Independent trees in graphs

IfG is a finite undirected graph ands is a vertex ofG, then two spanning treesT ₁ andT ₂ inG are calleds — independent if for each vertexx inG the paths fromx tos inT ₁ andT ₂ are openly disjoint. It is known that the following statement is true fork3: IfG isk-connected, then there arek pairwises — independent spanning, trees inG. As a main result we show that this statement is also true fork=4 if we restrict ourselves to planar graphs. Moreover we consider similar statements for weaklys — independent spanning trees (i.e., the tree paths from a vertex tos are edge disjoint) and for directed graphs.     

Reversible electrochemical switching of polyelectrolyte brush surface energy using electroactive counterions

Polyelectrolyte brushes with electroactive counterions provide an effective platform for surfaces with electrochemically switchable wetting properties. Polycationic poly(2-(methacryloyloxy)-ethyl-trimethyl-ammonium chloride) (PMETAC) brushes with ferricyanide ions ([Fe(CN)6] 3-) were used as the electrochemically addressable surface. After a negative potential of -0.5 V was applied to the [Fe(CN)6](3-)-coordinated PMETAC brushes, the [Fe(CN)6](3-) species were reduced to [Fe(CN)6](4-), and the surface became more hydrophilic. By application of alternating negative and positive potentials, PMETAC brushes were switched reversibly between the reduced state ([Fe(CN)6]4-) and oxidized state ([Fe(CN)6]3-), resulting in reversible changes in water contact angles. The time required for a complete contact angle change can be tuned from 1 to 20 s, by changing the brush thickness and the concentration of supporting electrolyte. We present an electrochemical brush transport model that includes the electrochemical reaction at the charged electrode and describes ion transport through the brush phase covering the electrode. The model quantitatively describes the response of the contact angle (hydrophilicity) to the applied voltage as a function of background ionic strength and brush thickness, supporting the proposed mechanism of ion transport through the brush and electrochemical reaction at the electrode. A typical diffusion constant for ferricyanide in a PMETAC brush of any thickness in 5 mM KCl supporting electrolyte was found to be 2 x 10(-15) m2 s(-1), 5 to 6 orders of magnitude smaller than its bulk solution value.     

Transient Modeling and Simulation of Gas Pipe Networks with Characteristic Diagram Models for Compressors

One challenge for the simulation and optimization of real gas pipe networks is the treatment of compressors. Their behavior is usually described by characteristic diagrams reflecting the connection of the volumetric flow and the enthalpy change or shaft torque. Such models are commonly used for an optimal control of compressors and compressor stations [4,7] using stationary models for the gas flow through the pipes. For transient simulations of gas networks, simplified compressor models have been studied in [1–3]. Here, we present a transient simulation of gas pipe networks with characteristic diagram models of compressors using a stable network formulation as (partial) differential-algebraic system. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Independent Trees in Planar Graphs Independent trees

We prove the following statement: Let G be a finite k-connected undirected planar graph and s be a vertex of G. Then there exist k spanning trees T₁,…,T_k in G such that for each vertex xps of G, the k paths from x to s in T₁,…,T_k are pairwise openly disjoint.     

Electron-beam lithography of cinnamate polythiophene films: conductive nanorods for electronic applications

We report the electron-beam induced crosslinking of cinnamate-substituted polythiophene proceeding via excited state [2+2]-cycloaddition. Network formation in thin films is evidenced by infrared spectroscopy and film retention experiments. For the polymer studied herin, the electron-stimulated process appears to be superior to photo (UV)-induced crosslinking as it leads to less degradation. Electron beam lithography (EBL) patterns cinnamate-substituted polythiophene thin films on the nanoscale with a resolution of around 100 nm. As a proof of concept, we fabricated nanoscale organic transistors using doped and cross-linked P3ZT as contact fingers in thin film transistors.

Electron beam lithography patterns selectively cinnamate-substituted polythiophene thin films via [2+2]-cycloaddition. A nanoscale organic field effect transistor is constructed using cross-linked and doped polythiophene as electrodes.     

Magnetic Field Mapping Around Individual Magnetic Nanoparticle Agglomerates Using Nitrogen-Vacancy Centers in Diamond

A modified diamond–photonics based metrology is proposed to explore the magnetic fields created by agglomerates of magnetic nanoparticles (MNPs). MNPs are promising for environmental and medical applications; those proposed for cancer magnetic hyperthermia treatments are small superparamagnetic <20 nm iron oxide particles. Inside cells, they assemble in larger MNP agglomerates, reaching cross-sections of several micrometers. Here, these conditions are reproduced and MNP agglomerates immobilized. Optically detected magnetic resonance (ODMR) signals recorded without a bias field in a confocal microscope and scanning across a homogenous shallow layer of fluorescent nitrogen-vacancy centers in a bulk diamond sample placed in direct contact with the MNP agglomerates are used to determine magnetic fields with a spatial resolution of 500 nm in a lateral direction. This spatial resolution allows determining magnetic field maps around individual MNP agglomerates, for which magnetic fields with strengths ranging from 0.03 mT to maximal 1.2 mT in the direct vicinity of the agglomerates and with detectable fields up to 5 µm away from the agglomerates, are determined. Based on the findings, a pathway to non-invasively study the micro/nano topology of MNP agglomerates is proposed.     

Laser desorption/ionization mass spectrometric analysis of small molecules using fullerene‐derivatized silica as energy‐absorbing material

In spite of the growing acceptance of matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry for the analysis of a wide variety of compounds, including polymers and proteins, its use in analyzing low‐molecular‐weight molecules (<1000m/z) is still limited. This is mainly due to the interference of matrix molecules in the low‐mass range. Here the derivatized fullerenes covalently bound to silica particles with different pore sizes are applied as thin layer for laser desorption/ionization (LDI) mass spectrometric analysis. Thus, an interference of intrinsic matrix ions can be eliminated or minimized in comparison with the state‐of‐the‐art weak organic acid matrices. The desorption/ionization ability of the developed fullerene–silica materials depends on the applied laser power, sample preparation and pore size of the silica particles. Thus, fullerene–silica serves as an LDI support for mass spectrometric analysis of molecules (<1500 Da). The performance of the fullerene–silica is demonstrated by the mass analysis of variety of small molecules such as carbohydrates, amino acids, peptides, phospholipids and drugs. Copyright © 2010 John Wiley & Sons, Ltd.     

Diamond deposition on siliconized stainless steel

Silicon diffusion layers in AISI 304 and AISI 316 type stainless steels were investigated as an alternative to surface barrier coatings for diamond film growth. Uniform 2 μm thick silicon rich interlayers were obtained by coating the surface of the steels with silicon and performing diffusion treatments at 800 °C. Adherent diamond films with low sp² carbon content were deposited on the diffused silicon layers by a modified hot filament assisted chemical vapor deposition (HFCVD) method. Characterization of as-siliconized layers and diamond coatings was performed by energy dispersive X-ray analysis, scanning electron microscopy, X-ray diffraction and Raman spectroscopy.     

Pairs trading and outranking: The multi-step-ahead forecasting case

Pairs trading is a popular speculation strategy. Several implementation methods are proposed in the literature: they can be based on a distance criterion or on co-integration. This article extends previous research in another direction: the combination of forecasting techniques (Neural Networks) and multi-criteria decision making methods (Electre III). The key contribution of this paper is the introduction of multi-step-ahead forecasts. It leads to major changes in the trading system and raises new empirical and methodological questions. The results of an application based on S&P 100 Index stocks are promising: this methodology could be a powerful tool for pairs selection in a highly non-linear environment.     

Innovative Combination of Dispersive Solid Phase Extraction Followed by NIR-Detection and Multivariate Data Analysis for Prediction of Total Polyphenolic Content

Recently polyphenols attracted great interest in the field of food and nutrition as well as in the pharmaceutical and cosmetics industries due to their health benefits through antioxidative behavior in the human body. However, because of the high number of compounds characterized as phenols and their structural diversity, quantification of polyphenols turns out to be a highly complex task. Although, a wide variety of analytical methods are used for the determination of total polyphenolic content, they are all found to be lacking in a variety of different tasks, such as their limits of detection and quantification, repeatability, accuracy and specificity. For this reason, a novel approach combining the advantages of solid phase purification, near infrared analysis and multivariate data analysis was investigated for the prediction of total polyphenolic content, suitable for a wide range of sample matrices. Dispersive solid phase extraction was performed and optimized using polyvinylpyrrolidone as sorbent, known to selectively bind polyphenols. Near-infrared detection of adsorbed polyphenols was carried out subsequently. Furthermore, the method was in-house validated, examining selectivity, repeatability and accuracy, working range, as well as multivariate limit of detection and limit of quantification, comparing it with two routinely used methods—namely, Folin–Ciocalteu photometric assay and Löwenthal titration. The novel established method was applied for the prediction of total polyphenolic content in tea and wine samples.