The Sherman equations as a nonlinear Perron eigenvalue problem

When a chemical sample composed of N elements is analyzed using sequential selective excitation by a tunable polyenergetic X-ray beam and selective measurement of the characteristic X-rays, the production of secondary fluorescence does not interfere with the measurements. This experimental situation leads to a particular case of the Sherman equations which can be written as a set of non-linear equations. The same kind of equations are also obtained when we excite a chemical sample with a polyenergetic X-ray beam and neglect the production of secondary fluorescence. This set of equations can be regarded as a non-linear eigenvalue problem. A non-linear extension of the Perron Frobenious theorem ensures that there is one and only one physically acceptable solution, and also leads to a method to obtaining it. The propagation off measurements errors of sample fluorescence to errors in the calculated sample concentrations, has been simulated, and the results show that the solution is well conditioned. The case of production of secondary fluorescence can not be treated, in general, as a nonlinear Perron eigenvalue problem, but it has been shown that it is rather plausible that Sherman equations corresponding to the actual chemical elements and that include the production of secondary fluorescence have one and only one physically acceptable solution. An exhaustive search could elucitate the existence and unicity of solutions for the equations corresponding to the actual chemical elements.     

Rigid ferrocenophane and its metal complexes with transition and alkaline-earth metal ions

The rigid [6]ferrocenophane, L¹, was synthesised by condensation of 1,1′-ferrocene dicarbaldehyde with trans-1,2-diaminocyclohexane in high dilution at r.t. followed by reduction. When other experimental conditions were employed, the [6,6,6]ferrocenephane (L²) was also obtained. Both compounds were characterised by single crystal X-ray crystallography. The protonation of L¹ and its metal complexation were evaluated by the effect on the electron-transfer process of the ferrocene (fc) unit of L¹ using cyclic voltammetry (CV) and square wave voltammetry (SWV) in anhydrous CH₃CN solution and in 0.1 M ⁿBu₄NPF₆ as the supporting electrolyte. The electrochemical process of L¹ between −300 and 900 mV is complicated by amine oxidation. On the other hand, an anodic shift from the fc/fc⁺ wave of L¹ of 249, 225, 81 and 61 mV was observed by formation of Zn²⁺, Ni²⁺, Pd²⁺ and Cu²⁺ complexes, respectively. Whereas Mg²⁺ and Ca²⁺ only have with L¹ weak interactions and they promote the acid-base equilibrium of L¹. This reveals that L¹ is an interesting molecular redox sensor for detection of Zn²⁺ and Ni²⁺, although the kinetics of the Zn²⁺ complex formation is much faster than that of the Ni²⁺ one. The X-ray crystal structure of [PdL¹Cl₂] was determined and showed a square–planar environment with Pd(II) and Fe(II) centres separated by 3.781(1) Å. The experimental anodic shifts were elucidated by DFT calculations on the [ML¹Cl₂] series and they are related to the nature of the HOMO of these complexes and a four-electron, two-orbital interaction.     

Inelastic electron tunneling spectroscopy of a single nuclear spin

Detection of a single nuclear spin constitutes an outstanding problem in different fields of physics such as quantum computing or magnetic imaging. Here we show that the energy levels of a single nuclear spin can be measured by means of inelastic electron tunneling spectroscopy (IETS). We consider two different systems, a magnetic adatom probed with scanning tunneling microscopy and a single Bi dopant in a silicon nanotransistor. We find that the hyperfine coupling opens new transport channels which can be resolved at experimentally accessible temperatures. Our simulations evince that IETS yields information about the occupations of the nuclear spin states, paving the way towards transport-detected single nuclear spin resonance.     

A multicomponent approach to the synthesis of 1,3-dicarbonylic compounds

A general synthesis of 1,3-dicarbonylic compounds using multicomponent reactions of isocyanides is described. The process involves a Passerini three-component condensation of glyoxal derivatives, isocyanides and acetic acid, followed by metal mediated reductive or solvolytic removal of the acid component. Noteworthy, reductive deacetoxylation of Passerini glyoxylamide adducts was successfully achieved using photochemically activated SmI₂. This procedure constitutes a novel convenient method for the direct synthesis of malonic retro-peptidic subunits.     

Hilbert function,generalized Poincaré series and topology of plane valuations

To a multi-index filtration (say, on the ring of germs of functions on a germ of a complex analytic variety) one associates several invariants: the Hilbert function, the Poincaré series, the generalized Poincaré series, and the generalized semigroup Poincaré series. The Hilbert function and the generalized Poincaré series are equivalent in the sense that each of them determines the other one. We show that for a filtration on the ring of germs of holomorphic functions in two variables defined by a collection of plane valuations both of them are equivalent to the generalized semigroup Poincaré series and determine the topology of the collection of valuations, i.e. the topology of its minimal resolution.     

Simulation-based optimisation of wastewater flow and composition for on-site treatment in the food and beverage industry utilising reference nets in combination with genetic algorithms

This study introduces the concept of computer modelling and simulation of complex bioprocesses and systems using an approach that combines the reference net formalism with machine learning and optimisation techniques. Reference nets are an extension of high level Petri Nets, which can be used as a central visualisation and modelling tool. The net-in-net paradigm used by reference nets makes it possible to model complex processes, such as those found in the food and beverage industry. A plugin/interface system based on the java programming language allows implementation of advanced mathematical modelling techniques at specific points in entire system simulations. Separate optimisation tools can also run and modify existing reference net models for fast solutions to efficiency problems. We present an example system that simulates a specific section of a beer brewery using the reference net formalism, which is optimised using a genetic algorithm. We show in detail how the different software packages can be combined for a simulation based optimisation approach. The optimisation technique specifically addresses the wastewater pollution load in regard to its chemical oxygen demand. A beer brewery was chosen as an example for this study due to the constantly increasing requirements to lower energy and water consumption in this industry. One possibility to lower the energy and water demands is to effectively treat wastewater produced by the brewery, which can introduce cost savings by providing recycled water and biogas. Most approaches to wastewater treatment are end-of-pipe solutions that do not consider the brewery as a whole. A brewery contains many processes that can be running concurrently and interacting with one another (e.g. brewing, clean-in-place and bottling) with each process producing varying amounts of wastewater with different pollution loads. Optimisation of the scheduling of the different processes with respect to the wastewater production will allow for more effective wastewater treatment, and therefore cost and energy savings. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical prediction for multiple roll systems with negative gaps

Multiple roll coaters with deformable rolls are widely spread for the coating of thin liquid films with a wet film thickness of only a few microns and below on continuous substrates. The presented analytical solution for multiple roll systems offers for the first time the possibility to predict the performance of multiple roll coaters with a nip feed system and negative gaps. The solution is based on a previously presented solution of the authors for roll pairs and extended to multiple roll systems. The results are validated with experimental data from literature and the main influencing factors of multiple roll systems are investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bubble dynamics: Long-time behavior and interaction in viscous liquids

A mathematical two-phase model is used to numerically investigate physical and rheological effects on small, individual bubbles in high-viscosity liquids under pressure impact. It is found out that bubbles remain stable over time at high viscosity and surface tension. The steady case is considered and connected to the stability behavior of the bubble. An upper bound for the bubble radius is derived and the new equilibrium state of the bubble can be predicted by means of stability theorems of differential equations. Finally, the interaction of a limited number of well separated bubbles in an Hele-Shaw flow is mathematically analyzed to visualize and physically interpret their trajectories. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Affinity partitioning of erythrocytic phosphofructokinase in aqueous two-phase systems containing poly(ethylene glycol)-bound cibacron blue. Influence of pH, ionic strength and substrates/effectors.

Phosphofructokinase (PFK) from rat erythrocyte haemolysates has a high affinity for Cibacron Blue F3G-A covalently bound to poly(ethylene glycol) (PEG-Cb) and thus the enzyme can be extracted into the top phase of poly(ethylene glycol)-dextran aqueous two-phase systems containing PEG-Cb. The pH, ionic strength and presence of substrates/effectors affect to different extents the affinity of the enzyme for PEG-Cb and the number of PEG-Cb molecules attached per molecule of PFK (the latter probably reflecting, at saturation, the influence on the aggregation state of the enzyme) and thus influence the yield of enzyme recovered in the top phase. Increasing the pH from 6 to 7 and then to 8 leads to a higher yield of PFK in the top phase. A change in pH from 6 to 7 and 8 results in an increased number of PEG-Cb molecules attached per molecule of enzyme while the affinity of PFK for PEG-Cb shows a minimum at pH 7. The ionic strength in the range 0.017-0.164 has less influence on the partitioning of PFK. The presence of substrates or effectors of the enzyme in general reduces the recovery of PFK in the top phase. Fructose 6-phosphate increases the number of PEG-Cb molecules attached but greatly reduces the affinity of PFK for PEG-Cb. In contrast, AMP slightly reduces the number of PEG-Cb molecules attached and the affinity of PFK for PEG-Cb. ATP and ATP-Mg2+ compete with PEG-Cb for the same binding sites in PFK.(ABSTRACT TRUNCATED AT 250 WORDS)