Abstract: Möbius bands have been studied extensively, mainly in topology. Generalized Möbius-Listing surfaces and bodies providing a full geometrical generalization, is a quite new field, motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. Our research is motivated by this reduction of complexity. In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, the conditions under which a single body results, displaying the Möbius phenomenon of a one-sided body, have been determined for even and odd polygons. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin. The Möbius phenomenon is important, since the process of cutting (or separation of zones in a GML body in general) then results in a single body, not in different, intertwined domains. In all previous works it was assumed that the cross section of the GML bodies is constant, but the main result of this paper is that it is sufficient that only one cross section on the whole GML structure meets the conditions for the Möbius phenomenon to occur. Several examples are given to illustrate this.

Abstract: In this article, it is shown that the efficiency of an electrochemical aptasensing device is influenced by the use of different nanoparticles (NPs) such as gold nanoparticles (Au), silver nanoparticles (Ag), hollow gold nanospheres (HGN), hollow silver nanospheres (HSN), silvergold core shell (Ag@Au), goldsilver core shell (Au@Ag), and silvergold alloy nanoparticles (Ag/Au). Among these nanomaterials, Ag@Au core shell NPs are advantageous for aptasensing applications because the core improves the physical properties and the shell provides chemical stability and biocompatibility for the immobilization of aptamers. Self-assembly of the NPs on a cysteamine film at the surface of a carbon paste electrode is followed by the immobilization of thiolated aptamers at these nanoframes. The nanostructured (Ag@Au) aptadevice for Escherichia coli as a target shows four times better performance in comparison to the response obtained at an aptamer modified planar gold electrode. A comparison with other (core shell) NPs is performed by cyclic voltammetry and differential pulse voltammetry. Also, the selectivity of the aptasensor is investigated using other kinds of bacteria. The synthesized NPs and the morphology of the modified electrode are characterized by UV-Vis absorption spectroscopy, scanning electron microscopy, energy dispersive X-ray analysis, and electrochemical impedance spectroscopy.

Abstract: For the isocratic ion chromatography (IC) separation of low-molecular-mass organic acids and inorganic anions three different anion-exchange columns were studied: IonPac AS14 (9 ìm particle size), Allsep A-2 (7 ìm particle size), and IC SI-50 4E (5 ìm particle size). A complete baseline separation for all analyzed anions (i.e., F−, acetate, formate, Cl−, NO2−, Br−, NO3−, HPO42− and SO42−) in one analytical cycle of shorter than 17 min was achieved on the IC SI-50 4E column, using an eluent mixture of 3.2 mM Na2CO3 and 1.0 mM NaHCO3 with a flow rate of 1.0 mL min−1. On the IonPac AS14 column, it was possible to separate acetate from inorganic anions in one run (i.e., less than 9 min), but not formate, under the following conditions: 3.5 mM Na2CO3 plus 1.0 mM NaHCO3 with a flow rate of 1.2 mL min−1. Therefore, it was necessary to adapt a second run with a 2.0 mM Na2B4O7 solution as an eluent under a flow rate of 0.8 mL min−1 for the separation of organic ions, which considerably enlarged the analysis time. For the Allsep A-2 column, using an eluent mixture of 1.2 mM Na2CO3 plus 1.5 mM NaHCO3 with a flow rate of 1.6 mL min−1, it was possible to separate almost all anions in one run within 25 min, except the fluoride-acetate critical pair. A Certified Multianion Standard Solution PRIMUS for IC was used for the validation of the analytical methods. The lowest RSDs (less than 1%) and the best LODs (0.02, 0.2, 0.16, 0.11, 0.06, 0.05, 0.04, 0.14 and 0.09 mg L−1 for F−, Ac−, For−, Cl−, NO2−, Br−, NO3−, HPO42− and SO42−, respectively) were achieved using the IC SI-50 4E column. This column was applied for the separation of concerned ions in environmental precipitation samples such as snow, hail and rainwater.

Abstract: The development of advanced methods for non-destructive selective imaging of painted works of art at the macroscopic level based on radiation in the X-ray and infrared range of the electromagnetic spectrum are concisely reviewed. Such methods allow to either record depth-selective, element-selective or species-selective images of entire paintings. Camera-based full field methods (that record the image data in parallel) can be discerned next to scanning methods (that build up distributions in a sequential manner by scanning a beam of radiation over the surface of an artefact). Six methods are discussed: on the one hand, macroscopic X-ray fluorescence and X-ray diffraction imaging and X-ray laminography and on the other hand macroscopic Mid and Near Infrared hyper- and full spectral imaging and Optical Coherence Tomography. These methods can be considered to be improved versions of the well-established imaging methods employed worldwide for examination of paintings, i.e., X-ray radiography and Infrared reflectography. Possibilities and limitations of these new imaging techniques are outlined.