative ring as intersections of primal isolated component ideals is investigated. In subsequent work by L. Fuchs and R. Reis, these ideas are developed in multiplicative lattices. The object of this note is to point out that, when specialized to the lattice of ideals of a commutative ring, the decomposition of L. Fuchs and R. Reis does not give the decomposition obtained in the paper by Fuchs, Heinzer and Olberding, and to give two variations of the decomposition of Fuchs and Reis. One of these variations, when specialized to the lattice of ideals of a ring, does give the decomposition obtained by Fuchs, Heinzer and Olberding, and the other one gives a decomposition which is superior in some ways. Received December 2, 2004; accepted in final form February 17, 2005.     

Mustafin varieties

A Mustafin variety is a degeneration of projective space induced by a point configuration in a Bruhat-Tits building. The special fiber is reduced and Cohen-Macaulay, and its irreducible components form interesting combinatorial patterns. For configurations that lie in one apartment, these patterns are regular mixed subdivisions of scaled simplices, and the Mustafin variety is a twisted Veronese variety built from such a subdivision. This connects our study to tropical and toric geometry. For general configurations, the irreducible components of the special fiber are rational varieties, and any blow-up of projective space along a linear subspace arrangement can arise. A detailed study of Mustafin varieties is undertaken for configurations in the Bruhat-Tits tree of PGL(2) and in the 2-dimensional building of PGL(3). The latter yields the classification of Mustafin triangles into 38 combinatorial types.     

Discrete Uncertainty Principles and Sparse Signal Processing

We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly sparse. After studying these principles and the functions that achieve exact or near equality in them, we identify certain consequences in a number of sparse signal processing applications.     

The Vlasov-Poisson Dynamics as the Mean Field Limit of Extended Charges

We consider the discrete Gaussian Free Field in a square box in \({\mathbb{Z}^2}\) of side length N with zero boundary conditions and study the joint law of its properly-centered extreme values (h) and their scaled spatial positions (x) in the limit as \({N \to \infty}\). Restricting attention to extreme local maxima, i.e., the extreme points that are maximal in an r_N-neighborhood thereof, we prove that the associated process tends, whenever \({r_N \to \infty}\) and \({r_N/N \to 0}\), to a Poisson point process with intensity measure \({Z{(\rm dx)}{\rm e}^{-\alpha h} {\rm d}h}\), where \({\alpha:= 2/\sqrt{g}}\) with g: = 2/π and where Z(dx) is a random Borel measure on [0, 1]². In particular, this yields an integral representation of the law of the absolute maximum, similar to that found in the context of Branching Brownian Motion. We give evidence that the random measure Z is a version of the derivative martingale associated with the continuum Gaussian Free Field.     

Computational s-block thermochemistry with the correlation consistent composite approach

The correlation consistent composite approach (ccCA) is a model chemistry that has been shown to accurately compute gas-phase enthalpies of formation for alkali and alkaline earth metal oxides and hydroxides (Ho, D. S.; DeYonker, N. J.; Wilson, A. K.; Cundari, T. R. J. Phys. Chem. A 2006, 110, 9767).The ccCA results contrast to more widely used model chemistries where calculated enthalpies of formation for such species can be in error by up to 90 kcal mol-1. In this study, we have applied ccCA to a more general set of 42 s-block molecules and compared the ccCA DeltaHf values to values obtained using the G3 and G3B model chemistries. Included in this training set are water complexes such as Na(H2O)n+ where n = 1 - 4, dimers and trimers of ionic compounds such as (LiCl)2 and (LiCl)3, and the largest ccCA computation to date: Be(acac)2, BeC10H14O4. Problems with the G3 model chemistries seem to be isolated to metal-oxygen bonded systems and Be-containing systems, as G3 and G3B still perform quite well with a 2.7 and 2.6 kcal mol-1 mean absolute deviation (MAD), respectively, for gas-phase enthalpies of formation. The MAD of the ccCA is only 2.2 kcal mol-1 for enthalpies of formation (DeltaHf) for all compounds studied herein. While this MAD is roughly double that found for a ccCA study of >350 main group (i.e., p-block) compounds, it is commensurate with typical experimental uncertainties for s-block complexes. Some molecules where G3/G3B and ccCA computed DeltaHf values deviate significantly from experiment, such as (LiCl)3, NaCN, and MgF, are inviting candidates for new experimental and high-level theoretical studies.     

Vaporization enthalpies and vapor pressures of the major components of opopanax oil, α-santalene,cis α-bisabolene,cis α-bergamotene

Structural Chemistry - The vapor pressures and vaporization enthalpies of the major components of opopanax oil, a medicinal that has been in use since biblical times, are evaluated by correlation...     

The Supramolecular Structural Chemistry of Pentafluorosulfanyl and Tetrafluorosulfanylene Compounds

The analysis of crystal structures of SF₅- or SF₄-containing molecules revealed that these groups are often surrounded by hydrogen or other fluorine atoms. Even though fluorine prefers F⋅⋅⋅H over F⋅⋅⋅F contacts, the latter appeared to be important in many compounds. In a significant number of datasets, the closest F⋅⋅⋅F contacts are below 95 % of the van der Waals distance of two F atoms. Moreover, a number of repeating structural motifs formed by contacts between SF₅ groups was identified, including different supramolecular dimers and infinite chains. Among SF₄-containing molecules, the study focused on SF₄Cl compounds, including the first solid-state structure analyses of these reactive species. Additionally, electrostatic potential surfaces of a series of Ph-SF₅ derivatives were calculated, pointing out the substituent influence on the ability of F⋅⋅⋅X contact formation (X=F or other electronegative atom). Interaction energies were calculated for different dimeric arrangements of Ph-SF₅, which were extracted from experimental crystal structure determinations.