Parallel implementation of the p‐version of the finite element method for elliptic equations on a shared‐memory architecture

An implementation of the p‐version of the finite element method for solving two‐dimensional linear elliptic problems on a shared‐memory parallel computer is analyzed. The idea is to partition the problem among the available processors and perform computations corresponding to different elements in parallel. The parallelization is based on a domain decomposition technique using the Lagrange multipliers. The numerical experiments carried out on the Sequent system indicate very high performance of the mixed finite element algorithm in terms of attained speedups. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Statistical Discrepancy and Affinity of Priority Vector Heuristics in Pairwise-Comparison-Based Methods

There are numerous priority deriving methods (PDMs) for pairwise-comparison-based (PCB) problems. They are often examined within the Analytic Hierarchy Process (AHP), which applies the Principal Right Eigenvalue Method (PREV) in the process of prioritizing alternatives. It is known that when decision makers (DMs) are consistent with their preferences when making evaluations concerning various decision options, all available PDMs result in the same priority vector (PV). However, when the evaluations of DMs are inconsistent and their preferences concerning alternative solutions to a particular problem are not transitive (cardinally), the outcomes are often different. This research study examines selected PDMs in relation to their ranking credibility, which is assessed by relevant statistical measures. These measures determine the approximation quality of the selected PDMs. The examined estimates refer to the inconsistency of various Pairwise Comparison Matrices (PCMs)—i.e., W = (w_ij), w_ij > 0, where i, j = 1,…, n—which are obtained during the pairwise comparison simulation process examined with the application of Wolfram’s Mathematica Software. Thus, theoretical considerations are accompanied by Monte Carlo simulations that apply various scenarios for the PCM perturbation process and are designed for hypothetical three-level AHP frameworks. The examination results show the similarities and discrepancies among the examined PDMs from the perspective of their quality, which enriches the state of knowledge about the examined PCB prioritization methodology and provides further prospective opportunities.     

Solid-state molecular organization and solution behavior of methane-1,1-diphosphonic acid derivatives of heterocyclic amines: the role of the topochemical ring modification and the intramolecular hydrogen bonds in monosubstituted piperid-1-ylmethane-1,1-diphosphonic acids

The crystal structures of 3-methylpiperid-1-ylmethane-1,1-diphosphonic (2), 4-methylpiperid-1-ylmethane-1,1-diphosphonic (3), 2-ethylpiperid-1-ylmethane-1,1-diphosphonic (4), and 2-methylpiperid-1-ylmethane-1,1-diphosphonic (5) acids have been determined and are discussed with respect to their molecular organization and crystal-packing preferences. The chair conformation, predominant also in solution, favors equatorial positioning of the bulky substituents of the heterocyclic N and C atoms. The molecular geometry also provides access to intramolecular hydrogen-bond formation between the axial protons located on the nitrogen atoms, as well as the carbon atoms closest to it, and phosphonic/phosphonate oxygen atoms. The molecules preferably arrange in monolayers, observed in all crystals with an exception of 3. The layers are held in place in the third direction through van der Waals interactions. The analysis of two-dimensional hydrogen-bonded networks is concentrated on revealing how the substituent's topology of the molecule affects the solid-state organization in well-defined structures and is aimed at unraveling the consequences and the possible conformational changes by stepwise network disruption upon crystal dissolution in water. The solution NMR studies are focused on revealing the role that the topochemistry of the substituent plays for the stereodynamics in 2-5. It is demonstrated that in contrast to piperid-1-ylmethane-1,1-diphosphonic acid (1), in which the ring inversion/rotation around the C-N bond concerted with the N-H...O hydrogen-bond breaking/formation process leads to a mixture of two interconverting conformers, the concerted N-H...O breaking/rotation/N-H...O formation process in 2 and 3 allows for a predominance of one conformer in solution. However, placement of a substituent at 2-position in the ring hampers the rotation around the C-N bond; this makes 4 and 5 significantly less flexible relative to compounds 1-3. In addition, both compounds 4 and 5 are proved to exist as a mixture of two conformers, the equilibrium of which in acidic solution is shifted towards the conformer found in solid state. In alkaline solutions of 4 and 5, the equilibrium is shifted towards the conformer that is forced by the flipping of the heterocyclic ring. These results correlate well with recently documented differences in the biological potency of this group of compounds.     

Renormalization group approach to lattice gauge field theories

We study four-dimensional pure gauge field theories by the renormalization group approach. The analysis is restricted to small field approximation. In this region we construct a sequence of localized effective actions by cluster expansions in one step renormalization transformations. We construct also -functions and we define a coupling constant renormalization by a recursive system of renormalization group equations.     

Dilithium tetrabromonickelate (II) as a source of soft nucleophilic bromide : Reaction with epoxides

Dilithium tetrabromonickelate (II) in THF serves as a source of “soft” nucleophilic bromide and reacts regioselectively with epoxides to give bromohydrins in high yield.     

A quantitative thermal analysis of cyclists’ thermo-active base layers

It is well known that clothes used in sporting activity are a barrier for heat exchange between the environment and athlete, which should help in thermoregulation improvement. However, it is difficult to evaluate which top is best for each athlete according to the characteristics of the sport. Researchers have tried to measure the athlete’s temperature distribution during exercise at the base layers of tops with different approaches. The aim of this case study was to investigate the use of thermography for thermo-active base layer evaluation. Six new base layers were measured on one cyclist volunteer during a progressive training on a cycloergometer. As a control condition, the skin temperature of the same volunteer was registered without any layer with the same training. A training protocol was selected approximate to cycling race, which started from the warm-up stage, next the progressive effort until the race finished and at the end “cool-down” stage was over. In order to show which layer provided the strongest and weakest barrier for heat exchange in comparison with environment, the temperature parameters were taken into consideration. The most important parameter in the studies was the temperature difference between the body and the layers, which was changing during the test time. The studies showed a correlation between the ergometer power parameter and the body temperature changes, which has a strong and significant value. Moreover, the mass of every layer was checked before and after the training to evaluate the mass of the sweat exuded during the test. From this data, the layer mass difference parameter was calculated and taken into consideration as a parameter, which may correspond with the mean heart rate value from each training. A high and positive correlation coefficient was obtained between the average heart rate and the mass difference for the base layers. Thermal analysis seems to have a new potential application in the objective assessment of sports clothing and may help in choosing the proper clothes, which could support heat transfer during exercising and protect the body from overheating.

     

Potassium salts of hypodiphosphoric acid

The synthesis and crystal structures of a series of six crystalline potassium salts of hypodiphosphoric acid, H₄P₂O₆, are reported, namely potassium hydrogen phosphonophosphonate, K⁺·H₃P₂O₆⁻, (I), dipotassium dihydrogen hypodiphosphate monohydrate, 2K⁺·H₂P₂O₆²⁻·H₂O, (II), dipotassium dihydrogen hypodiphosphate dihydrate, 2K⁺·H₂P₂O₆²⁻·2H₂O, (III), pentapotassium hydrogen hypodiphosphate dihydrogen hypodiphosphate dihydrate, 5K⁺·HP₂O₆³⁻·H₂P₂O₆²⁻·2H₂O, (IV), tripotassium hydrogen hypodiphosphate tetrahydrate, 3K⁺·HP₂O₆³⁻·4H₂O, (V), and tetrapotassium hypodiphosphate tetrahydrate, 4K⁺·P₂O₆⁴⁻·4H₂O, (VI). All the hypodiphosphate anions, viz. H₃P₂O₆⁻, H₂P₂O₆²⁻, HP₂O₆³⁻ and P₂O₆⁴⁻, adopt a staggered conformation. The P—P bond lengths [2.1722 (7)–2.1892 (10) Å] do not depend on the basicity of the anion. The compounds are organized into different types of one‐, two‐ or three‐dimensional polymeric hydrogen‐bonded networks, or simply exist in the form of isolated or dimeric units. The coordination numbers of the K⁺ cations range from 6 to 9, and the cationic sublattices are polymeric one‐, two‐ or three‐dimensional networks, or isolated [KO₆] or dimeric [K₂O₁₂] polyhedra.     

New liquid nitrogen cryogenic modulator for comprehensive two-dimensional gas chromatography

A new liquid nitrogen (LN2) jet-based thermal modulator for performing comprehensive two-dimensional (2D) gas chromatographic (GC x GC) separations has been designed and constructed. Temperature measurements of the trapping zone, a segment of uncoated fused silica capillary, show that it can be cooled to -196 degrees C in about 300 ms. A film of liquid nitrogen develops on the outside of the trapping capillary even when the oven temperature is in excess of 200 degrees C. Compounds as volatile as propane can be trapped by the modulator and held for periods of at least 1 min without breakthrough. The peak widths for n-alkanes are on the order of 80 ms at half height after passing through an 80cm second dimension column. Repeated analysis of gasoline demonstrated excellent run-to-run reproducibility of the system.     

Facts and artifacts about aromatic stability estimation

The stability of a set of 105 five-membered π-electron systems (involving aromatic, non-aromatic and anti-aromatic species) was evaluated using six isodesmic reactions of which two belong to the subclass of homodesmotic reactions, which are based on cyclic and acyclic reference systems. We demonstrate that the ‘Resonance Energies’ derived from isodesmotic schemes have obvious flaws and do not correct or cancel other contributions to the energy, such as the changes of hybridization, homoconjugation of heterosubstituted cyclopentadienes, conjugative interactions of CC or CX (X=N or P) with a π or pseudo π orbital at Y (Y=O, S, NH, PH), strain, etc. as effectively as possible. Likewise, ‘aromatic stabilization energies (ASE)’ derived from homodesmotic schemes based on the acyclic reference compounds do not give satisfactory results. We strongly recommend that only cyclic reference compounds should be used for ASE and other aromaticity evaluations. The analysis is based on ab initio optimized geometries at B3LYP/6-311+G^∗∗.