A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Chiral Derivatives of Achiral Molecules: Standard Classes and the Problem of a Right-Left Classification

Chemistry judging by its applications, physics according to its methods, and heavily reliant upon the tools of mathematics—that is what makes theoretical chemistry. And yet that is where its strength lies—in the variety of these sciences. It is quite natural that, in answer to specific problems, results and methods can sometimes be developed whose scope extends far beyond the original application. Rather it is a mark of quality if consequences can be found in chemistry and physics and the pathway leads via new mathematical procedures and concepts. Regrettably, any publication aiming to present such aspects will usually encounter little resonance since the linguistic confusion in science, its disciplines, and subdisciplines, lies like a veil over our understanding. The author nevertheless wishes to attempt to present, in a series of articles, results of research into chemical themes in a manner designed to appeal to the interest of chemists, without neglecting interdisciplinary aspects. All that is required to understand the argumentation is a lively interest. The first two articles are concerned with the chirality of molecules, and in particular with questions relating to the chirality phenomenon of molecules in the framework of molecular classes. In view of the algebraic nature of the mathematical methods adopted, it is not surprising that precise statements result. It appears of primary interest to establish the degree to which such statements can be considered valid for molecular models or molecules themselves.     

Analytical quality control by solid sampling GFAAS in the production of animal tissue reference materials: lead and cadmium in bovine liver reference materials

Summary The function of solid sampling graphite furnace atomic absorption spectrometry (SS-GFAAS) in the laboratory-internal preparation, production and standardization of bovine liver reference material is described. Analytical quality assurance was achieved by using a wet digestion decomposition procedure and GFAAS (WD-GFAAS) as well as three different methods of SS-GFAAS. It will be shown, that SS-GFAAS is an adequate and efficacious method of analytical quality control in the production of reference materials. Details are given about the preliminary steps of sample selection and preparation, applying SS-GFAAS both as a screening method and for the detection of contamination during the production of the reference materials. The element contents of the four bovine liver materials measured after decomposition with nitric acid in the open system by GFAAS and also by Flame-AAS, using the slotted tube atom trap, are compared statistically with the results obtained by SS-GFAAS. In solid sampling analyses three different systems were applied: a solid sampling ZAA-spectrometer with platform-boat, a D₂AA-spectrometer with solid sampling graphite tube and platform-drawer and an autoprobe-D₂AA-spectrometer with solid sampling autoprobe and graphite tube.     

Heteronuclear solid-state correlation spectroscopy

Two-dimensional NMR methods are proposed for correlating the spectra of abundant and dilute spins in solids. The techniques simplify assignment and permit determination of shielding tensors even when extensive overlaps occur. Spin diffusion among abundant spins can be observed indirectly.     

Theory of chirality functions,generalized for molecules with chiral ligands

The theory of chirality functions described in a previous publication is generalized to allow for chiral ligands. In the earlier theory, all symmetry operations of the molecular frame could be thought of as permutations of the ligands among the sites; in the present work, improper rotations not only permute the ligands, but convert them into mirror images. The group that generates all isomers from a given ordered molecule belonging to a frame with n sites is now the hyperoctahedral group of order 2ⁿ n! consisting of all possible combinations of permutations and site reflections. The representation theory of these groups is described, and applied to the problem of constructing qualitatively complete chirality functions, and of deciding which ligand partitions, and which isomer mixtures, are chiral. It is found useful to classify chiral representations of the covering group as ligand specific and class specific. The ligand specific representations describe chiral properties which are common to all frames and arise purely from the chirality of the ligands, while the class specific representations describe the chiral properties of the frame. A number of examples are explicitly worked out.     

Efficient and practical Ag-catalyzed cycloadditions between arylimines and the Danishefsky diene

An efficient Ag-catalyzed method for asymmetric addition of the Danishefsky diene to various aryl imines to afford cycloadducts in > or =89% ee and > or =85% isolated yield is reported. Reactions are effected with 0.1-1 mol % catalyst (4 degrees C), and the chiral ligand is readily prepared from commercially available materials, including the inexpensive i-Leu. These catalytic asymmetric cycloadditions can be carried out without the use of solvent or with undistilled THF in air. A first generation supported chiral catalyst that effectively promotes the cycloaddition reaction and can be recycled (five cycles) is described.     

Phase Equilibria and Critical Curves of Binary Ammonia–Hydrocarbon Mixtures

Liquid or dense supercritical ammonia has been suggested as an extraction fluid. It is indeed good solvent for very different classes of compounds, as can be seen from phase diagrams. Such diagrams for binary systems of ammonia and hydrocarbons are presented and discussed on the basis of their critical curves. Apparatus and methods for the measurement of phase equilibria and equation of state data of fluid mixtures at high pressure are described.