Zur Kennzeichnung der Lorentz-Transformationen

Let (V, f) be a real Minkowski space of any, not necessarily finite, dimension, and letd be the corresponding distance function (taking negative values for timelike distances). Then the following statement (among others) is proved: If ? :V →V is a surjective mapping such that $$d(P,Q) = a \Leftrightarrow d(P^\varphi ,Q^\varphi ) = a\forall P,Q \in V$$ is true for some fixeda εR,a<0, then ? is a Lorentz transformation (including a possible translation).     

Discrete Laplace cycles of period four

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction.     

Convergence of the Finite Difference Scheme for a Fast Diffusion Equation in Porous Media

We are concerned with an implicit scheme for the finite difference solution to a nonlinear parabolic equation with a multivalued coefficient that describes the fast diffusion in a porous medium. The boundary conditions contain the multivalued function as well. We prove the stability and the convergence of the scheme, emphasizing the precise nature of convergence in this specific case, and compute the error level of the approximating solution. The method is aimed to simplify the numerical computations for the solutions to equations of this type, without performing an approximation of the multivalued function. The theory is illustrated by numerical results.     

Mimicking the cell membrane with block copolymer membranes

Cell membranes are essential barriers in Nature. To understand their properties and functions and to develop desirable applications, a simple and elegant approach is to study membranes that mimic the cell membrane. Lipid bilayers represent simple models that are physiologically representative when in the form of mixtures of various lipids, but they are not adequately stable even when covered with amphipathic proteins or when combined with polymers, thus preventing technological applications. This makes necessary the design of completely synthetic membranes. In this respect, amphiphilic copolymers that self‐assemble under dilute aqueous conditions and generate supramolecular polymer vesicles or films are ideal candidates for synthetic membranes. Their versatility in terms of chemistry and properties (permeability, mechanical stability, thickness), if appropriately designed, enable the insertion of biological molecules, such as membrane proteins and biopores, or the attachment of biomolecules at their surfaces. Here, we present the domain of synthetic membranes based on amphiphilic copolymers beginning with their generation and up to their applications in medicine, the food industry, and technology. Even though significant progress has been made in combining them with membrane proteins, open questions remain with respect to desired properties that could accommodate biological molecules and support further development of the field, from both the point of view of fundamental understanding and of applications. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

The First Catalytic Synthesis of an Acrylate from CO2 and an Alkene—A Rational Approach

For more than three decades the catalytic synthesis of acrylates from the cheap and abundantly available C₁ building block carbon dioxide and alkenes has been an unsolved problem in catalysis research, both in academia and industry. Herein, we describe a homogeneous catalyst based on nickel that permits the catalytic synthesis of the industrially highly relevant acrylate sodium acrylate from CO₂, ethylene, and a base, as demonstrated, at this stage, by a turnover number of greater than 10 with respect to the metal.     

High-Sensitivity Immunofluorescence Staining: A Comparison of the Liposome Procedure and the FASER Technique on mGR Detection

Flow cytometry has become a widely-used and powerful tool for the characterization of cells according to their expression of specific proteins. However, sensitivity of this method is still limited since conventionally labeled antibodies can be conjugated with at maximum 1–10 dye molecules. This fact resulted in the need to develop new techniques in order to identify molecules which are expressed in very low but functionally relevant amounts. In the past, we have successfully used a liposome-based high-sensitivity immunofluorescence technique to measure the expression of low abundant membrane bound glucocorticoid receptors (mGR) on different cell types. The use of this technique allows the detection of as few as 50–100 antigen molecules per cell which is due to a 100-fold to 1000-fold increase in fluorescence signal intensity compared with conventional methods. The higher sensitivity is achieved since thousands of dye molecules can be enclosed in liposomes. Another modern high-sensitivity immunofluorescence staining method is the purchasable Fluorescence Amplification by Sequential Employment of Reagents (FASER) procedure. Here, we aimed at comparing sensitivity and specificity of these two techniques for the detection of the mGR. Our data demonstrate the FASER technique to be more sensitive and also more specific for the detection of mGR as compared to the liposome technique. However, both methods have advantages and disadvantages which are discussed in detail.     

Ylide Chemistry: An Account of Structural,Conformational and Redox Investigations

Abstract

Structural data of phosphorus ylides are summarized and discussed. Conformational preferences in solution and in the solid state, as followed by NMR spectroscopy and X-ray diffraction, indicate a strong gauche effect for the lone pairs of electrons at the ylidic carbon atom. One- and two-electron oxydation of ylide carbanions is accomplished with copper(II) as the oxidant, leading to oxidative coupling or to halogenation, respectively.     

A novel method for serum lipoprotein profiling using high performance capillary isotachophoresis

A new capillary isotachophoresis (cITP) method for lipoprotein profiling with superior lipoprotein coverage compared to previous methods has been developed, resolving twice as many lipoprotein species (18 peaks/fractions) in serum or plasma in less than 9.5 min. For this, a novel mixture of 24 spacers, including amino acids, dipeptides and sulfonic acids, was developed and fine-tuned, using predictive software (PeakMaster) and testing of spiked serum samples. Lipoprotein peaks were identified by serum-spiking with reference lipoproteins. Compatibility with common lipophilic stains for selective lipoprotein detection with either UV/Vis or laser-induced fluorescence was demonstrated. A special new capillary with a neutral coating (combining water-compatible OV1701-OH deactivation and methylation) was used for the first time for electrodriven separations, allowing very stable separations in a pH 8.8–9.4 gradient system, being functional for more than 100 injections. Excellent reproducibility was achieved, with coefficients of variation lower than 2.6% for absolute migration times. Comparison was performed with human plasma samples analyzed by NMR, leading to similar results with cITP after multivariate statistics, regarding group-clustering and lipoprotein species correlation. The new cITP method was applied to the analysis of serum samples from a LDL receptor knock-out mice model fed either a normal diet or a western-type diet. Differences in the lipoprotein levels and in the sublipoprotein types were detected, showing a shift to more atherogenic particles due to the high cholesterol diet. In summary, this novel method will allow more detailed and informative profiling of lipoprotein particle subtypes for cardiovascular disease research.