Generalized Euler Equations

Zusammenfassung Es sei vorausgesetzt, dass in einem optimalen Steuerprozess die Anzahl der Steuervariabeln s–1 ist, wos die Anzahl der Zustandsvariabeln bedeutet. Es wird gezeigt, dass dann die adjungierten Variabeln eliminiert werden können, so dass ein System von Differentialgleichungen entsteht, das als eine Verallgemeinerung der Eulerschen Gleichungen der Variationsrechnung angesehen werden kann. Dieses Resultat gilt sowohl für diskrete als auch für kontinuierliche Steuersysteme, falls die Steuervariabeln keinen einschränkenden Nebenbedingungen unterworfen werden.     

Isothermal sustained oscillations in a very simple surface reaction

A simple model is used to illustrate that a bimolecular Langmuir—Hinshelwood surface reaction with two empty sites in its reaction step, non-equilibrium in the adsorption steps, and coverage independent parameters may lead to sustained oscillatory reaction rates. The two empty sites in the reaction step play an essential role in the establishment of these oscillations. Numerical simulation is used to demonstrate the periodic behavior predicted by the model. Several similar surface reaction models with coverage independent parameters can also yield oscillations. A mechanism with one vacant site in the adsorption steps, two vacant sites in the reaction step and only two dimensionless non-zero parameters may lead to sustained oscillations.     

Adsorption of Cr(VI) from aqueous solutions by HNO3-purified and chemically activated pyrolytic tire char

Pyrolytic tire char adsorbents either demineralized by nitric acid (purified char, PC) or activated with KOH-calcination (activated char, AC) were used for Cr(VI) removal from aquatic solutions and studied by adsorption kinetics, isotherms, and thermodynamics. Adsorbent’s physicochemical characteristics were studied by several techniques such as X-ray diffraction, porosimetry, scanning electron microscopy, elemental analysis, and Boehm titration. For PC, acid treatment leads partially to a mesoporous structure while for AC, KOH activation creates also a microporosity enhancing the specific surface area at 443 m²g^?1. Cr(VI) adsorption onto both adsorbents followed better second-order kinetics and Langmuir isotherm models and it was exothermic (ΔH < 0) and spontaneous (ΔG < 0). The maximum Cr(VI) adsorption capacity for AC and PC was 114 and 79.47 mg g^?1, respectively, at pH = 4. The present work reveals that AC and PC can be efficient sorbents for the removal of heavy metal ions, contributing both positively to wastewater treatment and waste tire pyrolysis plants.     

Stability of periodic solutions for Lipschitz systems obtained via the averaging method

Existence and asymptotic stability of the periodic solutions of the Lipschitz system is hereby studied via the averaging method. The traditional dependence of on is relaxed to the mere strict differentiability of at for , giving room to potential applications for structured nonsmooth systems.

     

Synthesis and characterization of new Rh complexes bearing CO, PPh3 and chelating P,O- or Se,Se-ligands: Application to hydroformylation of styrene

The complexes [Rh(CO)(PPh₃){Ph₂PNP(O)Ph₂-P,O}] (3), [Rh(CO)₂{Ph₂P(Se)NP(Se)Ph₂-Se,Se′}] (5), and [Rh(CO)(PPh₃){Ph₂P(Se)NP(Se)Ph₂-Se,Se′}] (6), were synthesised by stepwise reactions of CO and PPh₃ with [Rh(cod){Ph₂PNP(O)Ph₂-P,O}] (2) and [Rh(cod){Ph₂P(Se)NP(Se)Ph₂-Se,Se′}] (4), respectively. The complexes 3, 5 and 6 have been studied by IR, as well as ¹H and ³¹P NMR spectroscopy. The ν(CO) bands of complexes 3 and 6 appear at approximately 1960 cm⁻¹, indicating high electron density at the Rh^I centre. The structure of complexes 3 and 6 has been determined by X-ray crystallography, and the ³¹P NMR chemical shifts have been resolved via low temperature NMR experiments. Both complexes exhibit square planar geometry around the metal centre, with the five-membered ring of complex 3 being almost planar, and the six-membered ring of complex 6 adopting a slightly distorted boat conformation. The C-O bond of the carbonyl ligand is relatively weak in both complexes, due to strong π-back donation from the electron rich Rh^I centre. The catalytic activity of the complexes 2, 3 and 6 in the hydroformylation of styrene has been investigated. Complexes 2 and 3 showed satisfactory catalytic properties, whereas complex 6 had effectively no catalytic activity.     

Constrained matrix optimization with applications

In this work we study a minimization problem for a matrix-valued function under linear constraints, in the case of a singular matrix. The proposed method differs from others on the restriction of the minimizing matrix to the range of the corresponding quadratic function. Moreover, we present two applications of the proposed minimization method in Linear Regression and B-spline smoothing.     

On the mechanism of proton conductivity in H3OSbTeO6

Pyrochlore-type H₃OSbTeO₆ is a remarkable proton conductor exhibiting an outstanding electrical conductivity even at ambient temperature. It consists of a three-dimensional interconnected (Sb,Te)O₆ framework, built from randomly distributed corner-shared SbO₆ and TeO₆ octahedra, forming large cages in which the H₃O⁺ ions are located. The dynamics of the caged species has been investigated by temperature-dependent neutron diffraction, quasielastic neutron scattering, and NMR experiments. Three types of motion may be discerned, namely, stochastic rotations of the H₃O group around its 3-fold axis, jumps between four equivalent positions within the cage, and long-range inter-cage translational diffusion. The onset of ionic conductivity is clearly reflected by structural changes. Details of the complex diffusion mechanism are given.     

Intermittent demand: Linking forecasting to inventory obsolescence

The standard method to forecast intermittent demand is that by Croston. This method is available in ERP-type solutions such as SAP and specialised forecasting software packages (e.g. Forecast Pro), and often applied in practice. It uses exponential smoothing to separately update the estimated demand size and demand interval whenever a positive demand occurs, and their ratio provides the forecast of demand per period. The Croston method has two important disadvantages. First and foremost, not updating after (many) periods with zero demand renders the method unsuitable for dealing with obsolescence issues. Second, the method is positively biased and this is true for all points in time (i.e. considering the forecasts made at an arbitrary time period) and issue points only (i.e. considering the forecasts following a positive demand occurrence only). The second issue has been addressed in the literature by the proposal of an estimator (Syntetos-Boylan Approximation, SBA) that is approximately unbiased. In this paper, we propose a new method that overcomes both these shortcomings while not adding complexity. Different from the Croston method, the new method is unbiased (for all points in time) and it updates the demand probability instead of the demand interval, doing so in every period. The comparative merits of the new estimator are assessed by means of an extensive simulation experiment. The results indicate its superior performance and enable insights to be gained into the linkage between demand forecasting and obsolescence.     

Triangular Ni(II) complexes from the use of 2-pyridyl oximes

The reactions of representative 2-pyridyl oximes with Ni^II salts in the presence of a base have been investigated. The synthetic study has led to the new triangular complexes [Νi₃(ppko)₆]·2H₂O·0.5EtOH·MeOH (1·2H₂O·0.5EtOH·MeOH), [Νi₃(mpko)₃(HCO₂)₂(mpkoH)₂](ClO₄) (2) and [Νi₃(ppko)₃(HCO₂)₂(ppkoH)₂](ClO₄) (3), where ppko⁻ is the anion of phenyl(2-pyridyl)ketone oxime and mpko⁻ is the anion of methyl(2-pyridyl)ketone oxime. The structures of compounds 1 and 2 have been determined by single crystal X-ray diffraction. The ppko⁻ ligand in 1 adopts four different coordination modes including the unique N_pyridylO_oximate chelating one which gives rise to a 6-membered chelating ring, while the neutral and the deprotonated oxime ligands in 2 adopt three different coordination modes. The magnetic properties of 1 and 2 have been studied by variable-temperature dc magnetic susceptibility techniques which indicate antiferromagnetic interactions.