A moment problem associated to rational Szegő functions

Leta ₁,...,a _p be distinct points in the finite complex plane ?, such that |a _j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ₀, μ _π ^(j) , ν _π ^(j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?^* outside {a ₁,...,a _p,b ₁,...,b _p}.     

Synthesis and Rearrangement of P‐Nitroxyl‐Substituted PIII and PV Phosphanes: A Combined Experimental and Theoretical Case Study

Low‐temperature generation of P‐nitroxyl phosphane 2 (Ph₂POTEMP), which was obtained by the reaction of Ph₂PH ( 1 ) with two equivalents of TEMPO, is presented. Upon warming, phosphane 2 decomposed to give P‐nitroxyl phosphane P‐oxide 3 (Ph₂P(O)OTEMP) as one of the final products. This facile synthetic protocol also enabled access to P‐sulfide and P‐borane derivatives 7 and 13 , respectively, by using Ph₂P(S)H ( 6 ) or Ph₂P(BH₃)H ( 11 ) and TEMPO. Phosphane sulfide 7 revealed a rearrangement to phosphane oxide 8 (Ph₂P(O)STEMP) in CDCl₃ at ambient temperature, whereas in THF, thermal decomposition of sulfide 7 yielded salt 10 ([TEMP‐H₂][Ph₂P(S)O]). As well as EPR and detailed NMR kinetic studies, indepth theoretical studies provided an insight into the reaction pathways and spin‐density distributions of the reactive intermediates.     

Pulsed EPR Dipolar Spectroscopy under the Breakdown of the High-Field Approximation: The High-Spin Iron(III) Case

Pulsed EPR dipolar spectroscopy (PDS) offers several methods for measuring dipolar coupling and thus the distance between electron-spin centers. To date, PDS measurements to metal centers were limited to ions that adhere to the high-field approximation. Here, the PDS methodology is extended to cases where the high-field approximation breaks down on the example of the high-spin Fe³⁺/nitroxide spin-pair. First, the theory developed by Maryasov et al. (Appl. Magn. Reson. 2006 , 30, 683–702) was adapted to derive equations for the dipolar coupling constant, which revealed that the dipolar spectrum does not only depend on the length and orientation of the interspin distance vector with respect to the applied magnetic field but also on its orientation to the effective g-tensor of the Fe³⁺ ion. Then, it is shown on a model system and a heme protein that a PDS method called relaxation-induced dipolar modulation enhancement (RIDME) is well-suited to measuring such spectra and that the experimentally obtained dipolar spectra are in full agreement with the derived equations. Finally, a RIDME data analysis procedure was developed, which facilitates the determination of distance and angular distributions from the RIDME data. Thus, this study enables the application of PDS to for example, the highly relevant class of high-spin Fe³⁺ heme proteins.     

Pore-Scale Level Set Simulations of Capillary-Controlled Displacement with Adaptive Mesh Refinement

Transport in Porous Media - Multiphase flow simulations on imaged porous rock structures require numerical methods that are accurate and robust when applied on complex geometries. A key element in...     

EPR on Medically Relevant NO Adsorbed to Zn-LTA

For medical purposes, materials are required that store and target specifically deliver exogenous nitric oxide (NO). Partially zinc-exchanged Na-LTA (Linde type A) zeolite (Zn-LTA) has high potential in this respect due to its non-toxicity and adsorption capacity for NO. In contrast to NO adsorbed to LTA zeolites prepared for catalytic purposes, lower dehydration temperature prior to NO adsorption is used to achieve a balance between production cost and high activity. In order to study the interaction of NO with the metal sites in the samples prepared under these medical conditions, continuous-wave X-band electron paramagnetic resonance has been applied. In contrast to Na-LTA with only one weakly interacting NO monomer, three different monomers, having stronger interaction to the metal sites than in Na-LTA, were observed in Zn-LTA. To improve the storage capacity of Zn-LTA, higher dehydration temperatures would be necessary.     

Simulation of a mixed-conducting membrane-based gas turbine power plant for CO<Subscript>2</Subscript> capture: system level analysis of operation stability and individual process unit degradation

A gas turbine power plant for CO₂ capture, based on oxygen-permeable membranes with mixed ionic-electronic conductivity, was analysed with respect to long-term stability by means of numerical simulation. Due to the attractive transport and physicochemical properties of mixed-conducting La₂NiO_4+δ, this nickelate was selected as a prototype membrane material for this application. Experiments showed very slow degradation of La₂NiO_4+δ membranes at oxygen chemical potentials close to atmospheric conditions, which are associated with kinetic demixing and other microstructure-related factors. Interaction with CO₂ in the intermediate temperature range also leads to lower oxygen permeation, whilst increasing oxygen pressure may cause partial phase decomposition and microstructural changes, thus again limiting the range of possible operation conditions. The relevant operational constraints were included in a detailed membrane-based gas turbine power plant model. The membrane performance degradation with time was approximated by a linear function with average rate of 3.3% per 1,000 operation hours. Furthermore, performance deterioration of the gas turbine compressor and turbine were also considered. Simulations revealed that the power plant is substantially affected by degradation of the ceramic membranes and turbomachinery components. The already rather small operating window was further narrowed when compared with a conventional gas turbine power plant. Two different designs of the membrane-based power plant were analysed: (1) with and (2) without additional combustors (afterburners) between the membrane reactor and the gas turbine. Afterburners increase thermal efficiency as well as power output, but also lead to non-negligible CO₂ emissions. In order to have a frame of comparison, results for a conventional gas turbine power plant with degradation of turbomachinery components are also presented. Simulations representing changes in ambient temperature and fuel composition as well as failure incidents were executed to analyse the susceptibility of the gas turbine power plant to external and internal changes.     

Ragnar Frisch and interior-point methods

The distinguished econometrician Ragnar Frisch (1895–1973) also played an important role in optimization theory. In fact, he was a pioneer of interior-point methods. This note reconsiders his contribution, relating it to history and modern developments.     

SLIM: A Short‐Linked,Highly Redox‐Stable Trityl Label for High‐Sensitivity In‐Cell EPR Distance Measurements

The understanding of biomolecular function is coupled to knowledge about the structure and dynamics of these biomolecules, preferably acquired under native conditions. In this regard, pulsed dipolar EPR spectroscopy (PDS) in conjunction with site‐directed spin labeling (SDSL) is an important method in the toolbox of biophysical chemistry. However, the currently available spin labels have diverse deficiencies for in‐cell applications, for example, low radical stability or long bioconjugation linkers. In this work, a synthesis strategy is introduced for the derivatization of trityl radicals with a maleimide‐functionalized methylene group. The resulting trityl spin label, called SLIM, yields narrow distance distributions, enables highly sensitive distance measurements down to concentrations of 90 nm , and shows high stability against reduction. Using this label, the guanine‐nucleotide dissociation inhibitor (GDI) domain of Yersinia outer protein O (YopO) is shown to change its conformation within eukaryotic cells.     

Local Thermodynamic Description of Isothermal Single-Phase Flow in Simple Porous Media

Transport in Porous Media - Darcy’s law for porous media transport is given a new local thermodynamic basis in terms of the grand potential of confined fluids. The local effective pressure...     

Accessibility as the objective of public transportation planning: an integrated transportation and land use model

The subject of this paper is planning of public transportation in sparsely populated areas.The paper consists of four main parts. In part I an analysis of the system to be planned is carried out. A comparison with a survey on the traffic and transportation models available in the literature, though very voluminous, reveals a lack of a general model-framework for planning public transportation in sparsely populated areas. It is the aim of the present paper to fill this gap.Part II discusses how to evaluate optional plans for the physical and socio-economic structure of a region and concludes that this must be done by means of accessibility. Acessibility is defined in this paragraph.In part III a model is presented which describes the interdependance between on one hand the demand of accessibility of the population and on the other hand the transportation system, both public and private, and the location of facilities and residential areas. The applicability of some standard transportation and traffic models is discussed briefly in this section.Finally part IV describes a case study, in which the models set out in part III are applied. Some results are presented with conclusions.