Normal generation and \ell ^2-Betti numbers of groups

The normal rank of a group is the minimal number of elements whose normal closure coincides with the group. We study the relation between the normal rank of a group and its first $\ell ^2$ -Betti number and conjecture the inequality $\beta _1^{(2)}(G) \le \mathrm{nrk}(G)-1$ for torsion free groups. The conjecture is proved for limits of left-orderable amenable groups. On the other hand, for every $n\ge 2$ and every $\varepsilon >0$ , we give an example of a simple group $Q$ (with torsion) such that $\beta _1^{(2)}(Q) \ge n-1-\varepsilon $ . These groups also provide examples of simple groups of rank exactly $n$ for every $n\ge 2$ ; existence of such examples for $n> 3$ was unknown until now.     

Thickness-Two Graphs Part Two: More New Nine-Critical Graphs,Independence Ratio,Cloned Planar Graphs,and Singly and Doubly Outerplanar Graphs

There are numerous means for measuring the closeness to planarity of a graph such as crossing number, splitting number, and a variety of thickness parameters. We focus on the classical concept of the thickness of a graph, and we add to earlier work in [4]. In particular, we offer new 9-critical thickness-two graphs on 17, 25, and 33 vertices, all of which provide counterexamples to a conjecture on independence ratio of Albertson; we investigate three classes of graphs, namely singly and doubly outerplanar graphs, and cloned planar graphs. We give a sharp upper bound for the largest chromatic number of the cloned planar graphs, and we give upper and lower bounds for the largest chromatic number of the former two classes.     

An improved implementation of the McCracken and Yanosik nine point finite difference procedure

The grid orientation phenomenon present in numerical models of fluid flow in a porous media can give rise to unrealistic predictions when simulating adverse mobility displacements. McCracken and Yanosik [11] proposed a nine point finite difference scheme for approximating the solution of the continuity equations that has the potential of eliminating many of the unrealistic predictions that are observed when using five point finite difference operators. Coats and Ramesh [5] have implemented this scheme in a steamflooding model, and have noted that serious grid effects are present in the simulation of an inverted seven spot pattern. Potempa [12,13] has described a procedure which exhibits minimal grid effects for the problem described by Coats and Ramesh [5]. This paper describes modifications to the McCracken and Yanosik procedure which allow for realistic simulations of this inverted seven spot pattern under a steam drive. These modifications are based upon an approximation scheme that has been previously reported [12,13], and affect the incorporation of upstream weighting in a similator.     

Hyphenation of quadrupole MS to GC and comprehensive two-dimensional GC for the analysis of suspected allergens: review and improvement

This survey reviews papers that have been previously published on the quantitative analysis of suspected allergens. The routine gas chromatography (GC)-mass spectrometry (MS) method allows their evaluation in most fragrances, but the application of an automated data treatment sometimes leads to over- or underestimations when target compounds are coeluted or shifted because of the presence of other fragrance ingredients. In such cases, an appropriate retreatment of data generated by the routine analysis is proposed to better estimate these shifted or coeluted peaks. A second and more sophisticated approach, based on comprehensive bidimensional GC hyphenated to quadrupole MS, overcomes coelution problems. However, its use is still time consuming because of the lack of a commercial program. In this work, a software prototype is tested to reprocess the data. It dramatically shortens the data treatment and offers good quantitative results.     

On-line coupling of size exclusion and capillary zone electrophoresis via a reversed-phase C18 trapping column for the analysis of structurally related enkephalins in cerebrospinal fluid

On-line coupled analytical techniques can be advantageous in the assay of smaller peptides in complex biological matrices such as plasma, cerebrospinal fluid (CSF) and tissues. The present study shows the feasibility of a recently developed system, consisting of a size-exclusion chromatographic (SEC) separation followed by a trapping procedure on an RP18 microcolumn with subsequent elution of the trapped fraction and separation by capillary zone electrophoresis (CZE) for the quantification of structural-related peptides in biological matrices, as demonstrated for a number of enkephalins in CSF. After SEC separation of the enkephalins from large proteins present in CSF a heart-cut of 200 nuL, containing the enkephalin peak, is taken, concentrated on the RP18 microcolumn and, after elution of the enkephalins with 80% acetonitrile, a fraction of the eluate is electrokinetically injected into the CZE system, where stacking and separation is achieved. The degradation of the peptides, caused by endogenous peptidases in the matrix, is sufficiently inhibited with imipramine HCl. The assay has a satisfactory linearity and intraday (9.70-16.3%) precision considering the complexity of this multidimensional separation system. The sensitivity of the method, with a concentration limit of quantification of 2.5 nug/mL, is comparable with other CZE assays for peptides and sufficient for the quantification of peptide drugs in biological matrices.     

Effect of Solvation on Chemical Reactions,I. Addition of a Single Water Molecule to the H− + H2O → OH− + H2 Reaction

The gas phase chemical reaction, H^? + H₂O → H₂ + OH, and the effect of an additional water molecule on the reaction, H^?(H₂O) + H₂O → H₂ + OH(H₂O), have been investigated. The optimal structures and energies of the reactants, products, two stable intermediates, and the transition state connecting the two intermediates have been determined. The additional water molecule does not affect the potential surface congruently: it destabilizes the H(H₂O) minimum, but stabilizes the H₂ ?OH minimum and the transition state connecting the two intermediates. However, it stabilizes the products more than the H₂ ?OH^? minimum. Finally, in line with the reduction in the barrier height, the transition state for the H(H₂0) to H₂ ?OH^? isomerization moves further along the reaction path.     

Computational investigation of irreversible inactivation of the zinc-dependent protease carboxypeptidase A

Zinc proteases are ubiquitous and the zinc ion plays a central function in the catalytic mechanism of these enzymes. A novel class of mechanism-based inhibitors takes advantage of the zinc ion chemistry in carboxypeptidase A (CPA) to promote covalent attachment of an inhibitor to the carboxylate of Glu-270, resulting in irreversible inhibition of the enzyme. The effect of the active site zinc ion on irreversible inactivation of CPA was probed by molecular orbital (MO) calculations on a series of active site models and the Cl(-) + CH(3)Cl S(N)2 reaction fragment. Point charge models representing the active site reproduced energetics from full MO calculations at 12.0 A separation between the zinc and the central carbon of the S(N)2 reaction, but at 5.0 A polarization played an important role in moderating barrier suppression. ONIOM MO/MO calculations that included the residues within 10 A of the active site zinc suggest that about 75% of the barrier suppression arises from the zinc ion and its ligands. A model of the pre-reactive complex of the 2-benzyl-3-iodopropanoate inactivator with CPA was constructed from the X-ray structure of l-phenyl lactate bound in the active site of the enzyme. The model was fully solvated and minimized by using the AMBER force field to generate the starting structure for the ONIOM QM/MM calculations. Optimization of this structure led to the barrierless S(N)2 displacement of the iodide of the inhibitor by Glu-270, assisted by interaction of the zinc ion with the leaving group. The resulting product is in good agreement with the X-ray structure of the covalently modified enzyme obtained by irreversible inhibition of CPA by 2-benzyl-3-iodopropanoate.     

Geometry optimization with QM/MM,ONIOM, and other combined methods. I. Microiterations and constraints

Hybrid energy methods such as QM/MM and ONIOM, that combine different levels of theory into one calculation, have been very successful in describing large systems. Geometry optimization methods can take advantage of the partitioning of these calculations into a region treated at a quantum mechanical (QM) level of theory and the larger, remaining region treated by an inexpensive method such as molecular mechanics (MM). A series of microiterations can be employed to fully optimize the MM region for each optimization step in the QM region. Cartesian coordinates are used for the MM region and are chosen so that the internal coordinates of the QM region remain constant during the microiterations. The coordinates of the MM region are augmented to permit rigid body translation and rotation of the QM region. This is essential if any atoms in the MM region are constrained, but it also improves the efficiency of unconstrained optimizations. Because of the microiterations, special care is needed for the optimization step in the QM region so that the system remains in the same local valley during the course of the optimization. The optimization methodology with microiterations, constraints, and step-size control are illustrated by calculations on bacteriorhodopsin and other systems.     

An ab initio study of the photochemical decomposition of 3, 3-dimethyldiazirine

Photochemical decomposition of 3,3-dimethyldiazirine (DMD) has been computationally investigated by using high-level ab initio calculations in conjunction with the 6-31G and cc-pvdz basis sets. The geometries of minima and transition states, as well as conical intersection points in the seam of crossing of two surfaces, have been optimized with the complete active space self-consistent field (CAS-SCF) method, and their energies, recalculated with second-order multireference perturbation (CAS/MP2) theory. The reaction path starting at the excited n-pi state of DMD is predicted to occur via a nonadiabatic mechanism, giving carbene and molecular dinitrogen (both in their singlet ground states) as the main products; the computed barrier height (1.0 kcal mol(-)(1)) agrees well with the experimental estimate of the activation energy in the singlet excited state (0.0-1.5 kcal mol(-)(1)). Ground state of dimethylcarbene is the only species where a 1,2-hydrogen shift takes place, being the only source of propene. The calculated potential energy barrier height for dimethylcarbene to propene isomerization (2.6 kcal mol(-)(1)) agrees well with the observed activation energy (2.56 kcal mol(-)(1)). No evidence for rearrangement in the first singlet excited state of DMD has been found; such a process would lead to a higher activation energy than the observed one. Consequently, 1,2-hydrogen migration concurrent with N(2) extrusion in the excited state has been ruled out.     

Native defect changes in cds single crystal platelets induced by vacuum heat treatments at temperatures up to 600°C

Physical properties of selected CdS single crystal platelets as-grown and after vacuum heat treatments at temperatures up to 600°C have been studied using u.v. excited edge emission, mass spectrometry, electrical resistivity and electron paramagnetic resonance (EPR). It was found that sulfur leaves the crystal at temperatures as low as 100°C creating a depletion layer. The native defect changes were monitored by edge emission studies at 4.2°K in combination with etch treatments. The defect structure throughout the crystal is not only dependent upon the temperature and atmosphere of the treatments, but is also strongly dependent upon the cooling rate.