Strong Grobner bases for polynomials over a principal ideal ring

Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.

An in vitro study of non-axial forces upon the retention of an O-ring attachment

Objective The purpose of this study was to evaluate the retention force of an O-ring attachment system in different inclinations to the ideal path of insertion, using devices to compensate angulations. Material and methods Two implants were inserted into an aluminum base, and ball attachments were screwed to implants. Cylinders with O-rings were placed on ball attachments and connected to the test device using positioners to compensate implant angulations (0 degrees, 7 degrees, and 14 degrees). Plexiglass bases were used to simulate implant angulations. The base and the test device were positioned in a testing apparatus, which simulated insertion/removal of an overdenture. A total of 2900 cycles, simulating 2 years of overdenture use, were performed and 36 O-rings were tested. The force required for each cycle was recorded with computer software. Longitudinal sections of ball attachment-positioner-cylinder with O-rings of each angulation were obtained to analyze the relationship among them, and O-ring sections tested in each angulation were compared with an unused counterpart. A mixed linear model was used to analyze the data, and the comparison was performed by orthogonal contrasts (alpha=0.05). Results At 0 degrees, the retention force decreased significantly over time, and the retention force was significantly different in all comparisons, except from 12 to 18 months. When the implants were positioned at 7 degrees, the retention force was statistically different at 0 and 24 months. At 14 degrees, significant differences were found from 6 and 12 to 24 months. Conclusions Within the limitations of this study, it was concluded that O-rings for implant/attachments perpendicular to the occlusal plane were adequately retentive over the first year and that the retentive capacity of O-ring was affected by implant inclinations despite the proposed positioners. To cite this article:Rodrigues RCS, Faria ACL, Macedo AP, Sartori IAM, de Mattos MGC, Ribeiro RF. An in vitro study of non-axial forces upon the retention of an O-ring attachment.Clin. Oral Impl. Res. 20, 2009; 1314-1319.doi: 10.1111/j.1600-0501.2009.01742.x.

Ring flexibility within tricyclic antidepressant drugs

The internal flexibility of the central seven-membered ring of a series of tricyclic antidepressant drugs (TCAs), imipramine {l}, amitriptyline {2}, doxepin {3}, and dothiepin {4}, has been investigated by H-1 and C-13 nuclear magnetic (NMR) techniques. Two dynamic processes were examined: ring inversion and bridge flexing. H-1 NMR lineshape analysis was used to obtain ring inversion barriers for 2-4. These studies yielded energy barriers of 14.3, 16.7, and 15.7 +/- 0.6 kcal/mol for the hydrochloride salts of doxepin, dothiepin, and amitriptyline, respectively. The barriers for the corresponding free bases were lower by 0.6 kcal/mol on average. (CT1)-C-13 relaxation measurements were used to determine the degree of bridge flexing associated with the central seven-membered ring for all four compounds. By fitting the T-1 data to a two-state jump model, lifetimes and amplitudes of rapid bridge flexing motions were determined. The results show that imipramine has the fastest rate of bridge flexing, followed by amitriptyline, doxepin, and dothiepin. The pharmacological profiles of the TCAs are complex and they interact with many receptor sites, resulting in numerous side effects and a general lack of understanding of their precise mode of action in different anxiety-related disorders. They all have similar three-dimensional structures, which makes it difficult to rationalize their differing relative potency in different assays/clinical settings. However, the clear finding here that there are significantly different degrees of internal mobility suggests that molecular dynamics should be an additional factor considered when trying to understand the mode of action of this clinically important family of molecules. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:713-721, 2001.

2-pyrazinylnitrene and 4-pyrimidylnitrene. Ring expansion to 1,3,5-triazacyclohepta-1,2,4,6-tetraene and ring opening to (2-isocyanovinyl)carbodiimide

Tetrazolo[1,5-a]pyrazine/2-azidopyrazine 9T/9A undergo photolysis in Ar matrix at cryogenic temperatures to yield 1,3,5-triazacyclohepta-1,2,4,6-tetraene 21 as the first observable intermediate, and 1-cyanoimidazole 11 and (2-isocyanovinyl)carbodiimide 22 as the final products. The latter tautomerizes to 2-(isocyanovinyl)cyanamide 23 on warming to 40 K. The same intermediate 21 and the same final products are obtained on matrix photolysis of the isomeric tetrazolo[1,5-c]pyrimidine/4-azidopyrimidine 24T/24A. These photolysis results as well as those of the previously reported thermal ring contraction of N-15-labeled 2-pyrazinyl- and 4-pyrimidylnitrenes to 1-cyanoimidazoles can all be rationalized in terms of selective ring opening of 21 or nitrine 10 to a nitrile ylide zwitterion 28 prior to formation of the final products, 11 and 22. The results are supported by high-level ab initio and DFT calculations (CASPT2-CASSCF(6,6), G3(MP2), and B3LYP/6-31+G*) of the energies and IR spectra of the intermediates and products.