A theory of pseudo-differential boundary value problems with discontinuous conditions I

Summary The paper deals with mixed boundary value problems and transmission problems for elliptic differential and pseudo-differential operators. These problems are considered as elements of an algebra (where is the considered domain, x=, YX a submanifold of codimension 1, where the conditions have a jump, and x is a certain compactification of X/Y), the elements of which are described on a symbolic level. By means of additional conditions (of trace and potential type, with respect to Y) a given mixed problem is extended to an operator, and the Fredholm property of is established under an ellipticity condition, the parametrix is constructed on symbolic level and ind is expressed. In the second part the authors also study classes of special cases, namely differential operators of second and higher order with mixed boundary conditions for dim 2, where explicit index expressions are derived.     

A Density Functional Theory Study on Electronic Structure and Second—order Nonlinear Optical Properties of Some Push—Pull Molecules

Time-dependent density-functional theory(TDDFT)has been applied to calculate the electronic structure and second-order nonlinear optical(NLO) properties of some organic molecules.The two-dimensional(2-D)charge transfer charateristics of calculated molecules were studied and compared with corresponding experimental results.All the theoretical results agree well with the measurement.For 2-D molecule with two-fold symmetry,the dominant charge transfer is off-diagonal,while for three-fold symmetry 2-D molecule,the dominant charge transfer is not only between branches and central group but also among branches.     

Cooperative effects in binuclear zirconocenes: Their synthesis and use as catalyst in propene polymerization

The mono- and bis-cyclopentadienyl compounds 1-(Cp″)-4-(CH₃)C₆H₄ (1) and 1, 4-(Cp″)₂C₆H₄ (2) (Cp″ = 3,4-dimethylcyclopenta-1,3-diene-1-yl) have been synthesized. The reactions of the lithium salts of 1 and 2 with CpZrCl₃ · dme (dme = dimethoxyethane) and Cp*ZrCl₃(CP* = C₅(CH₃)₅) yielded the mono- and bi-nuclear bridged zirconocenes 1-(Cp″ZrCpCl₂)-4-(CH₃)C₆H₄ (3), 1,4-(Cp″ZrCpCl₂)₂C₆H₄ (4) and 1,4-(Cp″ZrCp*Cl₂)₂C₆H₄ (5). When activated with methylaluminoxane (MAO), the mono- and bi-nuclear zirconocenes 3 and 4 catalyse the polymerization of propene. The influence of the catalyst composition on the polymerization kinetics and molecular weight is discussed.     

Propene polymerization using homogeneous MAO-activated metallocene catalysts: Me2Si(Benz[e]Indenyl)2ZrCl2/MAO vs. Me2Si(2-Me-Benz[e]Indenyl)2ZrCl2/MAO

Propene was polymerized at 40°C and 2-bar propene in toluene using methylalumoxane (MAO) activated rac-Me₂Si(Benz[e]Indenyl)₂ZrCl₂ ( BI ) and rac-Me₂Si(2-Me-Benz[e]Indenyl)₂ZrCl₂ ( MBI ). Catalyst BI /MAO polymerizes propene with high activity to afford low molecular weight polypropylene, whereas MBI /MAO is less active and produces high molecular weight polypropylene. Variation of reaction conditions such as propene concentration, temperature, concentration of catalyst components, and addition of hydrogen reveals that the lower molecular weight polypropylene produced with BI /MAO results from chain transfer to propene monomer following a 2,1-insertion. A large fraction of both metallocene catalyst systems is deactivated upon 2,1-insertion. Such dormant sites can be reactivated by H₂-addition, which affords active metallocene hydrides. This effect of H₂-addition is reflected by a decreasing content of head-to-head enchainment and the formation of polypropylene with n-butyl end groups. Both catalysts show a strong dependence of activity on propene concentration that indicates a formal reaction order of 1.7 with respect to propene. MBI /MAO shows a much higher dependence of the activity on temperature than BI /MAO. At elevated temperatures, MBI /MAO polymerizes propene faster than BI /MAO. © 1995 John Wiley & Sons, Inc.     

Analysis of human brain tissue, brain tumors and tumor cells by infrared spectroscopic mapping

This study uses infrared (IR) spectroscopic, point detection, mapping procedures to examine tissue samples from normal brain specimens and from astrocytic gliomas, the most frequent human brain tumors. Model systems were derived from cultured glioma cell lines. IR spectra of normal tissue sections distinguished white matter from gray matter by increased spectral contributions from lipids and cholesterol. Qualitatively the same differences were found in IR spectra of low and high grade glioma tissue sections pointing to a significant reduction of brain lipids with increasing malignancy. Whereas spectral contributions of proteins and lipids were similar in IR spectra of glioma cells and tissues, nucleic acid bands were more intense for cells suggesting higher proliferative activities. For statistical analyses of IR spectroscopic maps from 71 samples, a parameter for the lipid to protein ratio was introduced involving the CH(2) symmetric stretch band with lipids as main contributors and the amide I band of proteins. As this parameter correlated with the grade of gliomas obtained from standard histopathological examination, it was applied to classify brain tissue sections based on IR spectroscopic mapping.     

Near infrared Raman spectroscopic mapping of native brain tissue and intracranial tumors

This study assessed the diagnostic potential of Raman spectroscopic mapping by evaluating its ability to distinguish between normal brain tissue and the human intracranial tumors gliomas and meningeomas. Seven Raman maps of native specimens were collected ex vivo by a Raman spectrometer with 785 nm excitation coupled to a microscope with a motorized stage. Variations within each Raman map were analyzed by cluster analysis. The dependence of tissue composition on the tissue type in cluster averaged Raman spectra was shown by linear combinations of reference spectra. Normal brain tissue was found to contain higher levels of lipids, intracranial tumors have more hemoglobin and lower lipid to protein ratios, meningeomas contain more collagen with maximum collagen content in normal meninges. One sample was studied without freezing. Whereas tumor regions did not change significantly, spectral changes were observed in the hemoglobin component after snap freezing and thawing to room temperature. The results constitute a basis for subsequent Raman studies to develop classification models for diagnosis of brain tissue.     

Unusual peak defocusing in capillary GC on hexakis(2,6-diO-pentyl-3-O-acetyl)-α-cyclodextrin stationary phase

An unusual peak defocusing effect influencing chromatographic performance over a limited range of elution temperatures is described for hexakis(2,6-di-O-pentyl-3-O-acetyl)-α-cyclodextrin stationary phase. Since this phenomenon is likely to be dependent on minor details of the cyclodextrin molecule, full assignment of the ¹H- and ¹³C-NMR-spectra are given.     

The crystal and molecular structure of tris[(triphenylstannyl)methyl]methane

The title compound, C₅₈H₅₂Sn₃, belongs to the triclinic space group P$\text{1}$, with a 10.165, b 13.365, c 18.670 Å, α 96.28, β 93.88, γ 103.15°, V = 2443.8 ų, f_w = 1105.1, Z = 2, D_calc 1.501 g cm^?3, m.p. 206.5–208°C, λ(Mo-K_$\text{α}$) 0.71069 Å. The structure was refined on 2684 nonzero reflections to an R factor of 0.044. The crystal contains molecules in which the (SnCH₂)₃CH core possesses an approximate C₃ symmetry. The three SnC(H₂) bonds are gauche to the C(4)-H bond. Repulsive interactions involving the bulky Ph₃Sn substituents lead to large SnC(H₂)C(H) angles (av. 117.3°), whereas the C(H₂)C(H)C(H₂) angles at the tertiary carbon average 111.3°. Little distortion of the Ph₃Sn groups themselves is present, since the PhSnPh angles (av. 109.8°) are almost equal to the C(H₂)SnPh angles (av. 109.9°). The molecule as a whole has no symmetry because the aromatic rings in the three Ph₃Sn groups have different orientations. The phenyl groups create a pocket in the middle of the molecule which encloses and shields the tertiary hydrogen atom. The resulting inaccessibility of this hydrogen accounts in part for the low reactivity of the title compound in redox reactions.     

Approximate Atomic Green Functions

In atomic and many-particle physics, Green functions often occur as propagators to formally represent the (integration over the) complete spectrum of the underlying Hamiltonian. However, while these functions are very crucial to describing many second- and higher-order perturbation processes, they have hardly been considered and classified for complex atoms. Here, we show how relativistic (many-electron) Green functions can be approximated and systematically improved for few- and many-electron atoms and ions. The representation of these functions is based on classes of virtual excitations, or so-called excitation schemes, with regard to given bound-state reference configurations, and by applying a multi-configuration Dirac-Hartree-Fock expansion of all atomic states involved. A first implementation of these approximate Green functions has been realized in the framework of Jac, the Jena Atomic Calculator, and will facilitate the study of various multi-photon and/or multiple electron (emission) processes.