Paths through inverse limits

In Bani?, ?repnjak, Merhar and Milutinovi? (2010) [2] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions fn:X→X² converges to the graph of a continuous single-valued function f:X→X, then the sequence of corresponding inverse limits obtained from fn converges to the inverse limit obtained from f. In this paper a more general result is presented in which surjectivity of fn is not required. The result is also generalized to the case of inverse sequences with non-constant sequences of bonding maps. Finally, these new theorems are applied to inverse limits with tent maps. Among other applications, it is shown that the inverse limits appearing in the Ingram conjecture (with a point added) form an arc.     

Observations of cavitation erosion pit formation

Previous investigations showed that a single cavitation bubble collapse can cause more than one erosion pit (Philipp & Lauterborn [1]). But our preliminary study showed just the opposite – that in some cases a single cavitation pit can result from more than one cavitation event. The present study shows deeper investigation of this phenomenon. An investigation of the erosion effects of ultrasonic cavitation on a thin aluminum foil was made. In the study we observed the formation of individual pits by means of high speed cameras (>1000 fps) and quantitatively evaluated the series of images by stereoscopy and the shape from shading method. This enabled the reconstruction of the time evolution of the pit shape. Results show how the foil is deformed several times before a hole is finally punctured. It was determined that larger single pits result from several impacts of shock waves on the same area, which means that they are merely special cases of pit clusters (pit clusters where pits overlap perfectly). Finally it was shown that a thin foil, which is subjected to cavitation, behaves as a membrane. It was concluded that the physics behind erosion depends significantly on the means of generating cavitation (acoustic, hydrodynamic, laser light) and the specimen characteristics (thin foil, massive specimen), which makes comparison of results of materials resistance to cavitation from different experimental set-ups questionable.Further development of the shape from shading method in the scope of cavitation erosion testing will enable better evaluation of cavitation erosion models.     

Characterization of incipient cavitation in axial valve by hydrophone and visualization

As the effects of cavitation in valves are devastating, the choice of the correct valve for a given operating range is crucial. For this, the valve characteristic is needed, whereby one side of the operating range depends on the determination of the incipient cavitation.In this paper, the visualization method for incipient cavitation detection is presented. For the purpose of comparison, pressure oscillations inside the pipeline were simultaneously measured with a hydrophone. The effect of operating pressure was studied for two different openings of the valve.For each operating point of incipient cavitation, corresponding points were measured for developed cavitation and no-cavitation state, based on a constant-portion change of volumetric flow rate with regard to the incipient cavitation volumetric flow rate. The visualization and hydrophone signals were compared.The visualization method proved efficiency over hydrophone measurements because it is more sensitive to cavitation and the signal is independent of the operating pressure. The main drawback is the preparation of the observation window.     

Calibration of mass selective detector in non-target analysis of volatile organic compounds in the air

Volatile organic compounds (VOCs) play an important role in the chemistry of the atmosphere and in biogeochemistry. They contribute to the oxidative capacity of the atmosphere, particle and air pollutants, as well as to the production of greenhouse gases (for instance ozone). Among analytical techniques for their determination in the atmosphere gas chromatography coupled with mass spectrometry (GC-MS) offers several advantages. However, for an accurate quantification calibration with standard substances is necessary. A quantitative structure-property relationship (QSPR) model for the prediction of MS response factors was developed on basis of our experimental measurements for the quantification of ozone precursors present in the atmosphere. A linear correlation between chemical structures and response factors was established by using a 7-parameter MLR model. The average error in the prediction of response factors was calculated by cross-validation procedure and was below 20%, which is sufficient for the determination of VOCs in the air. The proposed procedure is time consuming so it is more suited for the quantification of tentatively identified organic compounds during the reprocessing of MS chromatograms in cases when the original sample is no longer available.     

Do all pieces make a whole? Thiele cumulants and the free energy decomposition

The partitioning of the free energy into additive contributions originating from different groups of atoms or force field terms has the potential to provide relationship between structure and biological activity of molecules. In this article, the theoretical foundation for the free energy decomposition in the free energy perturbation (FEP) methodology is formulated using Thiele cumulants, a powerful tool from the arsenal of probability theory and mathematical statistics. We establish that rigorous decomposition of the free energy into its components is precluded by the presence of mixed potential energy terms in Thiele cumulants of second and higher orders. However, we also show that the resultant nonadditivity error can be reduced to an arbitrary value by increasing the number of FEP steps. Consequently, the whole system can be in the limit of small perturbation steps adequately represented by the sum of its constituent parts.     

NMR spectral properties of the tetramantanes – nanometer‐sized diamondoids

Tetramantanes, and all diamondoid hydrocarbons, possess carbon frameworks that are superimposable upon the cubic diamond lattice. This characteristic is invaluable in assigning their ¹H and ¹³C NMR spectra because it translates into repeating structural features, such as diamond‐cage isobutyl moieties with distinctively complex methine to methylene signatures in COSY and HMBC data, connected to variable, but systematic linkages of methine and quaternary carbons. In all tetramantane C₂₂H₂₈ isomers, diamond‐lattice structures result in long‐range ⁴J_HH, W‐coupling in COSY data, except where negated by symmetry; there are two highly symmetrical and one chiral tetramantane (showing seven ⁴J_HH). Isobutyl‐cage methines of lower diamondoids and tetramantanes are the most shielded resonances in their ¹³C spectra (<29.5 ppm). The isobutyl methylenes are bonded to additional methines and at least one quaternary carbon in the tetramantanes. W‐couplings between these methines and methylenes clarify spin‐network interconnections and detailed surface hydrogen stereochemistry. Vicinal couplings of the isobutyl methylenes reveal positions of the quaternary carbons: HMBC data then tie the more remote spin systems together. Diamondoid ¹³C NMR chemical shifts are largely determined by α and β effects, however γ‐shielding effects are important in [123]tetramantane. ¹H NMR chemical shifts generally correlate with numbers of 1,3‐diaxial H–H interactions. Tight van der Waals contacts within [123]tetramantane's molecular groove, however, form improper hydrogen bonds, deshielding hydrogen nuclei inside the groove, while shielding those outside, indicated by Δδ of 1.47 ppm for geminal hydrogens bonded to C‐3,21 . These findings should be valuable in future NMR studies of diamondoids/nanodiamonds of increasing size. Copyright © 2015 John Wiley & Sons, Ltd.     

Historical iron gall ink containing documents — Properties affecting their condition

Iron gall ink, also referred to as iron gallotannate ink, is one of the most important inks in the history of western civilisation, and was in widespread use from the middle ages until the 20th century. Unfortunately, iron ions and acids present in these inks induce enhanced degradation of paper, thus severely damaging numerous historical artefacts. Yet, when examining documents, it is frequently observed that not all materials containing iron gall ink are suffering from ink corrosion. While some are completely destroyed, others may be in excellent condition even centuries after their creation. In order to establish the main properties of materials, common to severely degraded documents, the effects of the type and quantity of metal ions in the ink, as determined by in-air PIXE method, pH of the ink on paper, grammage of paper, its absorptivity and the width of ink lines were evaluated against the extent of corrosion. Using multiple linear regression analysis, a correlation has been obtained between the width of the applied ink lines, pH, grammage of paper and the extent of ink corrosion. Based on these factors, which can be acquired non-destructively from most historical documents, it is therefore possible to predict the stability of historical iron gall ink containing paper.     

Removal of pharmaceuticals from wastewater by biological processes,hydrodynamic cavitation and UV treatment

To augment the removal of pharmaceuticals different conventional and alternative wastewater treatment processes and their combinations were investigated. We tested the efficiency of (1) two distinct laboratory scale biological processes: suspended activated sludge and attached-growth biomass, (2) a combined hydrodynamic cavitation–hydrogen peroxide process and (3) UV treatment. Five pharmaceuticals were chosen including ibuprofen, naproxen, ketoprofen, carbamazepine and diclofenac, and an active metabolite of the lipid regulating agent clofibric acid.Biological treatment efficiency was evaluated using lab-scale suspended activated sludge and moving bed biofilm flow-through reactors, which were operated under identical conditions in respect to hydraulic retention time, working volume, concentration of added pharmaceuticals and synthetic wastewater composition. The suspended activated sludge process showed poor and inconsistent removal of clofibric acid, carbamazepine and diclofenac, while ibuprofen, naproxen and ketoprofen yielded over 74% removal. Moving bed biofilm reactors were filled with two different types of carriers i.e. Kaldnes K1 and Mutag BioChip? and resulted in higher removal efficiencies for ibuprofen and diclofenac. Augmentation and consistency in the removal of diclofenac were observed in reactors using Mutag BioChip? carriers (85% ± 10%) compared to reactors using Kaldnes carriers and suspended activated sludge (74% ± 22% and 48% ± 19%, respectively). To enhance the removal of pharmaceuticals hydrodynamic cavitation with hydrogen peroxide process was evaluated and optimal conditions for removal were established regarding the duration of cavitation, amount of added hydrogen peroxide and initial pressure, all of which influence the efficiency of the process. Optimal parameters resulted in removal efficiencies between 3–70%. Coupling the attached-growth biomass biological treatment, hydrodynamic cavitation/hydrogen peroxide process and UV treatment resulted in removal efficiencies of >90% for clofibric acid and >98% for carbamazepine and diclofenac, while the remaining compounds were reduced to levels below the LOD. For ibuprofen, naproxen, ketoprofen and diclofenac the highest contribution to overall removal was attributed to biological treatment, for clofibric acid UV treatment was the most efficient, while for carbamazepine hydrodynamic cavitation/hydrogen peroxide process and UV treatment were equally efficient.     

Quasidynamic propagation in diabatic landscapes for low energy nuclear fission

Successive procedure for evaluating diabatic contributions to the static energy surface is proposed, based on solving collective equation of motion simultaneously with equations for the single-particle occupation probabilities. The method is applied so far to²³⁵U(n _th,f) in terms of schematic asymmetric two center shell model. Shifts in fragment mass asymmetry due to diabatic dynamics are observed.This work was supported in part by the Bulgarian Ministry of Sciences (contract No. 802) and the Bundesministerium für Forschung und Technologie (Intern. Büro, Karlsruhe)