Nonlinear Models of Suspension Bridges: Discussion of the Results

In this paper we present several nonlinear models of suspension bridges; most of them have been introduced by Lazer and McKenna. We discuss some results which were obtained by the authors and other mathematicians for the boundary value problems and initial boundary value problems. Our intention is to point out the character of these results and to show which mathematical methods were used to prove them instead of giving precise proofs and statements.     

On qualitatively independent partitions and related problems

The paper is concerned with several related combinatorial problems one of which is that of estimating the numbers of qualitatively independent p-partitions. Besides nonconstructive basic estimates, a constructive procedure yielding not much worse ones is presented. In conclusion, some applications are shown.     

Eine Bemerkung über volle Einbettungen von Kategorien von Algebren

Ohne ZusammenfassungUnterstützt von der Alexander von Humboldt-Stiftung.     

On classes of relations and graphs determined by subobjects and factorobjects

The classes of relations and graphs determined by subobjects and factorobjects are studied. We investigate whether such classes are closed under products, whether they are finitely generated by products and subobjects and whether a class can be described alternatively by subobjects and factorobjects. This is related to good characterizations.     

Resonant Homoclinic Flip Bifurcations

This paper studies three-parameter unfoldings of resonant orbit flip and inclination flip homoclinic orbits. First, all known results on codimension-two unfoldings of homoclinic flip bifurcations are presented. Then we show that the orbit flip and inclination flip both feature the creation and destruction of a cusp horseshoe. Furthermore, we show near which resonant flip bifurcations a homoclinic-doubling cascade occurs. This allows us to glue the respective codimension-two unfoldings of homoclinic flip bifurcations together on a sphere around the central singularity. The so obtained three-parameter unfoldings are still conjectural in part but constitute the simplest, consistent glueings.     

Rapid determination of 5-hydroxymethylfurfural by DART ionization with time-of-flight mass spectrometry

DART (direct analysis in real time), a novel technique with wide potential for rapid screening analysis, coupled with high-resolution time-of-flight mass spectrometry (TOF-MS) has been used for quantitative analysis of 5-hydroxymethylfurfural (5-HMF), a typical temperature marker of food. The DART/TOF-MS method was optimised and validated. Quantification of 5-HMF was achieved by use of a stable isotope-labelled 5-HMF standard prepared from glucose. Formation of 5-HMF from saccharides, a potential source of overestimation of results, was evaluated. Forty-four real samples (honey and caramelised condensed sweetened milk) and 50 model samples of heated honey were analysed. The possibility of using DART for analysis of heated samples of honey was confirmed. HPLC and DART/TOF-MS methods for determination of 5-HMF were compared. The correlation equation between these methods was DART?=?1.0287HPLC?+?0.21340, R ²?=?0.9557. The DART/TOF-MS method has been proved to enable efficient and rapid determination of 5-HMF in a variety of food matrices, for example honey and caramel.     

Adsorption behavior of large plasmids on the anion-exchange methacrylate monolithic columns

The objective of this study was to investigate the behavior of large plasmids on the monolithic columns under binding and nonbinding conditions. The pressure drop measurements under nonbinding conditions demonstrated that the flow velocities under which plasmid passing monolith became hindered by the monolithic pore structure depended on the plasmid size as well as on the average monolith pore size; however, they were all very high exceeding the values encountered when applying CIM monolithic columns at their maximal flow rate. The impact of the ligand density and the salt concentration in loading buffer on binding capacity of the monolith for different sized plasmids was examined. For all plasmids the increase of dynamic binding capacity with the increase of salt concentration in the loading solution was observed reaching maximum of 7.1 mg/mL at 0.4M NaCl for 21 kbp, 12.0 mg/mL at 0.4 M NaCl for 39.4 kbp and 8.4 mg/mL at 0.5M NaCl for 62.1 kbp. Analysis of the pressure drop data measured on the monolithic column during plasmid loading revealed different patterns of plasmid binding to the surface, showing "car-parking problem" phenomena under certain conditions. In addition, layer thickness of adsorbed plasmid was estimated and at maximal dynamic binding capacity it matched calculated plasmid radius of gyration. Finally, it was found that the adsorbed plasmid layer acts similarly as the grafted layer responding to changes in solution's ionic strength as well as mobile phase flow rate and that the density of plasmid layer depends on the plasmid size and also loading conditions.