Feedback stabilization of snap-through buckling in a preloaded two-bar linkage with hysteresis

We study a linearly damped preloaded two-bar linkage that exhibits hysteresis due to the presence of multiple attracting equilibria. The dynamics at the unstable equilibrium, through which a snap-through buckle occurs, are not linearizable due to a solution-dependent singularity. We stabilize the unstable equilibrium using two distinct non-linear controllers. The feedback-linearization controller requires knowledge of the linkage parameters, whereas the robust version of the intrinsic non-linear proportional-derivative controller requires only an upper bound on the stiffness.     

Spectrophotometric determination of ruthenium(III) using diphenylcarbazone

Summary The purple violet ruthenium(III)-diphenylcarbazone complex which is formed at p _h 5–7, and has an absorption maximum at 530 nm with molar absorption coefficient 16.2·10⁴l.cm^–1.mole^–1 is suggested for the estimation of 20–125g ruthenium(III) spectrophotometrically in 30–60% ethanol. The complex is stable over p _h range 3.2–8.4. The limits of interference due to foreign ions have been studied.

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Zusammenfassung Der bei p _h 5 bis7 entstehende Ruthenium(III)-Diphenylcarbazon-Komplex hat ein Absorptionsmaximum bei 530 nm und einen Absorptionskoeffizienten von 16,2·10⁴ l.cm^–1.Mol^–1. Die spektrophotometrische Bestimmung von 20 bis 125g Ruthenium(III) in 30 bis 60%igem Äthanol mit Hilfe dieses zwischen p _h 3,2 und 8,4 beständigen Komplexes wurde vorgeschlagen. Die Störung durch Fremdionen wurde geprüft.

     

Synthesis and characterization of square-planar palladium(II) complexes containing anti- and syn-furan-2-aldoxime

Summary Fifteen palladium(II) square-planar complexes containing monodentate and/or bidentate anti- and syn-furan-2-aldoxime (FDH) have been isolated and characterized by elemental analysis, molecular weight determination, conductance studies, magnetic moments and i.r. spectral studies. The monodentate ligand coordinates through the nitrogen atom while the bidentate ligand coordinates through the furan oxygen atom and the nitrogen atom. The C-O-C stretching frequency of the furan ring may be taken as the criterion for the denticity of this ligand and is observed at 1240 and 1270 cm^– in anti- and syn-furan-2-aldoxime respectively. A shift to lower frequency occurs (in the complex) if the ligand is bidentate, however this frequency is unaffected if the ligand is monodentate.     

Ergodic properties of a system in contact with a heat bath: A one dimensional model

We consider a one-dimensional model of a system in contact with a heat bath: A particle (the system ormolecule) of massM, confined to the unit interval [0, 1], is surrounded by an infinite ideal gas (thebath of atoms) of point particles of massm with which it interacts via elastic collisions. The atoms are not affected by the walls at 0 and at 1. We obtain convergence to equilibrium for the molecule, from essentially any initial distribution on its position and velocity. The infinite composite system of molecule and bath has very good ergodic properties: it is a Bernoulli system.Supported in part by NSF Grants PHY 78-03816 and PHY 78-15920     

Interpretation of Mott–Schottky plots of photoanodes for water splitting

A large body of literature reports that both bismuth vanadate and haematite photoanodes are semiconductors with an extremely high doping density between 10¹⁸ and 10²¹ cm⁻³. Such values are obtained from Mott–Schottky plots by assuming that the measured capacitance is dominated by the capacitance of the depletion layer formed by the doping density within the photoanode. In this work, we show that such an assumption is erroneous in many cases because the injection of electrons from the collecting contact creates a ubiquitous capacitance step that is very difficult to distinguish from that of the depletion layer. Based on this reasoning, we derive an analytical resolution limit that is independent of the assumed active area and surface roughness of the photoanode, below which doping densities cannot be measured in a capacitance measurement. We find that the reported doping densities in the literature lie very close to this value and therefore conclude that there is no credible evidence from capacitance measurements that confirms that bismuth vanadate and haematite photoanodes contain high doping densities.

Electron injection from the contact dominates the Mott–Schottky plots of thin-film photoanodes, rather than the depletion capacitance.     

BF3·Et2O and trifluoroacetic acid/triethyl amine-mediated synthesis of functionalized piperidines

A two-step short and efficient strategy for the synthesis of substituted piperidones and piperidines in high diastereoselectivity (only trans-configuration), by employing cascade type reaction using BF₃·Et₂O or by carrying out one pot deprotection of ^tBoc group followed by intramolecular aza-Michael addition of α,β-unsaturated beta keto esters has been developed. Using a similar strategy a short access to hydroxy pipecolic acid is also described. Very simple and rapid experimental procedures involving mild conditions and only one or two chromatographic purifications are the main features of the process.     

Kolmogorov’s existence theorem for Markov processes inC* algebras

Given a family of transition probability functions between measure spaces and an initial distribution Kolmogorov’s existence theorem associates a unique Markov process on the product space. Here a canonical non-commutative analogue of this result is established for families of completely positive maps betweenC* algebras satisfying the Chapman-Kolmogorov equations. This could be the starting point for a theory of quantum Markov processes. Dedicated to the memory of Professor K G Ramanathan     

Renewal Approximations of the Switched Poisson Processes and Their Applications to Queueing Systems

The switched Poisson process (SPP), also known as the doubly stochastic Poisson process, has been widely used in the modelling of point processes whose rates vary subject to some random mechanism. The class of SPP includes a wide range of both renewal and non-renewal processes with squared coefficients of variation being larger than one. In this paper, we survey various approaches to approximate a non-renewal process by a renewal process. We derive the expressions for the first two moments of the inter-renewal time of a renewal process that approximates the SPP. We illustrate the quality of these approximations with numerical results in queueing applications. We believe that our approximations have potential applications in areas such as reliability, inventory control, telecommunications and maintenance.