Equilibrium attractivity of Runge-Kutta methods

For dissipative differential equations y' = f (y) it is knownthat contractivity of the exact solution is reproduced by algebraicallystable Runge–Kutta methods. In this paper we investigatewhether a different property of the exact solution also holdsfor Runge–Kutta solutions. This property, called equilibriumattractivity, means that the norm of the righthand side f neverincreases. It is a property dual to algebraic stability sinceneither is sufficient for the other, in general. We derive sufficientalgebraic conditions for Runge–Kutta methods and proveequilibrium attractivity of the high-order algebraically stableRadau-IIA and Lobatto-IIIC methods and the Lobatto-IIIA collocationmethods (which are not algebraically stable). No smoothnessassumptions on f and no stepsize restrictions are required but,except for some simple cases, f has to satisfy certain additionalproperties which are generalizations of the simple one-sidedLipschitz condition using more than two argument points. Thesemultipoint conditions are discussed in detail.     

Structural Electricity Models and Asymptotically Normal Estimators to Quantify Parameter Risk

ABSTRACT

We estimate a structural electricity (multi-commodity) model based on historical spot and futures data (fuels and power prices, respectively) and quantify the inherent parameter risk using an average value at risk approach (‘expected shortfall’). The mathematical proofs use the theory of asymptotic statistics to derive a parameter risk measure. We use far in-the-money options to derive a confidence level and use it as a prudent present value adjustment when pricing a virtual power plant. Finally, we conduct a present value benchmarking to compare the approach of temperature-driven demand (based on load data) to an ‘implied demand approach’ (demand implied from observable power futures prices). We observe that the implied demand approach can easily capture observed electricity price volatility whereas the estimation against observable load data will lead to a gap, because – amongst others – the interplay of demand and supply is not captured in the data (i.e., unexpected mismatches).     

Strong Laws and Summability for φ-Mixing Sequences of Random Variables

In this note the almost sure convergence of stationary, -mixing sequences of random variables according to summability methods is linked to the fulfillment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these laws.     

Donor number estimation for oxygen- and nitrogen-containing solvents via proton NMR shift of chloroform

A linear correlation was determined for oxygen- and nitrogen-containing solvents between the proton NMR shift of chloroform, dilute in a solvent, and the donor number (DN) of that solvent. Results are given for water and for 13 organic solvents. The best straight line is given by DN=7.4–16.6 (CHCl ₃ ) where (CHCl ₃ ) is the shift of pure chloroform relative to that of chloroform in dilute solution. Donor numbers of several solvents were estimated from the correlation.     

Coupling sol-gel synthesis and microwave-assisted techniques: a new route from amorphous to crystalline high-surface-area aluminium fluoride

A non-aqueous sol-gel Al-based fluoride has been subjected to the microwave solvothermal process. The final material depends on the temperature heat treatment used. Three types of material have been prepared: 1) for low temperature heat treatment (90 degrees C) X-ray amorphous alkoxy fluoride was obtained; 2) for the highest temperature used (200 degrees C) the metastable form beta-AlF3 was obtained with a very large surface area of 125 m2 g(-1). The mechanism of the amorphous=crystalline transformation has been rationalised by the occurrence of a decomposition reaction of the gel fluoride induced by the microwave irradiation. 3) Finally, at intermediate temperature (180 degrees C) a multi-component material mixture exhibiting a huge surface area of 525 m2 g(-1) has been obtained and further investigated after mild post-treatment fluorination using F2 gas. The resulting aluminium-based fluoride still possesses a high-surface-area of 330 m2 g(-1). HRTEM revealed that the solid is built from large particles (50 nm) identified as alpha-AlF3, and small ones (10 nm), relative to an unidentified phase. This new high-surface-area material exhibits strong Lewis acidity as revealed by pyridine adsorption and catalytic tests. By comparison with other materials, it has been shown that whatever the composition/structure of the Al-based fluoride materials, the number of strong Lewis acid sites is related to the surface area, highlighting the role of surface reconstruction occurring on a nanoscopic scale on the formation of the strongest Lewis acid sites.     

Evidence that phosphatidylinositol promotes curved membrane interfaces

We have identified the phase behavior of phosphoinositol (PI) lipid extracts from bovine liver and wheat in dioleoylphosphatidylcholine (DOPC) model membranes under physiological conditions (pH 7.4) and show, for the first time, that the physicochemical properties of phosphatidylinositol lipids are capable of driving changes in membrane curvature. Ten mole percent phosphoinositol (PI) extract in DOPC is sufficient to induce the formation of the inverse hexagonal (H II) and inverse micellar cubic ( Fd3 m) phases at 37 degrees C. The phase behavior of several hydrated lipid samples was analyzed using small-angle X-ray scattering, and their lattice parameters were calculated.     

Visibility spectroscopy with electron waves using a Wien filter: higher order corrections

Fourier spectroscopy, one of the most precise spectrometry methods in light optics, has been realized in the past years with electron waves by including a crossed-field analyzer (Wien filter) as a wave packet shifting device into a biprism interferometer. To fully exploit the high precision of this method of determining the energy spectrum, higher order corrections stemming from the Wien filter's focusing action are necessary in the evaluation of the measurement. We show that these can be taken into account by using a transformation variable being proportional to the quotient of electric field strength of the Wien capacitor over fringe spacing. Finally, we make some remarks about the possibility of interference of inelastically scattered electrons.     

High transmission 3D printed flex‐PCB‐based ion funnel

In this study a novel fabrication method for a radio frequency (RF) ion funnel is presented. RF ion funnels are important devices for focusing ion clouds at low vacuum conditions for mass spectrometry or deposition‐related applications. Typically, ion funnels are constructed of stainless steel plate ring electrodes with a decreasing diameter where RF and direct current potentials are applied to the electrodes to focus the ion cloud. The presented novel design is based on a flexible circuit board that serves both as the signal distribution circuit and as the electrodes of the ion funnel. The flexible circuit board is rolled into a 3D printed scaffold to create a funnel shape with ring electrodes formed by the copper electrodes of the flexible circuit board. The design is characterized in direct comparison with a conventional steel‐plate electrode design. The discussed results show that the new funnel has similar performance to the conventionally designed funnel despite much lower manufacturing costs. Copyright © 2015 John Wiley & Sons, Ltd.