Nonlinear breakup of a self-gravitating column

Using the method of strained coordinates, a weakly nonlinear theory of the breakup of a gravitating column is presented. It is shown that the self-gravitating column breaks into the main celestial bodies and their satellites whose dimensions are sensitive to the wavenumbers.     

Discovery and crystal structure of a novel chlorocarbon host: perchlorofluorene-9-spirocyclohexa-2′,5′-diene

Chlorination of triphenylene (1a) employing a mixture of aluminium trichloride and sulphur monochloride in sulphuryl chloride leads to rearrangement with formation of the title chlorocarbon (2), a new host, as main product. X-ray crystal structure analyses of the unsolvated spirocycle (2) as well as of its inclusion compounds with guests benzene and cyclohexa-1,4-diene are described.     

Fractal fingerprinting of chromatographic profiles based on wavelet analysis and its application to characterize the quality grade of medicinal herbs

Extracting chemical fingerprints is an important step for representing and interpreting chromatographic data. In this paper, the chromatographic profile is decomposed into components at different resolution levels using wavelet analysis, then the fractal dimensions of these components are computed as the chemical fingerprints. The chromatographic fingerprint is characterized by the vector composed of these chemical fingerprints, which can represent the chemical patterns of different categories of complex samples. Computer simulations reveal that the fractal fingerprints are more stable than the original chromatographic profile data with respect to variations of peak retention time. To demonstrate the validity of this method, the evaluation of the quality of the medicinal herb Angelica sinensis (Oliv.) diels is investigated. Principal component analysis of the fractal fingerprints indicates that samples belonging to the same quality grade are clustered together, while those belonging to different quality grades are separated. Using these fractal fingerprints taken from the chromatographic scans as inputs for an artificial neural network (ANN). The quality grades of two sets of the herbs were verified by cross-validation, indicating that 96.7% of the herbs are correctly identified with respect to their quality grades evaluated by experienced experts, and 100.0% of the herbs are correctly identified with respect to their quality grades determined by pharmacodynamical evaluation.     

AM1 molecular orbital studies of the structures,conformations, protonation energies,and electronic properties of triazine dihydrofolate reductase inhibitors

The structural, conformational, and electronic properties of three triazine antifolates were determined by AM1 molecular orbital calculations, and the results were compared with other theoretical studies and with X-ray crystallographic studies of these and similar triazines both in the crystalline state and as complexes bound to dihydrofolate reductase. Calculated protonation energies confirm crystal structure data indicating N-protonation analogous to that reported for MTX in similar environments. Overall, the calculated structural and conformational properties are in good agreement with X-ray crystallographic results for these and similar triazines as found in the crystalline state and in enzymebound ternary complexes. However, for one triazine AM1 predicts a conformation with the bulky aromatic substituent twisted about 60° away from coplanarity with the triazine ring, in contrast to the nearly coplanar conformation found in the crystalline state. Intermolecular interactions favoring the coplanar conformation may thus be operative in the crystalline environment. The unique conformational preferences and greater conformation flexibility of triazines in general and of this triazine in particular may provide a key to understanding their biological activity.     

Allopurinol complexes with first row transition metal perchlorates

Summary Complexes of allopurinol (apH) with Fe^III and several 3d metal(II) (e.g. Fe, Co, Ni and Cu) perchlorates were prepared. The solid complexes isolated included two monomeric hexacoordinated adducts of the type [Fe(apH)₃-(OClO₃) (OH₂)₂]ClO₄ and [Fe(apH)₃(OClO₃)₂(OH₂)]ClO₄, involving N(8)-bound neutral apH ligands, and polymeric Co, Ni or Cu complexes containing both neutral apH and monoanionic ap^- ligands. The latter three complexes involved both N(8)-bound terminal apH and N(1), N(8)- or N(1), N(9)-bound bridging ap^- ligands, and were of the following types: [(apH)₂Cu(ap)] _n (ClO₄) _n , tetrahedral; [(apH)(H₂O)(OClO₃)Co(ap)] _n , pentacoordinated; and [(apH)₂(H₂O)(OClO₃)Ni(ap)] _n , hexacoordinated.Presented in part at the 203rd. American Chemical Society National Meeting; see Ref. 1.     

Prediction of the orientations of adsorbed protein using an empirical energy function with implicit solvation

When simulating protein adsorption behavior, decisions must first be made regarding how the protein should be oriented on the surface. To address this problem, we have developed a molecular simulation program that combines an empirical adsorption free energy function with an efficient configurational search method to calculate orientation-dependent adsorption free energies between proteins and functionalized surfaces. The configuration space is searched systematically using a quaternion rotation technique, and the adsorption free energy is evaluated using an empirical energy function with an efficient grid-based calculational method. In this paper, the developed method is applied to analyze the preferred orientations of a model protein, lysozyme, on various functionalized alkanethiol self-assembled monolayer (SAM) surfaces by the generation of contour graphs that relate adsorption free energy to adsorbed orientation, and the results are compared with experimental observations. As anticipated, the adsorbed orientation of lysozyme is predicted to be dependent on the discrete organization of the functional groups presented by the surface. Lysozyme, which is a positively charged protein, is predicted to adsorb on its 'side' on both hydrophobic and negatively charged surfaces. On surfaces with discrete positively charged sites, attractive interaction energies can also be obtained due to the presence of discrete local negative charges present on the lysozyme surface. In this case, 'end-on' orientations are preferred. Additionally, SAM surface models with mixed functionality suggest that the interactions between lysozyme and surfaces could be greatly enhanced if individual surface functional groups are able to access the catalytic cleft region of lysozyme, similar to ligand-receptor interactions. The contour graphs generated by this method can be used to identify low-energy orientations that can then be used as starting points for further simulations to investigate conformational changes induced in protein structure following initial adsorption.     

A Remark on Real Parameter Global Bifurcation

We study the nonlinear eigenvalue problem F(x,) = L()x +R(x,) = 0 where F : X × R X with X a Hilbert space. IfL() is a polynomial in , then it is shown that 0> 0 is a global bifurcation point of the eigenvalue problem provided astandard transversality condition is satisfied, the dimension of the nullspace of L(0) is an odd number and L() is composed of asequence of positive operators on the finite dimensional null space ofL(0).     

Aberration-correction results from a segmented microelectromechanical deformable mirror and a refractive lenslet array

Quadratic aberration is successfully corrected with a segmented microelectromechanical deformable mirror in conjunction with a refractive lenslet array. Use of the lenslet array greatly improves the effective fill factor of the correcting element. Experimental results show correction approaching the diffraction limit for an extreme spherical aberration.