Invariant Banach limits and applications

Let ?_∞ be the space of all bounded sequences x=(x₁,x₂,…) with the norm

     

Integrability of higher pentagram maps

We define higher pentagram maps on polygons in $\mathbb{P }^d$ for any dimension $d$ , which extend R. Schwartz’s definition of the 2D pentagram map. We prove their integrability by presenting Lax representations with a spectral parameter for scale invariant maps. The corresponding continuous limit of the pentagram map in dimension $d$ is shown to be the $(2,d+1)$ -equation of the KdV hierarchy, generalizing the Boussinesq equation in 2D. We also study in detail the 3D case, where we prove integrability for both closed and twisted polygons and describe the spectral curve, first integrals, the corresponding tori and the motion along them, as well as an invariant symplectic structure.     

Structure of precipitates and orientation relationships in Al,Ge, Mo-doped higher manganese silicide crystals

Abstract

The structure of Al, Ge, Mo-doped Higher Manganese Silicide (HMS) crystals with the general formulas Mn(Si_0.99Ge_0.01)_1.75, Mn(Si_0.995Ge_0.005)_1.75 and (Mn_0.98Mo_0.02)[(Si_0.98Ge_0.02)_1.75]_0.99Al_0.01 was investigated by scanning and transmission electron microscopy, electron diffraction and X-ray energy dispersive spectrometry in a wide scale range from a few mm to several Å. Several secondary phases were identified in the Mn₄Si₇ matrix: Ge_1?xSi_x (0.1 < x < 0.9) solid solution precipitates with Ge concentration ranging from 5 at. % up to 93 at.%, MoSi₂ platelets, MnSi and Mn₅Si₃ precipitates. Their morphology, structure and crystallographic relationships with the HMS matrix were determined. Mostly local strains in the matrix and precipitates due to lattice misfits at interfaces derived from crystallographic relationships were found two orders of magnitude higher than deformation induced by thermal expansion mismatch. Only a few exceptions of specific relationships were found when the lattice misfit and thermal mismatch have close values. The largest misfit of about 22% was observed between MnSi and Mn₄Si₇ what led to big and numerous cracks in crystals. Therefore, doping can improve the material performance (1) by preventing the formation of MnSi precipitates with metallic properties and (2) by reduction of cracking and crack propagation because of larger MnSi /Mn₄Si₇ lattice misfit compared to Ge_1?xSi_x /Mn₄Si₇ or MoSi₂/Mn₄Si₇ misfits.     

Biodegradable liposome–chitosan complexes: enzyme-mediated release of encapsulated substances

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Application of comprehensive two-dimensional gas chromatography mass spectrometry and different types of data analysis for the investigation of cigarette particulate matter

In tobacco research, the comparison of different tobacco blends as well as the puff-dependent behaviour of cigarettes is a matter of particular interest. For the investigation of smoke characteristics, GC x GC offers different ways for data analysis, namely, compound target analysis, automated peak-based compound classification and comprehensive pixel-based data analysis. This study will show the application as well as the pros and cons of these types of data analysis for very complex matrices like cigarette particulate matter. In addition, new aspects about the recently discovered puff-dependent behaviour of compounds in cigarette smoke will be presented. Automated peak-based compound classification including mass spectrometric pattern recognition is used for the classification of tobacco particulate matter samples and the puff-dependent investigation of different compound classes. This compound group specific analysis is further reinforced by applying an even more comprehensive pixel-based analysis. This kind of analysis is used to generate fingerprints of different types of cigarettes. The combination of fast feature reduction methods like analysis of variance (ANOVA) and t-test with multivariate feature transformation methods like partial least squares discriminate analysis (PLSDA) for feature selection provides a powerful tool for a detailed inspection of different types of cigarettes.     

Flat-structural Motives in Small Alumino-Carbon Clusters C(n)Al(m) (n = 2-3, m = 2-8)

Small clusters consisting of a carbon diatom or triatom and several aluminum atoms are investigated ab initio, at an MP2 level of theory. The mainly ionic character of C-Al bonding predominantly leads to structures different from corresponding hydrocarbons (also if starting from analogous initial geometries), while still producing closed-shell ground states. It is found that in many cases stable geometries correspond to flat CAl(3) units. These include unique metal-framed dicarbon and tricarbon all-flat species with unusual planar tetra-coordination. Another frequent feature is a hyper-coordination of carbon atoms, supported by their high negative charges and critically examined via atom-in-molecule calculations. Also characterized are anionic states, electronic excitation and ionization, electron attachment and detachment, and charge distributions.     

Symmetric Tensors And Geometry of {\mathbb{P}} ^N Subvarieties

This paper using a geometric approach produces vanishing and nonvanishing results concerning the spaces of twisted symmetric differentials on subvarieties , with k ≤ m. Emphasis is given to the case of k = m which is special and whose nonvanishing results on the dimensional range dim X > 2/3(N − 1) are related to the space of quadrics containing X and the variety of all tangent trisecant lines of X. The paper ends with an application showing that the twisted symmetric plurigenera, along smooth families of projective varieties X_t are not invariant even for α arbitrarily large. Received: September 2006, Revision: May 2007, Accepted: June 2007     

One-dimensional and comprehensive two-dimensional gas chromatography coupled to soft photo ionization time-of-flight mass spectrometry: a two- and three-dimensional separation approach

Soft laser photo-ionization mass spectrometry is presented as a separation dimension hyphenated with gas chromatographic techniques. Single photon ionization (SPI) is a universal soft ionization method which ionizes organic molecules with an ionization potential below 10.5 eV if 118 nm laser radiation is used. The inherently soft ionization of photo ionization techniques can further be utilized together with gas chromatography as a comprehensive two-dimensional separation method (GC x MS), using the GC retention time as first separation dimension and the molecular mass as second separation dimension. Some GC x MS chromatograms of diesel petroleum samples using SPI are presented and discussed. Finally, it is demonstrated that the coupling of soft SPI mass spectrometry with comprehensive two-dimensional gas chromatography (GC x GC) provides a three-dimensional separation technique (GC x GC x SPI-MS).