Krull-Schmidt fails for serial modules

We answer a question posed by Warfield in 1975: the Krull-Schmidt Theorem does not hold for serial modules, as we show via an example. Nevertheless we prove a weak form of the Krull-Schmidt Theorem for serial modules (Theorem 1.9). And we show that the Grothendieck group of the class of serial modules of finite Goldie dimension over a fixed ring is a free abelian group.

     

Dramatic changes in geometry after ionization: experimental and theoretical studies on the electronic properties of fluorocarbonyl (mono-, di-, and tri-) sulfur compounds

In this work, we present a complete study on He I photoelectron spectroscopy (PES) for the fluorocarbonyl mono-, di-, and trisulfur compounds FC(O)SCl, FC(O)SSCH(3), and FC(O)SSSC(O)F. After optimizations of the structure for stable conformers at different levels of theory, a complete theoretical study involving the calculation of the ionization energies using orbital valence Green's functional (OVGF) was performed. Calculations of radical-cationic forms were carried out in order to compare their properties with those of the neutral molecules. The first IP values are 10.7, 9.0, and 10.5 eV for FC(O)SCl, FC(O)SSCH(3), and FC(O)SSSC(O)F, respectively. The groups bonded to the S atom mainly influence the ionizations originating from the sulfur lone pairs. A wide electronic delocalization in the FC(O)S moiety can be deduced from experimental and theoretical results, which leads to a strong energetic stabilization of the n' '(S) (sulfur lone pair pi orbital). Other conclusions relate to effects on the substituents attached to the S atom and the importance of the molecular planarity in the orbital stabilization of the FC(O)S moiety for the neutral molecules. It is worthwhile mentioning that FC(O)SCl retains its planar structure after ionization, but drastic changes occur in the geometry of both FC(O)SSCH(3) and FC(O)SSSC(O)F. The FC(O)SSCH(3) molecule adopts a heavy atom planar structure after ionization. The FC(O)SSS moiety becomes a planar form after the ionization of the FC(O)SSSC(O)F molecule, whereas the second C(O)F group maintains its original conformation with respect to the SSS group.     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

Fused pyrazolopyrimidines. I. Pyrazolo[4,3-e]-v-triazolo[1,5-a]pyrimidine. A new heterocyclic system

5-Azido-4-cyano-1-phenylpyrazole reacts with benzylcyanide in the presence of sodium methoxide to give the title ring system.     

Infrared active fundamental vibrations of TCNQ and chloranil monovalent anions

The interpretation of the infrared active fundamentals of TCNQ and chloranil monovalent anions is given for the first time. The rationalization of the infrared spectra was made possible by the recently achieved vibrational assignment of the corresponding neutral molecules and is mainly based on a set of judicious adjustments of their empirical valence force fields.     

Comparative performance of MM3(92) and two TINKER MM3 versions for the modeling of carbohydrates

The 1992 version of MM3 was largely used for modeling mono-, di-, and trisaccharides. In later versions of MM3 improvements were made in some parameters that may be important for carbohydrates. This corrected MM3 force field is part of the Tinker package, freely available (as its 4.1 version), and included in the Chem 3D Ultra 8.0 package (as the 3.7 version). The latter version lacks the corrections to the standard bond lengths produced by electronegativity and anomeric effects, whereas the Tinker 4.1 version only lacks the latter correction. The present work compares the performance of the three MM3 versions (and in some cases, DFT and/or HF/ab initio procedures) on several carbohydrate model problems as the chair and rotamer equilibria in 2-hydroxy- and 2-methoxytetrahydropyran, hydrogen bonding in cis-2,3-dihydroxytetrahydropyran, and the potential energy surfaces around the glycosidic bonds of two sulfated disaccharides and two trisaccharides. Tinker MM3 can be used accurately to estimate carbohydrate energies and geometries, and-with the help of some programming-to pursue studies on the potential energy surfaces of di- and trisaccharides. In most cases results obtained using the three MM3 versions are similar, although large energy differences are obtained when comparing a rotameric distribution around a O-C-O-H dihedral, which is almost forced to the exo-anomeric position by the Tinker versions. In other systems smaller energy differences are found, but they can nevertheless lead to a different global minimum when comparing conformers of similar energy. MM3(92) establishes better the differences between the bond lengths in both anomers, as an expected expression of the anomeric correction.